Publications

Karl Heinz Hoffmann.

“Künstliche Intelligenz”.

In: Digitale Welt - Künstliche Intelligenz - Ethische Herausforderungen.

Ed. by Martin Barth and Gregor Maria Hoff.

Vol. 46.

Grenzfragen.

Verlag Karl Alber, 2023,

Pp. 79–107.

Karl Heinz Hoffmann, Christopher Essex, Janett Prehl, and Katrin Kulmus.

“The entropy production paradox for fractional diffusion”.

In: J. Non-Equilib. Thermodyn. 48.2 (2023), pp. 137–148.

doi: 10.1515/jnet-2023-0020.

Dispersive diffusion and wave propagation seem to be unconnected and fundamentally different evolution equations. In the context of anomalous diffusion however modeling approaches based on fractional diffusion equations have been presented, which allow to build a continuous bridge between the two regimes. The transition from irreversible dispersive diffusion to reversible wave propagation shows an unexpected increase in entropy production. This seemingly paradoxical behavior of fractional diffusion is reviewed and compared to the behavior of a tree-based diffusion model.

Karl Heinz Hoffmann and Nikolaus Korber, eds.

Fortschritt.

Baden-Baden: Verlag Karl Alber, 2023.

doi: 10.5771/9783495998847.

“Progress” is a dazzling concept used to describe developments in all areas of life. Progress is of particular interest in the sciences, where it manifests itself in innovations in the natural sciences and technology, for example. Whether one trusts in progress and looks hopefully into the future or longs for a golden past and distrusts progress depends on the observer. Modern science cannot be separated from the hope for progress and new knowledge. In this book, examples from different sciences are used to look at progress in those ﬁelds. In addition, the scientiﬁc environment, in the form of the communication and promotion of science, is also taken into account. With contributions by Prof. Dr. Thomas Heinemann, Prof. Dr. Gregor Maria Hoff, Prof. Dr. Wim Kösters, Prof. Dr. Ulrich Lüke, Prof. Dr. Gregor Nickel, Prof. Dr. Thomas Schmidt, Prof. Dr. Jörg Siekmann, Prof. Dr. Manfred Stöckler and Dr. Eva-Maria Streier

Andreas Fischer, Abdellah Khodja, Raphael Paul, and Karl Heinz Hoffmann.

“Heat-only-driven Vuilleumier refrigeration”.

In: Appl. Sci. 12.4 (2022), p. 1775.

doi: 10.3390/app12041775.

Vuilleumier refrigerators are devices which provide cooling power by using heat from a source at a temperature above the ambient. This feature makes Vuilleumier refrigerators particularly useful in situations where waste heat is abundant but electrical energy is scarce even as auxiliary operating power. For an operation by heat only with no need of auxiliary power, the Vuilleumier refrigerators must be designed in such a way that the mechanical losses occurring during operation are compensated by power gained from pressure differences. Here, we study the optimal design of such a device with heat-only operation maximizing the cooling power.

Karl Heinz Hoffmann, Andreas Fischer, and J. Christian Schoen.

“Controlled dynamics and preferential trapping on energy landscapes”.

In: Front. Nanosci. 21 (2022), pp. 211–245.

doi: 10.1016/B978-0-12-824406-7.00017-8.

An important feature of the dynamics on complex multiminimum energy landscapes is the occurrence of trapping in certain regions of its state space. This is particularly apparent in, e.g., the ﬁeld of nanoscale systems like proteins or in materials science, where such regions represent metastable compounds of relevance for applications. Guiding the dynamics of a system into those regions to create such compounds requires an optimally tuned control of the system dynamics. Here we review the important features of relevant energy landscapes and the corresponding determining elements of the optimally controlled dynamics. In particular, the competitive trapping power of state space regions is related to coarse-grained properties of the landscape.

Raphael Paul and Karl Heinz Hoffmann.

“Optimizing the piston paths of Stirling cycle cryocoolers”.

In: J. Non-Equilib. Thermodyn. 47.2 (2022), pp. 195–2003.

doi: 10.1515/jnet-2021-0073.

The ideal Stirling cycle provides a clear control strategy for the piston paths of ideal representations of Stirling cycle machines. For non-equilibrium Stirling cycle machines however, piston paths aiming to emulate the ideal cycle?s four strokes will not necessarily yield best performance. In this contribution, we ask the question: What are the COP-optimal piston paths for speciﬁc non-equilibrium Stirling cryocoolers? To this end, we consider a low-effort Stirling cryocooler model that consists of a set of coupled ordinary differential equations and takes several loss phenomena into account. For this model and an exemplary parameter set, piston path optimizations are done with an indirect iterative gradient method based on optimal control theory. The optimizations are repeated for two different kinds of volume constraints for the working spaces: one representing an alpha-Stirling conﬁguration, the other a beta-Stirling conﬁguration. Compared to harmonic piston paths, the optimal piston paths lead to signiﬁcant improvements in COP of ca. 88% for the alpha-Stirling and ca. 117% for the beta-Stirling at the maximum-COP operational frequency. Additionally – and even though the optimizations were performed for maximum COP – cooling power was increased with even lager ratios.

Karoline Griesbach, Matthias Beggiato, and Karl Heinz Hoffmann.

“Lane change prediction with an echo state network and recurrent neural network in the urban area”.

In: IEEE Transact. Intell. Trans. Sys. 23.7 (2021), pp. 6473–6479.

doi: 10.1109/TITS.2021.3058035.

The prediction of lane changes can reduce traffic accidents and improve traffic ﬂow. In this paper two classiﬁers, Echo State Network and a recurrent neural network with Long Short Term Memory cells, were compared to predict lane changes using the input variables steering angle and indicator. The input variables were extracted from a data set which was generated from a naturalistic driving study in the urban area of Chemnitz, Germany. Both classiﬁers predicted left and right lane changes successfully. They achieved high true positive rates and low false positive rates. The Echo State Network predicted left and the recurrent neural network predicted right lane changes better.

Abdellah Khodja, Raphael Paul, Andreas Fischer, and Karl Heinz Hoffmann.

“Optimized cooling power of a Vuilleumier refrigerator with limited regeneration”.

In: Energies 14.24 (2021), p. 8376.

doi: 10.3390/en14248376.

Vuilleumier refrigerators provide cooling power by utilizing a heat source at temperatures above the ambient. This is particularly helpful in situations where waste heat is available and other power sources are limited. Vuilleumier refrigerators come in different technical conﬁgurations; here we analyze the thermodynamic performance of a conﬁguration utilizing two displacer pistons with integrated regenerators. More speciﬁcally, we optimize the cooling power by optimizing the piston movement for a range of operation speeds. The optimization is based on the AS motion class for cyclic dynamics and uses an endoreversible model for the refrigerator. Our focus is on the inﬂuence of the regeneration extent present, and we ﬁnd performance gains of about 17% for high regeneration extent and of about 28% for lower regeneration extent.

Robin Masser and Karl Heinz Hoffmann.

“Optimal control for a hydraulic recuperation system using endoreversible thermodynamics”.

In: Appl. Sci. 11.11 (2021), p. 1562.

doi: 10.3390/app11115001.

Energy savings in the traffic sector are of considerable importance for economic and environmental considerations. Recuperation of mechanical energy in commercial vehicles can contribute to this goal. One promising technology rests on hydraulic systems, in particular for trucks which use such system also for other purposes such as lifting cargo or operating a crane. In this work the potential for energy savings is analyzed for commercial vehicles with tipper bodies, as these already have a hydraulic onboard system. The recuperation system is modeled based on endoreversible thermodynamics, thus providing a framework in which realistic driving data can be incorporated. We further used dissipative engine setups for modeling both the hydraulic and combustion engine of the hybrid drive train in order to include realistic efficiency maps. As a result, reduction in fuel consumption of up to 26% as compared to a simple baseline recuperation strategy can be achieved with an optimized recuperation control.

Raphael Paul and Karl Heinz Hoffmann.

“A class of reduced-order regenerator models”.

In: Energies 14.21 (2021), p. 7295.

doi: 10.3390/en14217295.

We present a novel class of reduced-order regenerator models that is based on Endoreversible Thermodynamics. The models rest upon the idea of an internally reversible (perfect) regenerator, even though they are not limited to the reversible description. In these models, the temperatures of the working gas that alternately streams out on the regenerator?s hot and cold sides are deﬁned as functions of the state of the regenerator matrix. The matrix is assumed to feature a linear spatial temperature distribution. Thus, the matrix has only two degrees of freedom that can, for example, be identiﬁed with its energy and entropy content. The dynamics of the regenerator is correspondingly expressed in terms of balance equations for energy and entropy. Internal irreversibilities of the regenerator can be accounted for by introducing source terms to the entropy balance equation. Compared to continuum or nodal regenerator models, the number of degrees of freedom and numerical effort are reduced considerably. As will be shown, instead of the obvious choice of variables energy and entropy, if convenient, a different pair of variables can be used to specify the state of the regenerator matrix and formulate the regenerator?s dynamics. In total, we will discuss three variants of this endoreversible regenerator model, which we will refer to as ES, EE, and EEn-regenerator models.

Raphael Paul and Karl Heinz Hoffmann.

“Cyclic control optimization algorithm for Stirling engines”.

In: Symmetry 13.5 (2021), p. 873.

doi: 10.3390/sym13050873.

The ideal Stirling cycle describes a speciﬁc way to operate an equilibrium Stirling engine. This cycle consists of two isothermal and two isochoric strokes. For non-equilibrium Stirling engines, which may feature various irreversibilities and whose dynamics is characterized by a set of coupled ordinary differential equations, a control strategy that is based on the ideal cycle will not necessarily yield the best performance?for example, it will not generally lead to maximum power. In this paper, we present a method to optimize the engine’s piston paths for different objectives; in particular, power and efficiency. Here, the focus is on an indirect iterative gradient algorithm that we use to solve the cyclic optimal control problem. The cyclic optimal control problem leads to a Hamiltonian system that features a symmetry between its state and costate subproblems. The symmetry manifests itself in the existence of mutually related attractive and repulsive limit cycles. Our algorithm exploits these limit cycles to solve the state and costate problems with periodic boundary conditions. A description of the algorithm is provided and it is explained how the control can be embedded in the system dynamics. Moreover, the optimization results obtained for an exemplary Stirling engine model are discussed. For this Stirling engine model, a comparison of the optimized piston paths against harmonic piston paths shows signiﬁcant gains in both power and efficiency. At the maximum power point, the relative power gain due to the power-optimal control is ca. 28%, whereas the relative efficiency gain due to the efficiency-optimal control at the maximum efficiency point is ca. 10%.

Raphael Paul, Abdellah Khodja, Andreas Fischer, and Karl Heinz Hoffmann.

“Cooling cycle optimization for a Vuilleumier refrigerator”.

In: Entropy 23.12 (2021), p. 1562.

doi: 10.3390/e23121562.

Vuilleumier refrigerators are a special type of heat-driven cooling machines. Essentially, they operate by using heat from a hot bath to pump heat from a cold bath to an environment at intermediate temperatures. In addition, some external energy in the form of electricity can be used as an auxiliary driving mechanism. Such refrigerators are, for example, advantageous in situations where waste heat is available and cooling power is needed. Here, the question of how the performance of Vuilleumier refrigerators can be improved is addressed with a particular focus on the piston motion and thus the thermodynamic cycle of the refrigerator. In order to obtain a quantitative estimate of the possible cooling power gain, a special class of piston movements (the AS motion class explained below) is used, which was already used successfully in the context of Stirling engines. We ﬁnd improvements of the cooling power of more than 15%.

Raphael Paul, Abdellah Khodja, Andreas Fischer, Robin Masser, and Karl Heinz Hoffmann.

“Power-optimal control of a Stirling engine?s frictional piston motion”.

In: Entropy 24.3 (2021), p. 362.

doi: 10.3390/e24030362.

The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular mechanical friction. We use a low-effort endoreversible Stirling engine model, which allows for the incorporation of ﬁnite heat and mass transfer as well as the friction caused by the piston motion. Instead of performing a parameterization of the piston motion and optimizing these parameters, we here use an indirect iterative gradient method that is based on Pontryagin?s maximum principle. For the varying friction coefficient, the optimization results are compared to both, a harmonic piston motion and optimization results found in a previous study, where a parameterized piston motion had been used. Thus we show how much performance can be improved by using the more sophisticated and numerically more expensive iterative gradient method.

Raphael Paul, Abdellah Khodja, and Karl Heinz Hoffmann.

“An endoreversible model for the regenerators of Vuilleumier refrigerators”.

In: Int. J. Thermodyn. 24.2 (2021), pp. 184–192.

doi: 10.5541/ijot.877687.

We introduce a reduced-order endoreversible model of a Vuilleumier refrigerator for waste heat recovery. Based on the Vuilleumier cycle, in this refrigerator a working gas is alternately displaced between three subsystems that are in thermal contact with external heat reservoirs. Regarding refrigeration performance, very crucial components of the Vuilleumier machine are its two regenerators. For obtaining a sufficiently accurate model of the Vuilleumier machine, it is hence essential to incorporate a proper description of the regenerators. This can be achieved by using one- dimensional continuum models, e.g. with a ﬁnite volume approach, which brings about a large number of degrees of freedom and signiﬁcant numerical effort. As opposed to that, the model presented in this paper utilizes a novel modeling ansatz for the regenerators that reduces the number of degrees of freedom per regenerator to three. It leads to a considerable reduction in numerical effort and computation time and is hence predestined for applications like design and control optimizations. For an exemplary set of design parameters and operational conditions, we validate the model against a detailed ﬁnite volume model of the regenerators in order to work out limitations and perspectives.

Christopher Essex, Shantanu Basu, Janett Prehl, and Karl Heinz Hoffmann.

“A multiple power-law distribution for initial mass function”.

In: Mon. Not. R. Astron. Soc. 494.2 (2020), pp. 1579–1586.

doi: 10.1093/mnras/staa755.

We introduce a new multi-power-law distribution for the initialmass function (IMF) to explore its potential properties. It follows on prior work that introduced mechanisms accounting for mass accretion in star formation, developed within the framework of general evolution equations for the mass distribution of accreting and non-accreting (proto)stars. This paper uses the same fundamental framework to demonstrate that the interplay between a mass-dependent and a time-dependent step-like dropout rate from accretion leads to IMFs that exhibit multiple power laws for an exponential mass growth. While the mass-dependent accretion and its dropout is intrinsic to each star, the time-dependent dropout might be tied to a speciﬁc history such as the rapid consumption of nebular material by nearby stars or the sweeping away of some material by shock waves. The time-dependent dropout folded into the mass-dependent process of star formation is shown to have a signiﬁcant inﬂuence on the IMFs.

Karoline Griesbach, Karl Heinz Hoffmann, and Matthias Beggiato.

“Prediction of lane change by echo state networks”.

In: Transp. Res. Part C Emerg. Technol. 121 (2020), p. 102841.

doi: 10.1016/j.trc.2020.102841.

Lane change prediction can reduce traffic accidents and improve traffic ﬂow. To predict lane changes variables which describe lane changes are needed. Recent studies used different classiﬁers and different inputs for lane change classiﬁcation and prediction. Here, different methods are used to extract the relevant input variables from a data set which was generated from a naturalistic driving study in the urban area of Chemnitz, Germany. First variables which show different characteristics for left and no lane changes were chosen. The variables contained driver attributes (for instance gazes), environment attributes (for instance distance to other vehicles) and vehicle attributes (for instance velocity). Second, different combinations of these input variables were analyzed with the principal component analysis. In the end, the best combinations were used to classify left lane changes with an Echo State Network and a feedforward neural network. The Echo State Network achieved high area under the curve values, true positive rates and low false positive rates for the classiﬁcation with a majority of the input combinations. The feedforward neural network predictions were inferior of those to the Echo State Network.

Robin Masser and Karl Heinz Hoffmann.

“Endoreversible Modeling of a Hydraulic Recuperation System”.

In: Entropy 22.4 (2020), p. 383.

doi: 10.3390/e22040383.

Hybrid drive systems able to recover and reuse braking energy of the vehicle can reduce fuel consumption, air pollution and operating costs. Among them, hydraulic recuperation systems are particularly suitable for commercial vehicles, especially if they are already equipped with a hydraulic system. Thus far, the investigation of such systems has been limited to individual components or optimizing their control. In this paper, we focus on thermodynamic effects and their impact on the overall systems energy saving potential using endoreversible thermodynamics as the ideal framework for modeling. The dynamical behavior of the hydraulic recuperation system as well as energy savings are estimated using real data of a vehicle suitable for application. Here, energy savings accelerating the vehicle around 10% and a reduction in energy transferred to the conventional disc brakes around 58% are predicted. We further vary certain design and loss parameters – such as accumulator volume, displacement of the hydraulic unit, heat transfer coefficients or pipe diameter – and discuss their inﬂuence on the energy saving potential of the system. It turns out that heat transfer coefficients and pipe diameter are of less importance than accumulator volume and displacement of the hydraulic unit.

Wolfgang Muschik and Karl Heinz Hoffmann.

“Modeling, simulation, and reconstruction of 2-reservoir heat-to-power processes in ﬁnite-time thermodynamics”.

In: Entropy 22 (2020), p. 997.

doi: 10.3390/e22090997.

The connection between endoreversible models of Finite-Time Thermodynamics and the corresponding real running irreversible processes is investigated by introducing two concepts which complement each other: Simulation and Reconstruction. In that context, the importance of particular machine diagrams for Simulation and (reconstruction) parameter diagrams for Reconstruction is emphasized. Additionally, the treatment of internal irreversibilities through the use of contact quantities like the contact temperature is introduced into the Finite-Time Thermodynamics description of thermal processes.

Raphael Rüdiger Paul.

“Optimal Control of Stirling Engines”.

PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Dec. 2020.

In this thesis a method for power optimization of the piston paths of Stirling engines is developed, which is based on Optimal Control Theory. For the efficient practical feasibility of this task, low numerical effort of the utilized thermodynamic model is crucial. In detailed models of Stirling engines, a large part of the numerical effort results from the description of the regenerator, which is a short-time heat storage. Therefore, in the ﬁrst part of this thesis the focus is on the development of an efficient regenerator model. Here, a novel ansatz is chosen which arises from the perspective of Endoreversible Thermodynamics: The regenerator is described as an endoreversible subsystem that has two contact points, at which it exchanges particles, entropy, and energy with the adjacent subsystems through irreversible interactions. Internal irreversibilities of the regenerator are included in the model as entropy source terms. In the second part of the thesis an iterative optimization algorithm is worked out, which can maximize the power output of Stirling engines under periodic boundary conditions for given cycle time. The algorithm starts with predeﬁned initial piston paths, which are gradually shifted over the course of the iterations and thus approach the optimal paths. To determine this gradual shift, in every iteration not only the system of differential equations describing the thermodynamics of the Stirling engine needs to be solved, but also a conjugate system of differential equations. The algorithm here exploits the existence of a limit cycle of the conjugate system under time reversal to solve it for periodic boundary conditions. By means of the endoreversible regenerator model, with this iterative optimization algorithm Optimal Control Theory is applied for the ﬁrst time to optimize the piston paths of an exemplary Stirling engine in $α$ -conﬁguration.

Masser Robin, Abdellah Khodja, Mathias Scheunert, Karsten Schwalbe, Andreas Fischer, Raphael Paul, and Karl Heinz Hoffmann.

“Optimized Piston Motion for an Alpha-Type Stirling Engine”.

In: Entropy 20.6 (2020), p. 700.

doi: 10.3390/e22060700.

The Stirling engine is one of the most promising devices for the recovery of waste heat. Its power output can be optimized by several means, in particular by an optimized piston motion. Here, we investigate its potential performance improvements in the presence of dissipative processes. In order to ensure the possibility of a technical implementation and the simplicity of the optimization, we restrict the possible piston movements to a parametrized class of smooth piston motions. In this theoretical study the engine model is based on endoreversible thermodynamics, which allows us to incorporate non-equilibrium heat and mass transfer as well as the friction of the piston motion. The regenerator of the Stirling engine is modeled as ideal. An investigation of the impact of the individual loss mechanisms on the resulting optimized motion is carried out for a wide range of parameter values. We ﬁnd that an optimization within our restricted piston motion class leads to a power gain of about 50% on average.

Mathias Scheunert, Robin Masser, Abdellah Khodja, Raphael Paul, Karsten Schwalbe, Andreas Fischer, and Karl Heinz Hoffmann.

“Power-Optimized Sinusoidal Piston Motion and Its Performance Gain for an Alpha-Type Stirling Engine with Limited Regeneration”.

In: Energies 13.17 (2020), p. 4564.

doi: 10.3390/en13174564.

The recuperation of otherwise lost waste heat provides a formidable way to decrease the primary energy consumption of many technical systems. A possible route to achieve that goal is through the use of Stirling engines, which have shown to be reliable and efficient devices. One can increase their performance by optimizing the piston motion. Here, it is investigated to which extent the cycle averaged power output can be increased by using a special class of adjustable sinusoidal motions (the AS class). In particular the inﬂuence of the regeneration effectiveness on the piston motion is examined. It turns out that with the optimized piston motion one can achieve performance gains for the power output of up to 50% depending on the loss mechanisms involved. A remarkable result is that the power output does not depend strongly on the limitations of the regenerator, in fact—depending on the loss terms—the inﬂuence of the regenerator practically vanishes.

Karoline Griesbach.

“Lane Change Prediction in the Urban Area”.

https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa2-345467.

PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Feb. 2019.

Karoline Griesbach, Karl Heinz Hoffmann, and Matthias Beggiato.

“Lane Change Prediction Using an Echo State Network”.

In: Intelligent Human Systems Integration 2019.

Ed. by Tareq Karwowski Waldemar und Ahram.

Springer International Publishing, Cham. ﬁle, 2019,

Pp. 69–75.

doi: 10.1007/978-3-030-11051-2_11.

Lane change prediction can reduce accidents and increase the traffic ﬂow. An Echo State Network is implemented for the prediction of left lane changes in an urban area. The Echo State Network has three input variables: turn signal, head rotation in y-direction and steering angle. The input variables were generated from a Naturalistic Driving study in the urban area of Chemnitz, Germany. A successful prediction for left mandatory and discretionary lane changes was realized.

Karl Heinz Hoffmann, Peter Salamon, and Kim Schmidt.

“Quantum Finite-Time Availability”.

In: AAPP - Physical, Mathematical, and Natural Sciences 97.1 (2019), A10.

doi: 10.1478/AAPP.97S1A10.

The availability of a thermodynamic system with respect to an environment is the maximum work, which can be gained from bringing it into equilibrium with its environment by a reversible process. If the process has to proceed in ﬁnite time, there will be unavoidable losses diminishing the availability; this consequence is captured by the Finite-Time Availability. Here we consider the consequences of an availability extracting process for a paradigmatic quantum system, the parametric harmonic oscillator. Differences and similarities between its Quantum Finite-Time Availability and the classical Finite-Time Availability of an ideal gas in a cylinder with a piston are discussed.

Kathrin Kulmus, Christopher Essex, Janett Prehl, and Karl Heinz Hoffmann.

“The entropy production paradox for fractional master equations”.

In: Physica A 525 (2019), pp. 1370–1378.

doi: 10.1016/j.physa.2019.03.114.

Time-fractional evolution equations for probability distributions provide a means to describe an important class of stochastic processes. Their solutions show features, which are essential in modeling a variety of phenomena in real world applications. One aspect, which has been observed in time-fractional diffusion equations, shows a surprising and unexpected behavior of the entropy production rate induced by these equations. The entropy production rate increases as one moves away from the fully irreversible case, corresponding to classical diffusion. This rate is analyzed for a new class of systems with state spaces that are ﬁnite and denumerable. We ﬁnd that the entropy production paradox reemerges nonetheless, but in a new and unexpected form.

Robin Masser and Karl Heinz Hoffmann.

“Dissipative Endoreversible Engine with Given Efficiency”.

In: Entropy 21.11 (2019), p. 1117.

doi: 10.3390/e21111117.

Endoreversible thermodynamics is a ﬁnite time thermodynamics ansatz based on the assumption that reversible or equilibrated subsystems of a system interact via reversible or irreversible energy transfers. This gives a framework where irreversibilities and thus entropy production only occur in interactions, while subsystems (engines, for instance) act as reversible. In order to give an opportunity to incorporate dissipative engines with given efficiencies into an endoreversible model, we build a new dissipative engine setup. To do this, in the ﬁrst step, we introduce a more general interaction type where energy loss not only results from different intensive quantities between the connected subsystems, which has been the standard in endoreversible thermodynamics up to now, but is also caused by an actual loss of the extensive quantity that is transferred via this interaction. On the one hand, this allows the modeling of leakages and friction losses, for instance, which can be represented as leaky particle or torque transfers. On the other hand, we can use it to build an endoreversible engine setup that is suitable to model engines with given efficiencies or efficiency maps and, among other things, gives an expression for their entropy production rates. By way of example, the modeling of an AC motor and its loss ﬂuxes and entropy production rates are shown.

Raphael Paul, Abdellah Khodja, and Karl Heinz Hoffmann.

“Nodal modeling of a Vuilleumier refrigerator for waste heat recovery on refrigerator trucks”.

In: Proceedings of the 32nd International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems.

Ed. by Wojciech Stanek, Paweł Gładysz, Sebastian Werle, and Wojciech Adamczyk.

ECOS 2019, Wrocław, Poland, 23-28 June 2019.

Poland: Institute of Thermal Technology, Silesian University of Technology, 2019.

This paper presents a nodal simulation model of a Vuilleumier refrigerator that is applied for mobile waste heat recovery on light and medium duty refrigerator trucks. The model is predicated on the concept of endoreversible thermodynamics. The bulk of the Vuilleumier machine is decomposed into a network of reversible subsystems with irreversible interactions. The formulation of conservation laws and interactions is based on ﬂuxes of heat, mass, and enthalpy. The regenerators are treated using a ﬁnite volume approach with central ﬂux scheme. For an exemplary set of design parameters and operational conditions, the paper presents preliminary simulation results and accordingly pred ictions for refrigerator performance measures.

Janett Prehl and Constantin Huster.
“Polymers article morphology on reaction mechanism dependency for twin polymerization”.
In: Polymers 11.5 (2019), p. 878.
doi: 10.3390/polym11050878.
An in-depth knowledge of the structure formation process and the resulting dependency of the morphology on the reaction mechanism is a key requirement in order to design application-oriented materials. For twin polymerization, the basic idea of the reaction process is established, and important structural properties of the ﬁnal nanoporous hybrid materials are known. However, the effects of changing the reaction mechanism parameters on the ﬁnal morphology is still an open issue. In this work, the dependence of the morphology on the reaction mechanism is investigated based on a previously introduced lattice-based Monte Carlo method, the reactive bond ﬂuctuation model. We analyze the effects of the model parameters, such as movability, attraction, or reaction probabilities on structural properties, like the speciﬁc surface area, the radial distribution function, the local porosity distribution, or the total fraction of percolating elements. From these examinations, we can identify key factors to adapt structural properties to fulﬁll desired requirements for possible applications. Hereby, we point out which implications theses parameter changes have on the underlying chemical structure.

Karsten Schwalbe and Karl Heinz Hoffmann.
“Stochastic Novikov Engine with Fourier Heat Transport”.
In: J. Non-Equilib. Thermodyn. 44.4 (2019), pp. 417–424.
doi: 10.1515/jnet-2019-0063.
The Stochastic Novikov engine is an endoreversible model for heat engines where the heat supply takes place at a ﬂuctuating temperature. These ﬂuctuations can be observed for example at solar thermal power plants. While recently the inﬂuence of the temperature ﬂuctuations on the engine’s performance has been studied for Newtonian heat transport, the relation between the used heat transport type and the performance measures remained open. Therefore, we here consider a Stochastic Novikov engine with Fourier heat transport. Based on a short summary of the concept of a Stochastic Novikov engine and the corresponding different control types, the maximum work output and the corresponding efficiency are derived. In particular, we discuss the inﬂuence of the distribution’s parameters on the engine’s performance assuming a uniform temperature distribution. We ﬁnd that the heat transport type has a signiﬁcant effect on some of the engine’s fundamental properties.

Kathrin Allmaier.
“Modelling fractal diffusion”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Jan. 2018.

Bjarne Andresen, Peter Salamon, Karl Heinz Hoffmann, and Anatoli M. Tsirlin.
“Optimal Processes for Controllable Oscillators”.
In: Automat. Remote Control 79.12 (2018), pp. 2103–2113.
doi: 10.1134/S0005117918120019.
We consider the problem of optimal parametric control for a single oscillator or an ensemble of oscillators due to a change in one of the coefficients of the system of equations characterizing them. We obtain solutions for the problem of ﬁnding the maximal change in the energy of oscillations for a given time.

René Haber and Karl Heinz Hoffmann.
“A performance comparison of density-of-states methods”.
In: Comm. Comp. Phys. 24.2 (2018), pp. 383–407.
doi: 10.4208/cicp.OA-2017-0058.
Nowadays equilibrium thermodynamic properties of materials can be ob- tained very efficiently by numerical simulations. If the properties are needed over a range of temperatures it is highly efficient to determine the density of states ﬁrst. For this purpose histogram- and matrix-based methods have been developed. Here we present a performance comparison of a number of those algorithms. The comparison is based on three different benchmarks, which cover systems with discrete and con- tinuous state spaces. For the benchmarks the exact density of states is known, for one benchmark – the FAB system – the exact inﬁnite temperature transition matrix Q is also known. In particular the Wang-Landau algorithm in its standard and 1/t variant are compared to Q-methods, where estimates of the inﬁnite temperature transition matrix are obtained by random walks with different acceptance criteria. Overall the Q-matrix methods perform better or at least as good as the histogram methods. In addition, dif- ferent methods to obtain the density of states from the Q-matrix and their efficiencies are presented.

Karl Heinz Hoffmann, Christopher Essex, Shantanu Basu, and Janett Prehl.
“A Dual Power Law Distribution for the Stellar Initial Mass Function”.
In: Mon. Not. R. Astron. Soc. 478.2 (2018), pp. 2113–2118.
doi: 10.1093/mnras/sty1251.
We introduce a new dual power-law (DPL) probability distribution function for the mass distribution of stellar and substellar objects at birth, otherwise known as the initial mass function (IMF). The model contains both deterministic and stochastic elements, and provides a uniﬁed framework within which to view the formation of brown dwarfs and stars resulting from an accretion process that starts from extremely low-mass seeds. It does not depend upon a top down scenario of collapsing (Jeans) masses or an initial lognormal or otherwise IMF-like distribution of seed masses. Like the modiﬁed lognormal power-law (MLP) distribution, the DPL distribution has a power law at the high-mass end, as a result of exponential growth of mass coupled with equally likely stopping of accretion at any time interval. Unlike the MLP, a power-law decay also appears at the low-mass end of the IMF. This feature is closely connected to the accretion stopping probability rising from an initially low value up to a high value. This might be associated with physical effects of ejections sometimes (i.e. rarely) stopping accretion at early times followed by outﬂow driven accretion stopping at later times, with the transition happening at a critical time (therefore mass). Comparing the DPL to empirical data, the critical mass is close to the substellar mass limit, suggesting that the onset of nuclear fusion plays an important role in the subsequent accretion history of a young stellar object.

Karl Heinz Hoffmann, Kathrin Kulmus, Christopher Essex, and Janett Prehl.
“Between Waves and Diffusion: Paradoxical Entropy Production in an Exceptional Regime”.
In: Entropy 20.11 (2018), pp. 881–1–15.
doi: 10.3390/e20110881.
The entropy production rate is a well established measure for the extent of irreversibility in a process. For irreversible processes, one thus usually expects that the entropy production rate approaches zero in the reversible limit. Fractional diffusion equations provide a fascinating testbed for that intuition in that they build a bridge connecting the fully irreversible diffusion equation with the fully reversible wave equation by a one-parameter family of processes. The entropy production paradox describes the very non-intuitive increase of the entropy production rate as that bridge is passed from irreversible diffusion to reversible waves. This paradox has been established for time- and space-fractional diffusion equations on one-dimensional continuous space and for the Shannon, Tsallis and Renyi entropies. After a brief review of the known results, we generalize it to time-fractional diffusion on a ﬁnite chain of points described by a fractional master equation.

Karl Heinz Hoffmann and Janett Prehl.
“Modeling the structure formation process of twin polymerization”.
In: Reac. Kinet. Mech. Cat. 123 (2018), pp. 367–383.
doi: 10.1007/s11144-017-1303-y.
Twin polymerization is an elegant technique to synthesize nanostructured organic–inorganic polymers with deﬁned domain sizes of 0.5–3 nm. Although various classes of chemical structures undergoing twin polymerization have been found, the theoretical understanding of the overall twin polymerization process and especially of structure formation of the composite material is still at the beginning. Here, we introduce three different theoretical modeling approaches to investigate and analyze the structure formation process of twin polymerization on different levels of detail. We develop new methods and extend existing ones that range from reactive molecular dynamics simulations to reaction kinetics to reactive bond ﬂuctuation models. We compare the obtained simulation results with experimental and quantum chemical data and ﬁnd very good to reasonable agreement between theoretical modeling and experimental results. In doing so we achieve detailed insights to the structure formation process of twin polymerization on different length scales.zation on different length scales.

Constantin Huster, Kevin Nagel, Stefan Spange, and Janett Prehl.
“A reactive bond ﬂuctuation model (rBFM) for twin polymerization: Comparison of simulated morphologies with experimental data”.
In: Chem. Phys. Lett. 713 (2018), pp. 145–148.
doi: 10.1016/j.cplett.2018.10.016.
With twin polymerization (TP), nanostructured organic-inorganic hybrid materials are produced, which serve as intermediates for nano- and microporous materials. To manipulate the synthesis process appropriately for applications a detailed understanding of the emerging structures is desired.Here, we present a reactive bond ﬂuctuation model (rBFM), that bases on a 3D lattice-based Monte-Carlo method, to model the full structure formation process of the complex TP process. Thus, we can analyze the ﬁnal structures and compare them with experimental data. We show that the rBFM can capture the full TP process and that we ﬁnd a good agreement between simulation and experiment.

Janett Prehl, Benjamin Fiedler, and Joachim Friedrich.
“Modeling and simulation of nanostructure formation of TP”.
In: Twin Polymerization: New Strategy for Hybrid Materials Synthesis.
Ed. by Stefan Spange and Michael Mehring.
Berlin, Germany: De Gruyter, 2018.
Chap. 3.3, pp. 135–166.
doi: 10.1515/9783110499360.
Twin polymerization is a novel approach where two distinct polymers are produced from a single source monomer, thus being an excellent tool for the synthesis of hybrid materials. The author introduces the principles of various twin polymerization processes, their classiﬁcation and practical use. The book is supplied with numerous individual examples, demonstrating the potential of this strategy in materials synthesis.

Janett Prehl, Robin Masser, Peter Salamon, and Karl Heinz Hoffmann.
“Modeling reaction kinetics of twin polymerization via differential scanning calorimetry”.
In: J. Non-Equilib. Thermodyn. 43.4 (2018), pp. 347–357.
doi: 10.1515/jnet-2018-0057.
We present a kinetic model for the reaction mechanism of acid-catalyzed twin polymerization. Our model characterizes the reaction mechanism not by the reactants, intermediate structures, and products, but via reaction-relevant moieties. We apply our model for three different derivatives of 2,2’-Spirobi[4H-1,3,2-benzodioxasiline] and determine activation energies, reaction enthalpies, and reaction rate constants for the reaction steps in our mechanism. We compare our ﬁndings to previously reported values obtained from density functional theory calculations. Furthermore, with this approach we are also able to follow the time development of the concentrations of the reaction-relevant moieties.

Karsten Schwalbe and Karl Heinz Hoffmann.
“Novikov engine with ﬂuctuating heat bath temperature”.
In: J. Non-Equilib. Thermodyn. 43.2 (2018), pp. 141–150.
doi: 10.1515/jnet-2018-0003.
The Novikov engine is a model for heat engines that takes the irreversible character of heat ﬂuxes into account. Using this model, the maximum power output as well as the corresponding efficiency of the heat engine can be deduced, leading to the well known Curzon-Ahlborn efficiency. The classical model assumes constant heat bath temperatures, which is not a reasonable assumption in case of ﬂuctuating heat sources. Therefore, in this article the inﬂuence of stochastic ﬂuctuations of the hot heat bath’s temperature on the optimal performance measures is investigated. For this purpose, a Novikov engine with ﬂuctuating heat bath temperature is considered. Doing so, an generalization of the Curzon-Ahlborn efficiency is found. The results can help to quantify how the distribution of ﬂuctuating quantities effects the performance measures of power plants.

Karsten Schwalbe and Karl Heinz Hoffmann.
“Optimal Control of an Endoreversible Solar Power Plant”.
In: J. Non-Equilib. Thermodyn. 43.3 (2018), pp. 255–271.
doi: 10.1515/jnet-2018-0021.
While in the classic Curzon–Ahlborn and Novikov engines the temperatures of the heat baths are kept ﬁxed or follow a deterministic time function, it is the aim of this work to study the impact of ﬂuctuating heat bath temperatures. As an example serves a solar power plant, where the stochastically varying cloud cover leads to ﬂuctuations in the temperature of the hot heat bath. This solar thermal power plant is modeled as a stochastic endoreversible system. On the basis of this model the maximum expected work output of the power plant and the corresponding optimal control policy is derived. For the considered system it is found that the maximum expected work output changes with the reversion speed of the hot temperature depending on the relation of the starting hot temperature and the temperature of the power plant’s receiver. Additionally, it is found that the maximum expected work output increases with the hot temperature’s ﬂuctuation strength.

Karsten Schwalbe and Karl Heinz Hoffmann.
“Performance Features of a Stationary Stochastic Novikov Engine”.
In: Entropy 20 (2018), pp. 52–1–13.
doi: 10.3390/e20010052.
In this article a Novikov engine with ﬂuctuating hot heat bath temperature is presented. Based on this model, the performance measure maximum expected power as well as the corresponding efficiency and entropy production rate is investigated for four different stationary distributions: continuous uniform, normal, triangle, quadratic, and Pareto. It is found that the performance measures increase monotonously with increasing expectation value and increasing standard deviation of the distributions. Additionally, we show that the distribution has only little inﬂuence on the performance measures for small standard deviations. For larger values of the standard deviation, the performance measures in the case of the Pareto distribution are signiﬁcantly different compared to the other distributions. These observations are explained by a comparison of the Taylor expansions in terms of the distributions’ standard deviations. For the considered symmetric distributions, an extension of the well known Curzon-Ahlborn efficiency to a stochastic Novikov engine is given.

Karsten Schwalbe and Karl Heinz Hoffmann.
“Stochastic Novikov engine with time dependent temperature ﬂuctuations”.
In: Appl. Thermal Eng. 142 (2018), pp. 483–488.
doi: 10.1016/j.applthermaleng.2018.07.045.
In this article a Stochastic Novikov engine is used to model a solar power plant. This heat engine is characterized by a ﬂuctuating hot heat bath temperature. The distribution function of these ﬂuctuations is derived based on a stochastic solar irradiation model. Using this distribution the control problem of determining the maximum of the expected work output is solved. This work output as well as the corresponding efficiency is deduced in dependence of the chosen control type. Considering this work output and this efficiency, which can be considered as performance measures of the solar power plant, the inﬂuence of the system parameters is discussed. It turns out that these performance measures increase monotonously with the parameter of the hot temperature’s distribution function and that more control leads to higher efficiencies.

A. M. Tsirlin, I. N. Grigorevskiy, and K. Schwalbe.
“Thermodynamical estimation of the bounds on performance of irreversible binary distillation”.
In: Int. J. Heat Mass Transfer 118 (2018), pp. 289–296.
doi: 10.1016/j.ijheatmasstransfer.2017.10.119.
The limits of the ability of a distillation system to seperate a binary mixture are considered for two different cases. In the ﬁrst case the heat supply solely takes place at the column bottom and the heat removal at the condenser. In the second case the heat supply and removal is distributed over the column height. For both cases, the limiting column capacity and the minimum heat consumption are related to the external stream compositions and to the heat and mass transfer coefficients.

Karl Heinz Hoffmann and J. Christian Schön.
“Combining pressure and temperature control in dynamics on energy landscapes”.
In: Eur. J. Phys. 90 (2017), pp. 84–1–12.
doi: 10.1140/epjb/e2017-70510-5.
Complex systems from science, technology or mathematics usually appear to be very different in their speciﬁc dynamical evolution. However, the concept of an energy landscape with its basins corresponding to locally ergodic regions separated by energy barriers provides a unifying approach to the description of complex systems dynamics. In such systems one is often confronted with the task to control the dynamics such that a certain basin is reached with the highest possible probability. Typically one aims for the global minimum, e.g. when dealing with global optimization problems, but frequently other local minima such as the metastable compounds in materials science are of primary interest. Here we show how this task can be solved by applying control theory using magnesium ﬂuoride as an example system, where different modiﬁcations of $M g F 2$ are considered as targets. In particular, we generalize previous work restricted to temperature controls only and present controls which simultaneously adjust temperature and pressure in an optimal fashion.

Jens Lang and Janett Prehl.
“An embarrassingly parallel algorithm for random walk simulations on random fractal structures”.
In: J. Comp. Sci. 19 (2017), pp. 1–10.
doi: 10.1016/j.jocs.2016.11.014.
Anomalous diffusion is often simulated by random walks on random fractal structures. As existing simulation methods either lack a high degree of parallelism or impose restrictions on the choice of fractal structures, a new approach is proposed here..
We present a parallel algorithm for simulating random walks on fractal structures that is suitable for a wide variety of hardware architectures. The degree of parallelism of the algorithm equals the number of random walkers, which is achieved by its communication-avoiding design. In contrast to other approaches, the random fractal structure is not pre-computed at whole. Instead, only the surrounding of each random walker is calculated by the parallel threads while the random walker moves around on the fractal structure.

Robin Masser, Karsten Schwalbe, and Karl Heinz Hoffmann.
“Energy Recuperation System for Skip Trucks”.
In: Proceedings of ECOS 2017 - The 30th Environmental Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy systems.
Ed. by Asfaw Beyene, David MacPhee, and Abel Hernandez-Guerrero.
Vol. 1.
San Diego, California, USA: San Diego State University, 2017,
P. 650.
The reduction of the energy consumption by means of recuperation systems has been in the focus of research during the last decades. Following this goal, our work aims to reduce the fuel consumption of commercial vehicles, in particular of skip trucks. This is done by the installation of a module, consisting of a bladder accumulator and a hydraulic pump driven by the cardan shaft that is installed to store energy. The energy may then be used as additional propulsion, to support the thermal management and to operate the skipping mechanism. The latter application offers the advantage that the skipping mechanism can be operated without the need for running the combustion engine. Compared to other recuperation systems, hydraulic systems offer high energy and power density with relatively low weight. The hydraulic recuperation system is modeled applying endoreversible thermodynamics taking heat losses into account. Based on this model, system parameters and control strategies can be optimized in terms of power and efficiency. The resulting fuel and operational cost savings are estimated evaluating recorded urban driving data.

Janett Prehl, Thomas Schönfelder, Joachim Friedrich, and Karl Heinz Hoffmann.
“Site Dependent Atom Type ReaxFF for the Proton-Catalyzed Twin Polymerization”.
In: J. Phys. Chem. C 121.29 (2017), pp. 15984–15992.
doi: 10.1021/acs.jpcc.7b03219.
ReaxFF is an efficient member of reactive molecular dynamics approaches to model chemical reactions for different chemical environments. Here it is applied to the structure formation process of twin polymerization, a newly developed method to obtain nanostructured functional materials. To achieve this, a site dependent atom type (SDAT) generalization of the classical ReaxFF approach is presented, which employs more then one atom type per chemical element. The efficacy of this SDAT-ReaxFF approach is demonstrated for two different cases: a benzene–benzyl reaction as well as for the twin polymerization.

Karsten Schwalbe.
“Stochastic Fluctuations in Endoreversible Systems”.
URL: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-219268.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Feb. 2017.
In this thesis, the inﬂuence of stochastic ﬂuctuations on the performance of endoreversible engines is investigated for the ﬁrst time. For this, a Novikov-engine with three different heat transport laws (Newtonian, Fourier, asymmetric) is considered. While the maximum work output and corresponding efficiency can be deduced easily in the case of constant heat bath temperatures, this changes, if these temperatures are allowed to ﬂuctuate stochastically. In the latter case, stochastic optimal control theory has to be used to ﬁnd the maximum of the expected work output and the corresponding control policy. In general, solving such problems leads to a non-linear, partial differential equation coupled to an optimization, called the stochastic Hamilton-Jacobi-Bellman equation. However, as presented in this thesis, calculations can be simpliﬁed, if one assumes that the ﬂuctuations are independent of the considered control variable. In this case, analytic considerations show that the equations for performance measures like work output and efficiency keep their original form, but terms have to be replaced by appropriate time averages and expectation values, depending on the considered control type. Based on an analysis of the performance measures in the case of a uniform distribution of the hot temperature of the Novikov engine, conclusions on their monotonicity behavior are drawn. The comparison of several, time independent, symmetric distributions reveals a to date unknown extension to the Curzon-Ahlborn efficiency in the case of small ﬂuctuations. Furthermore, an analysis of a Novikov engine with asymmetric heat transport, where the behavior of the hot temperature is described by an Ornstein-Uhlenbeck process, is performed. Finally, a Novikov engine with Fourier heat transport is considered, where the dynamics of the hot temperature depends on the control variable. By solving the corresponding Hamilton-Jacobi-Bellman equation, new conclusions how to optimally control such systems are drawn.

Anatoly Tsirlin, Ivan Andreevich Sukin, Alexander Balunov, and Karsten Schwalbe.
“The Rule of Temperature Coefficients for Selection of Optimal Separation Sequence for Multicomponent Mixtures in Thermal Systems”.
In: J. Non-Equilib. Thermodyn. 42.4 (2017), pp. 359–369.
doi: 10.1515/jnet-2017-0024.
In this paper an estimate for the reversible molar heat supply needed for fully separating a certain mixture is given on the basis of thermodynamic balance equations. It is shown that in order to estimate this heat supply one should solve the problem of selecting the optimal separation sequence. The algorithm solving this task is given. This algorithm allows to select the separation sequence on the basis of preliminary calculations, knowing only the properties of the component that one wants to separate. The solution algorithm is demonstrated for an exemplary system: a gas-fractionation plant.

Frank Boldt, Peter Salamon, and Karl Heinz Hoffmann.
“Fastest Effectively Adiabatic Transitions for a Collection of Harmonic Oscillators”.
In: J. Phys. Chem. A 120.19 (2016), pp. 3218–3224.
doi: 10.1021/acs.jpca.5b11698.
We discuss fastest effectively adiabatic transitions (FEATs) for a collection of noninteracting harmonic oscillators with shared controllable real frequencies. The construction of such transitions is presented for given initial and ﬁnal equilibrium states, and the dependence of the minimum time control on the interval of achievable frequencies is discussed. While the FEAT times and associated FEAT processes are important in their own right as optimal controls, the FEAT time is an added feature which provides a measure of the quality of a shortcut to adiabaticity (STA). The FEAT time is evaluated for a previously reported experiment, wherein a cloud of Rb atoms is cooled following a STA recipe that took about twice as long as the FEAT speed limit, a time efficiency of 50%.

René Haber and Karl Heinz Hoffmann.
“Extending the parQ transition matrix method to grand canonical ensembles”.
In: Phys. Rev. E 93 (2016), pp. 063314–1–8.
doi: 10.1103/PhysRevE.93.063314.
Phase coexistence properties as well as other thermodynamic features of ﬂuids can be effectively determined from the grand canonical density of states (DOS). We present an extension of the parQ transition matrix method in combination with the efasTM method as a very fast approach for determining the grand canonical DOS from the transition matrix. The efasTM method minimizes the deviation from detailed balance in the transition matrix using a fast Krylov-based equation solver. The method allows a very effective use of state space transition data obtained by different exploration schemes. An application to a Lennard-Jones system produces phase coexistence properties of the same quality as reference data.

Janett Prehl, Frank Boldt, Karl Heinz Hoffmann, and Christopher Essex.
“Symmetric Fractional Diffusion and Entropy Production”.
In: Entropy 18.7 (2016), pp. 275–1–11.
doi: 10.3390/e18070275.
The discovery of the entropy production paradox (Hoffmann et al., 1998) raised basic questions about the nature of irreversibility in the regime between diffusion and waves. First studied in the form of spatial movements of moments of H functions, pseudo propagation is the pre-limit propagation-like movements of skewed probability density function (PDFs) in the domain between the wave and diffusion equations that goes over to classical partial differential equation propagation of characteristics in the wave limit. Many of the strange properties that occur in this extraordinary regime were thought to be connected in some manner to this form of proto-movement. This paper eliminates pseudo propagation by employing a similar evolution equation that imposes spatial unimodal symmetry on evolving PDFs. Contrary to initial expectations, familiar peculiarities emerge despite the imposed symmetry, but they have a distinct character.

Peter Salamon, Anca Segall, J. Christian Schön, Karl Heinz Hoffmann, and Bjarne Andresen.
“Rate constants, timescales, and free energy barriers”.
In: J. Non-Equilib. Thermodyn. 41.1 (2016), pp. 13–18.
doi: 10.1515/jnet-2015-0038.

Thomas Streubel.
“Situation Assessment at Intersections for Driver Assistance and Automated Vehicle Control”.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Jan. 2016.
The development of driver assistance and automated vehicle control is in process and ﬁnds its way more and more into urban traffic environments. Here, the complexity of traffic situations is highly challenging and requires system approaches to comprehend such situations. The key element is the process of situation assessment to identify critical situations in advance and derive adequate warning and intervention strategies. This thesis introduces a system approach to establish a situation assessment process with the focus on the prediction of the driver intention. The system design is based on the Situation Awareness model by Endsley. Further, a prediction algorithm is created using Hidden Markov Models. To deﬁne the parameters of the models, an existing database is used and previously analyzed to identify reasonable variables that indicate an intended driving direction while approaching the intersection. Here, vehicle dynamics are used instead of driver inputs to enable a further extension of the prediction, i.e. to predict the driving intention of other vehicles detected by sensors. High prediction rates at temporal distances of several seconds before entering the intersection are accomplished. The prediction is integrated in a system for situation assessment including an intersection model. A Matlab tool is created with an interface to the vehicle CAN bus and the intersection modeling which uses digital map data to establish a representation of the intersection. To identify differences and similarities in the process of approaching an intersection dependent on the intersection shape and regulation, a naturalistic driving study is conducted. Here, the distance to the intersection and velocity is observed on driver inputs related to the upcoming intersection (leaving the gas pedal, pushing the brake, using the turn signal). The ﬁndings are used to determine separate prediction models dependent on shape and regulation of the upcoming intersection. The system runs in real-time and is tested in a real traffic environment.

Katharina Wagner and Karl Heinz Hoffmann.
“Chemical reactions in endoreversible thermodynamics”.
In: Eur. J. Phys. 37 (2016), p. 015101.
doi: 10.1088/0143-0807/37/1/015101.
Endoreversible thermodynamics is a theory for the (approximate) description of thermodynamic non-equilibrium systems, which allows us to capture the ever present irreversibilities of real processes. For instance in heat engines the dissipation due to ﬁnite heat transport capabilities, as well as the resulting limitations in the energy ﬂuxes, can be incorporated into the theory. It has thus been very successful in closing the gap between observed and theoretically predicted efficiencies. Here an extension of the theory is provided, with which chemical reactions can be included in the formalism. This opens up a wide ﬁeld of applications for endoreversible modeling and the investigation of dissipative processes, for instance in fuel cells or batteries.

Karoline Griesbach.
“Spurwechselverhalten im urbanen Raum”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Nov. 2015.
Die Vorhersage des Spurwechsels und dessen Integration in Fahrerassistenzsysteme kann Verkehrsunfälle reduzieren. In der vorliegenden Arbeit werden bisherige Ans̈atze mit neuronalen Netzen und kognitiven Architekturen für die Spurwechselvorhersage zusammengefasst. Des Weiteren wurden neuronale Netze für die Vorhersage des )purwechsels entwickelt. Um den Spurwechsel vorherzusagen wurden neuronale Netze mit der Delta-Lernregel, dem Backpropagation-Verfahren und dem Backpropagation-Verfahren mit Momentumterm entwickelt. Es wurde die Vorhersage für den linken und rechten Spurwechsel 5 s, 7 s und 10 s vor einem Spurwechsel untersucht. Es gab zwei Datens̈atze, die Trainingsdaten, mit dem das neuronale Netz lernt und die Validierungsdaten, mit dem der Lernerfolg des neuronalen Netzes getestet wird. Des Weiteren unterschieden sich die Datens̈atze für den linken Spurwechsel, indem sowohl das Lernen nur für den Spurwechseltyp ‘langsam vorausfahrendes Fahrzeug’ getestet wurde als auch das Lernen von allen Spurwechseltypen (Auffahrt, Abbiegestreifen, Einscherer, Hindernis langsam vorausfahrendes Fahrzeug und Unbekannt). Als Eingaben dienten Informationen über die Blinkerbetätigung, die Kopfbewegung, den Lenkradeinschlag, die Blickrichtung und die Zeit bis zum Aufprall (TTC). Die beste Vorhersage traf ein neuronales Netz mit dem Backpropagation-Verfahren, was den Spurwechsel im urbanen Raum nach links mit einer Richtig-Positiv-Rate (tpr) is 72,09% und Falsch-Positiv-Rate (fpr) is 0,00% vorhersagen konnte. Als Trainings- und Validierungsdaten wurden alle linken Spurwechseltypen betrachtet. Die Vorhersage des rechten Spurwechsels im urbanen Raum war mit dem entwickelten Netz nicht erfolgreich. Die für war über 50,00%.

Karl Heinz Hoffmann, Bjarne Andresen, and Peter Salamon.
“Finite-Time Thermodynamics Tools to Analyze Dissipative Processes”.
In: Proceedings of the 240 Conference: Science’s Great Challenges.
Ed. by Aaron R. Dinner and Stuart A. Rice.
Vol. 157.
Advances in Chemical Physics.
Wiley, 2015,
Pp. 57–67.
doi: 10.1002/9781118959602.ch5.
The ﬁeld of ﬁnite-time thermodynamics considers questions such as: does dissipation necessarily occur if a thermodynamic process takes place in ﬁnite time. This chapter presents four concepts: the tricycle, thermodynamic length, work deﬁciency, and network thermodynamics. These concepts highlight the basic features of ﬁnite-time thermodynamics and shed some light on the staging free energy problem. The concepts are also promising candidates for further development and application in biological systems. Beyond the realm of macroscopic systems, these concepts have been extended during the past years also to the realm of quantum systems. While network thermodynamics has proven its usefulness in macroscopic applications like the analysis of internal combustion engines, the complexity of biological systems remains a challenge.

Karl Heinz Hoffmann and Peter Salamon.
“Finite-time availability in a quantum system”.
In: EPL 109.4 (2015), pp. 40004–1–6.
doi: 10.1209/0295-5075/109/40004.
Classically, availability refers to the work available in any reversible process that brings about equilibrium between the system and its environment. Here we introduce an additional meaning of availability as the maximum work associated with the change of an external parameter in the Hamiltonian of a quantum system. This availability can be gained in a FEAT process and for times larger than or equal to the FEAT time, there exists an optimal control that achieves the available work. For shorter times, quantum friction effects are unavoidable and the available work is thereby lowered. This ﬁnite-time availability is quantiﬁed here as a function of the time available.

Karl Heinz Hoffmann, Kim Schmidt, and Peter Salamon.
“Quantum ﬁnite time availability for parametric oscillators”.
In: J. Non-Equilib. Thermodyn. 40.2 (2015), pp. 121–129.
doi: 10.1515/jnet-2015-0025.
The availability of a thermodynamic system out of equilibrium with its environment describes its ability to perform work in a reversible process which brings it to equilibrium with this environment. Processes in ﬁnite time can usually not be performed reversibly thus leading to unavoidable losses. In order to account for these losses the concept of ﬁnite time availability was introduced. We here add a new feature through the introduction of quantum ﬁnite time availability for an ensemble of parametric oscillators. For such systems there exists a certain critical time, the FEAT time. Quantum ﬁnite time availability quantiﬁes the available work from processes which are shorter than the FEAT time of the oscillator ensemble.

Robin Masser.
“Entwicklung und Implementierung einer Zeitadaptivität für Galerkin-basierte und variationelle Integratoren”.
in English.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Sept. 2015.
Steigende Anforderungen an Zeitintegratoren hinsichtlich Genauigkeit und Stabilität ziehen steigende Komplexität und Rechenaufwand nach sich. Um dennoch die Wirtschaftlichkeit der Simulationen zu waren, ist eine effiziente Regulierung des Rechenaufwandes notwendig. Ein vielversprechender Ansatz dafür sind Verfahren mit adaptiven Zeitschrittweiten. In dieser Arbeit erfolgt eine konsistente Herleitung und Diskretisierung eines continuous Galerkin-Integrators und eines variationellen Integrators. Eine hinreichend allgemeine Darstellung erlaubt es sowohl zeitliche Formfunktionen als auch numerische Integrationsverfahren beliebig zu variieren. Eine solche Implementierung ist demnach im Stande unterschiedliche Integratoren abzubilden. Anschließend wird für beide Integratoren mit Hilfe einer Zeittransformation nach Sundman eine adaptive Zeitschrittweitensteuerung eingeführt. Für die Steuerfunktion wird dabei ein system-unspeziﬁscher Ansatz genutzt, welcher durch ein implizites sowie durch ein explizites Verfahren umgesetzt wird. Das System selbst ist ein eindimensionales Kontinuum mit Zwangsbedingungen, welches ein elastisches bzw. viskoelastisches Seil repräsentiert. Der Einﬂuss von Formfunktionen und Quadraturverfahren auf Konvergenz und Erhaltungseigenschaften der Integratoren wird anhand ausgewählter Beispiele untersucht, wobei ein möglicher Einﬂuss durch gewählte Zwangsbedingungen berücksichtigt wird. Es zeigt sich, dass die Wahl des Quadraturverfahrens die Konvergenzordnung und Energieerhaltung beider Integratoren maßgeblich beeinﬂusst, wohingegen die Variation von Formfunktionen darauf keinen nennenswerten Effekt hat. Die Untersuchung der Effizienz der Zeitadaptivität wird mit typischerweise gewählten Lagrange-Formfunktionen und einer Gauss-Quadratur durchgeführt. Als Kriterium der Effizienz wird dabei der Fehler in der Energie betrachtet. Für das viskoelastische Seil wird im Gegensatz zum rein elastischen Seil mit Hilfe der implementierten Zeitadaptivität eine Effizienzsteigerung erreicht.

Peter Salamon, Bjarne Andresen, Karl Heinz Hoffmann, James D. Nulton, Anca M. Segall, and Forest L. Rohwer.
“Free Energies of Staging a Scenario and Perpetual Motion Machines of the Third Kind”.
In: Proceedings of the 240 Conference: Science’s Great Challenges.
Ed. by Aaron R. Dinner and Rice A. Stuart.
Vol. 157.
Advances in Chemical Physics.
Wiley, 2015,
Pp. 43–55.
doi: 10.1002/9781118959602.ch4.

Ivan Tchernook, Janett Prehl, and Joachim Friedrich.
“Corrigendum to ‘Quantum chemical investigation of the counter anionin the acid catalyzed initiation of 2,2’-spirobi[4H-1,3,2-benzodioxasiline] polymerization’ [Polymer 60 (2015) 241–251]”.
In: Polymer 74 (2015), pp. 272–274.
doi: 10.1016/j.polymer.2015.07.058.

Ivan Tchernook, Janett Prehl, and Joachim Friedrich.
“Quantum chemical investigation of the counter anion in the acid catalyzed initiation of 2,2’-spirobi[4H-1,3,2-benzodioxasiline] polymerization”.
In: Polymer 60 (2015), pp. 241–251.
doi: 10.1016/j.polymer.2015.01.042.
The recently discovered twin polymerization offers a remarkable access to new versatile hybrid materials. In order to develop an advanced model system to understand the reaction mechanism in detail we present an exemplary quantum chemical study on the role of the counter anion in the acid (triﬂuoroacetatic acid) catalyzed twin polymerization of 2,2’-spirobi[4H-1,3,2-benzodioxasiline]. Using three different model systems the reaction mechanism is investigated with respect to the inﬂuence of the anion (triﬂuoroacetate) in the reaction system. The extended model system with two monomers and two acid molecules exhibits lowest activation barriers for the ﬁrst step of the organic network formation. The formation of the electrophile and the electrophilic substitution are supported by the present counter anion. The reaction mechanism of this initiating process is also inﬂuenced by sterical effects, since the size of the acid molecule is quite comparable to the size of other molecular structure units. The obtained sophisticated data base on the reaction mechanism and the energetics provides an important basis for structure formation modeling in future.

Katharina Wagner and Karl Heinz Hoffmann.
“Endoreversible modeling of a PEM fuel cell”.
In: J. Non-Equilib. Thermodyn. 40.4 (2015), pp. 283–294.
doi: 10.1515/jnet-2015-0061.
Fuel cells are known for high efficiencies in converting chemical energy into electrical energy. Nonetheless, the processes taking place in a fuel cell still possess a number of irreversibilities that limit the power output to values below the reversible limit. To analyze these, we developed a model that captures the main irreversibilities occurring inside a proton exchange membrane or polymer electrolyte membrane fuel cell. We used the methods of endoreversible thermodynamics, which enable us to study the entropy production of the different sources of irreversibility in detail. Additionally, performance measures like efficiency and power output can be calculated with such a model, and the inﬂuence of different parameters, such as temperature and pressure, can be easily investigated. The comparison of the model predictions with realistic fuel cell data shows that the functional dependencies of the fuel cell characteristics can be captured quite well.

Katharina Wagner and Karl Heinz Hoffmann.
“ETA-Graphics – an interface to endoreversible thermodynamics”.
In: Eur. J. Phys. 36 (2015), pp. 025010–1–11.
doi: 10.1088/0143-0807/36/2/025010.
Endoreversible thermodynamics is a theory for the description of irreversible thermodynamic processes. In this theory a non-equilibrium system is divided into a set of reversible subsystems which interact irreversibly with one another by exchanging energy and extensive quantities. These extensities act as carriers for the energy. ETA-Graphics is a graphics-based interface to endoreversible thermodynamics that can be used as an educational aid. It enables students to visually design endoreversible systems by drawing reversible subsystems and connecting them with irreversible (or reversible) interactions. Through special dialogs users specify the properties of the system, e.g., in form of transport laws for energy and extensive quantities. Based on the input ETA-Graphics allows students to analyse the endoreversible systems and their properties. Therefore, performance measures, i.e., efficiency and total power output, are calculated. Additionally, graphical representations of the results are shown.

Frank Boldt.
“A Framework for Modeling Irreversible Processes Based on the Casimir Companion”.
URL: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-145179.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, May 2014.

René Haber.
“Transition Matrix Monte Carlo Methods for Density of States Prediction”.
URL: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-146873.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, May 2014.
Ziel dieser Arbeit ist zunächst die Entwicklung einer Vergleichsgrundlage, auf Basis derer Algorithmen zur Berechnung der Zustandsdichte verglichen werden können. Darauf aufbauend wird ein bestehendes ̈ubergangsmatrixbasiertes Verfahren für das großkanonisch Ensemble um ein neues Auswerteverfahren erweitert. Dazu werden numerische Untersuchungen verschiedener Monte-Carlo-Algorithmen zur Berechnung der Zustandsdichte durchgeführt. Das Hauptaugenmerk liegt dabei auf Verfahren, die auf Übergangsmatrizen basieren, sowie auf dem Verfahren von Wang und Landau. Im ersten Teil der Forschungsarbeit wird ein umfassender Überblick über Monte-Carlo-Methoden und Auswerteverfahren zur Bestimmung der Zustandsdichte sowie über verwandte Verfahren gegeben. Außerdem werden verschiedene Methoden zur Berechnung der Zustandsdichte aus Übergangsmatrizen vorgestellt und diskutiert. Im zweiten Teil der Arbeit wird eine neue Vergleichsgrundlage für Algorithmen zur Bestimmung der Zustandsdichte erarbeitet. Dazu wird ein neues Modellsystem entwickelt, an dem verschiedene Parameter frei gewählt werden können und für das die exakte Zustandsdichte sowie die exakte Übergangsmatrix bekannt sind. Anschließend werden zwei weitere Systeme diskutiert für welche zumindest die exakte Zustandsdichte bekannt ist: das Ising Modell und das Lennard-Jones System. Der dritte Teil der Arbeit beschäftigt sich mit numerischen Untersuchungen an einer Auswahl der vorgestellten Verfahren. Auf Basis der entwickelten Vergleichsgrundlage wird der Einﬂuss verschiedener Parameter auf die Qualität der berechneten Zustandsdichte quantitativ bestimmt. Es wird gezeigt, dass Übergangsmatrizen in Simulationen mit Wang-Landau-Verfahren eine wesentlich bessere Zustandsdichte liefern als das Verfahren selbst. Anschließend werden die gewonnenen Erkenntnisse genutzt um ein neues Verfahren zu entwickeln mit welchem die Zustandsdichte mittels Minimierung der Abweichungen des detaillierten Gleichgewichts aus großen, dünnbesetzten Übergangsmatrizen gewonnen werden kann. Im Anschluss wird ein Lennard-Jones-System im großkanonischen Ensemble untersucht. Es wird gezeigt, dass durch das neue Verfahren Zustandsdichte und Dampfdruckkurve bestimmt werden können, welche qualitativ mit Referenzdaten übereinstimmen.

René Haber, Janett Prehl, Karl Heinz Hoffmann, and Heiko Herrmann.
“Random walks of oriented particles on fractals”.
In: J. Phys. A: Math. Gen. 47.17 (2014), pp. 155001–1–14.
doi: 10.1088/1751-8113/47/15/155001.
Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising ﬁnding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features.

Kim Schmidt, Matthias Beggiato, Karl Heinz Hoffmann, and Josef F. Krems.
“A mathematical model for predicting lane changes using the steering wheel angle”.
In: J. Saf. Res. 49 (2014), pp. 85–90.
doi: 10.1016/j.jsr.2014.02.014.

Thomas Schönfelder.
“Development of a Reactive Simulation Concept for Twin Polymerization”.
URL: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-148145.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, May 2014.
Die vorliegende Arbeit konzentriert sich auf die Entwicklung und Validierung eines reaktiven Kraftfelds (ReaxFF) ur die Strukturbildungsprozesse der Zwillingspolymerisation (ZP). Die ZP ist eine neue Synthesemethode zur Herstellung nanostrukturierter Hybridmaterialien, wie beispielsweise nanostrukturierter Kohlenstoffe als Gasspeichermedium. Die ZP beruht dabei auf der Verwendung geeigneter Zwillingsmonomere, die kovalent gebundene organische und anorganische Strukturkomponenten aufweisen. Innerhalb der Polymerisation werden die Komponenten neu verkn̈upft, sodass mehrere ineinander verwobene Teilpolymere - zum Beispiel Phenolharz und Siliziumdioxid - als organisch-anorganische Mischung entstehen. Die Nanostrukturierung innerhalb des Prozesses liegt dabei an dem gekoppelten Wachstum durch die anangliche kovalente Bindung im Zwillingsmonomer. Ein Überblick über die chemischen Details wird im zweiten Kapitel gegeben. Weiterhin werden für die Modellbildung genutzte reduzierte Testsysteme vorgestellt. Basierend auf dieser komplexen Strukturbildung wird im dritten Kapitel die gewählte Modellierungsmethode der reaktiven Molekulardynamik mit dem Kraftfeld ReaxFF vorgestellt. Zur die Modellierung mit ReaxFF werden Referenzdaten ben̈otigt um einen Parametersatz für das Kraftfeld zu entwickeln, welcher das chemische Modell darstellen kann. Dazu wird im vierten Kapitel eine Übersichtuber die benutzten Methoden zur Referenzdatenerzeugung gegeben. Im fünften Kapitel fokussiert sich die Arbeit auf die ananglich als Referenz zur Verfügung gestellte Theorie und ihre Erweiterung zur Unterstützung der Kraftfeldmodellierung. Ausgehend von den erhaltenen Referenzdaten werden die Kraftfeldresultate für die erste Parametrisierung (TP-a) vorgestellt. Diese zeigte eine ununstige Mittelung aus aromatischen Ringeigenschaften und nichtaromatischen Buckeneigenschaften, welche dann mit einer erweiterte Kraftfelddeﬁnition (TP-b) aufgehoben werden konnte. In den Simulationen konnten damit alle deﬁnierte Schritte der ZP nachgewiesen werden, allerdings mit verbleibenden Problemen aufgrund der Charakteristik des geladenen Gesamtsystems. Zur das sechste Kapitel wird daher die Implementierung eines Kraftfeldes für die vollständige Darstellung einer S̈aure durchgeführt. Ein weiterer wichtiger Aspekt ur diese Erweiterung ist die damit verbundene Aufklärung der Rolle des Anions in der Strukturbildung. Das siebte Kapitel fasst die Arbeit zusammen und erlaubt den Ausblick auf zuk̈unftige Verbesserung der Modellierung. Weiterhin werden Aussagen zur Transferierbarkeit der Ergebnisse innerhalb der Zwillingspolymerisierung getroffen.

Thomas Schönfelder, Joachim Friedrich, Janett Prehl, Steffen Seeger, Stefan Spange, and Karl Heinz Hoffmann.
“Reactive force ﬁeld for electrophilic substitution at an aromatic system in twin polymerization”.
In: Chem. Phys. 440 (2014), pp. 119–126.
doi: 10.1016/j.chemphys.2014.06.003.
Twin polymerization is a new synthesis concept, which enables the formation of two different macromolecular structures from organic–inorganic hybrid materials in one single process step. To gain insights into formation processes we implement a ﬁrst-principles-based ReaxFF reactive force ﬁeld for C/H/O/Si for the initial electrophilic substitution of an aromatic system. We show that established parametrizations that have been developed to model chemical reactions of (hydro) carbon or carbon nanotubes systems successfully cannot reproduce this reaction although they include the same chemical elements and in parts same reaction mechanisms. Thus, we develop a new parametrization being capable in reproducing this aromatic reaction properly and compare it to the established ones to identify the differences.

Karsten Schwalbe, Andreas Fischer, Karl Heinz Hoffmann, and Jens Mehnert.
“Applied endoreversible thermodynamics: Optimization of powertrains”.
In: Proceedings of ECOS 2014 - 27th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems.
Ed. by R. Zevenhouen.
ECOS 2014, June 15-19, 2014, Turku, Finland.
Turku, Finland, 2014,
Pp. 45–55.
For the last decades, the theory of Endoreversible Thermodynamics has proven to be an important tool to investigate non-equilibrium thermal systems. In this theory, systems are considered as a network of reversible subsystems with irreversible interactions. A remarkable beneﬁt of the Endoreversible Thermodynamics is the adaptivity of the desired level of detail for the model so that the complexity of the system remains relatively easy to handle. In this way, simpliﬁed models of good quality can be deduced for various systems, e.g. energy transformation devices or energy storage devices. The applicability of Endoreversible Thermodynamics to practically relevant systems is demonstrated by the ”Powertrain” example. Therefore, both a combustion engine and a hydraulic energy storage (for recuperation purposes) are considered. The complex processes inside the engine and the energy storage are mapped to a simpliﬁed Endoreversible model. Synthesizing these Endoreversible models, we derive an estimate for the systems’ full range operational behavior which can be used to optimize design and process parameters of the powertrain.

Thomas Streubel and Karl Heinz Hoffmann.
“Fahrverhaltenanalyse an Kreuzungen auf Basis von Fahrdaten”.
In: AmE 2014 (GMM-FB 78).
GMM-Fachbericht 78.
Automotive meets Electronics, Beiträge der 5. GMM-Fachtagung vom 18. bis 19. Februar in Dortmund.
GMM, 2014,
Pp. 5–1–6.
Kreuzungen sind ein wesentlicher Bestandteil der urbanen Infrastruktur. Je nach ihrer Beschaffenheit und dem Verkehrsaufkommen können sie ein hohes Maß an Komplexität annehmen und so den Fahrer vor besondere Herausforderungen stellen. Fahrerassistenzsysteme zielen darauf ab in genau solchen Situationen den Fahrer zu unterstützen. Inwieweit dies notwendig ist, lässt sich am Fahrerverhalten abschätzen. Um ein besseres Verständnis für das natürliche Annäherungsverhalten an eine Kreuzung zu gewinnen, soll hier anhand von Fahrdaten der Prozess der Annäherung nachvollzogen werden. Die Fahrdaten stammen aus dem Projekt ”Sichere Intelligente Mobilität Testfeld Deutschland” (simTD). Dies war ein großangelegter Feldtest für Car-to-Car (C2C) Kommunikation. Hierbei wurden Daten verschiedener Fahrzeuge und Fahrer ausgewertet, die bei freier Fahrt auf dem Testgelände in Friedberg aufgezeichnet wurden. Ziel ist die Analyse der einzelnen Handlungsschritte während der Annäherung an eine speziﬁsche 4-Wege Kreuzung. Der Fokus liegt in einer qualitativen Charakterisierung des Handlungsablaufs bei Abbiegeszenarien. Dabei werden quantitative Aussagen über den zeitlichen und räumlichen Verlauf einzelner Phasen – Beginn des Blinkens, der Verzögerung und des Abbiegevorgang sowie Gangschaltzeitpunkte – getroffen. Abhängig von der Richtung, aus der sich der Kreuzung angenähert wird, muss man zwischen dem Annäherungsverhalten bei Vorfahrt und bei Vorfahrtachten unterscheiden. Innerhalb dieser beiden Gruppen sind jeweils beide Abbiegerichtungen möglich.

Thomas Streubel and Karl Heinz Hoffmann.
“Prediction of Driver Intended Path at Intersections”.
In: Intelligent Vehicles Symposium Proceedings.
Intelligent Vehicles Symposium, 8-11 June 2014, Dearborn, MI.
IEEE, 2014,
Pp. 134–139.
doi: 10.1109/IVS.2014.6856508.
The complexity of situations occurring at intersections is demanding on the cognitive abilities of drivers. Advanced Driver Assistance Systems (ADAS) are intended to assist particularly in those situations. However, for adequate system reaction strategies it is essential to develop situation assessment. Especially the driver’s intention has to be estimated. So, the criticality can be inferred and efficient intervention strategies can take action. In this paper, we present a prediction framework based on Hidden Markov Models (HMMs) and analyze its performance using a large database of real driving data. Our focus is on the variation of the model parameters and the choice of the dataset for learning. The direction of travel while approaching a 4-way intersection is to be estimated. A solid prediction is accomplished with high prediction rates above 90% and mean prediction times up to 7 seconds before entering the intersection area.

Katharina Wagner.
“An Extension to Endoreversible Thermodynamics for Multi-Extensity Fluxes and Chemical Reaction Processes”.
URL: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-146781.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Apr. 2014.
In this thesis extensions to the formalism of endoreversible thermodynamics for multi-extensity ﬂuxes and chemical reactions are introduced. These extensions make it possible to model a great variety of systems which could not be investigated with standard endoreversible thermodynamics. Multi-extensity ﬂuxes are important when studying processes with matter ﬂuxes or processes in which volume and entropy are exchanged between subsystems. For including reversible as well as irreversible chemical reaction processes a new type of subsystems is introduced – the so called reactor. It is similar to endoreversible engines, because the ﬂuxes connected to it are balanced. The difference appears in the balance equations for particle numbers, which contain production or destruction terms, and in the possible entropy production in the reactor. Both extensions are then applied to an endoreversible fuel cell model. The chemical reactions in the anode and cathode of the fuel cell are included with the newly introduced subsystem – the reactor. For the transport of the reactants and products as well as the proton transport through the electrolyte membrane, the multi-extensity ﬂuxes are used. This fuel cell model is then used to calculate power output, efficiency and cell voltage of a fuel cell with irreversibilities in the proton and electron transport. It directly connects the pressure and temperature dependencies of the cell voltage with the dissipation due to membrane resistance. Additionally, beside the listed performance measures it is possible to quantify and localize the entropy production and dissipated heat with only this one model.

Frank Boldt, James D. Nulton, Bjarne Andresen, Peter Salamon, and Karl Heinz Hoffmann.
“Casimir companion: An invariant of motion for Hamiltonian systems”.
In: Phys. Rev. A 87 (2013), pp. 022116–1–4.
doi: 10.1103/PhysRevA.87.022116.
In this paper an invariant of motion for Hamiltonian systems is introduced: the Casimir companion. For systems with simple dynamical algebras (e.g., coupled spins, harmonic oscillators) our invariant is useful in problems that consider adiabatically varying the parameters in the Hamiltonian. In particular, it has proved useful in optimal control of changes in these parameters. The Casimir companion also allows simple calculation of the entropy of nonequilibrium ensembles.

Jörn Getzlaff, Thomas Lambert, Karl Heinz Hoffmann, and Andreas Fischer.
“”OptiVent” - A New Approach for Controlling Mass Air Flow and Combustion in Direct Injection SI-Engines”.
In: SAE Int., Tech. Papers (2013), pp. 2013–01–0592.
doi: 10.4271/2013-01-0592.
Combustion concepts for future SI engines try to meet C0₂-emission commitments and legislation all over the world. Where the Diesel engine has an advantage by principle, the efficiency of the SI engine has to be improved signiﬁcantly, while of course the exhaust emissions must not become worse. An approach is to reduce the gas exchange losses using fully variable valve trains on the intake side of the combustion engine. OptiVent is a patented new way of controlling the mass air ﬂow in the cylinder of a combustion engine using opening valves during the compression phase of a four stroke engine. This technology regards a wider range of variability on the valvetrain components of the engine especially for opening the valves more than one time during a cycle. On the other hand it is necessary to combine this technology with direct injection to avoid fuel losses in the exhaust system and raising the exhaust hydrocarbon emission of the engine. Chemnitz University of Technology and the West Saxon University of Applied Sciences in Zwickau had performed numerical investigations on the potential of the OptiVent engine control and combustion system, using a fully variable valve train on the exhaust valves of the engine. The paper presents results from numerical simulations of the gas exchange, the mechanical losses of an engine with cylinder deactivation using OptiVent and regarding the effort for the starting process of engines with this new technology. The simulations show the potential of the new OptiVent-way of air mass control, so that the research can progress toward developing a running engine and testing it on a test bench. The research is funded by government and industrial partners.

René Haber, Janett Prehl, Heiko Hermann, and Karl Heinz Hoffmann.
“Diffusion of oriented particles in porous media”.
In: Phys. Lett. A 377 (2013), pp. 2840–2845.
doi: j.physleta2013.08.036.
Diffusion of particles in porous media often shows subdiffusive behavior. Here, we analyze the dynamics of particles exhibiting an orientation. The features we focus on are geometrical restrictions and the dynamical consequences of the interactions between the local surrounding structure and the particle orientation. This interaction can lead to particles getting temporarily stuck in parts of the structure. Modeling this interaction by a particular random walk dynamics on fractal structures we ﬁnd that the random walk dimension is not affected while the diffusion constant shows a variety of interesting and surprising features.

Karl Heinz Hoffmann, Bjarne Andresen, and Peter Salamon.
“Optimal control of a collection of parametric oscillators”.
In: Phys. Rev. E 87 (2013), pp. 062106–1–9.
doi: 10-1103/PhysRevE.87.062106.
The problem of effectively-adiabatic control of a collection of classical harmonic oscillators sharing the same time-dependent frequency is analyzed. The phase differences between the oscillators remain ﬁxed during the process. This fact that leads us to adopting the coordinates: energy, Lagrangian, correlation, which have proved useful in a quantum description and which have the advantage of treating both the classical and quantum problem in one uniﬁed framework. A representation theorem showing that two classical oscillators can represent an arbitrary collection of classical or quantum oscillators is proved. A new invariant, the Casimir companion, consisting of a combination of our coordinates is the key to determining the minimum reachable energy. We present a condition for two states to be connectable using 1-jump controls and enumerate all possible switchings for 1-jump effectively-adiabatic controls connecting any initial to any reachable ﬁnal state. Examples are discussed. One important consequence is that an initially microcanonical ensemble of oscillators will be transformed into another microcanonical ensemble by effectively-adiabatic control. Likewise, a canonical ensemble becomes another canonical ensemble.

Karl Heinz Hoffmann and J. Christian Schön.
“Controlled dynamics on energy landscapes”.
In: Eur. Phys. J. B 86 (2013), pp. 220–1–10.
doi: 10.1140/epjb/e2013-31042-4.

Robin Masser.
“Predicting the Reaction Behavior of Integrated Nanoscale and Reactive Multilayer Systems”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Oct. 2013.
Due to local heat generation, exothermic self-propagating high-temperature synthesis (SHS) of intermetallic compounds attain increasing interest in the ﬁeld of wafer bonding. With numerical models of self-sustaining reactions in thin multilayer ﬁlms, reliable predictions can be made about speed and structure of the reaction front. The inﬂuence of thicknesses of deposited layers and premixing between them caused by deposition is investigated. This work deals with heat losses into various substrate materials and material compounds, and minimal number of bilayers required for a self-propagating reaction front. Furthermore, the effect of temperature-dependent heat capacities is investigated. Numerical computations were performed for integrated Al/Pd multilayers and are compared to experimental data.

Janett Prehl, Frank Boldt, Christopher Essex, and Karl Heinz Hoffmann.
“Time Evolution of Relative Entropies for Anomalous Diffusion”.
In: Entropy 15.8 (2013). open access, pp. 2989–3006.
doi: 10.3390/e15082989.
The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly, the entropy does not order the bridging regime between diffusion and waves at all. However, it has been found that relative entropies, with an appropriately chosen reference distribution, do. Relative entropies, thus, provide a physically sensible way of setting which process is ”nearer” to pure diffusion than another, placing pure wave propagation, desirably, ”furthest” from pure diffusion. We examine here the time behavior of the relative entropies under the evolution dynamics of the underlying one-parameter family of dynamical equations based on space-fractional derivatives.

Thomas Streubel, Marco Moebus, and Karl Heinz Hoffmann.
“Generische Umfeldmodellierung – Autonome Fahrzeugsteuerung durch eine Risikokarte”.
In: VDI Wissensforum: 16. Internationaler Kongress – Elektronik im Fahrzeug.
VDI-Berichte 2188.
16. Internationaler Kongress – Elektronik im Fahrzeug, 16./17.10.2013, Baden-Baden.
VDI Verlag, 2013,
Pp. 651–661.
We introduce a generic concept for environment modeling with artiﬁcial potential ﬁelds and its utilization for a temporary vehicle control. This approach is known in robotics and is already used for autonomous robot control successfully. However, the requirements differ highly in a vehicle environment considering relative velocities, driving dynamics and path restrictions. Nevertheless, artiﬁcial potential ﬁelds exhibit some advantages in the automotive context such as the opportunity to model the environment generically across multiple scenarios, including both lateral and longitudinal aspects in an elegant way. Road edges and vehicles are modeled by potential hills. Thus, the potential ﬁeld can be interpreted as a risk map. Therefore, the driving task simpliﬁes to staying in low potential areas. Since the gradient of a ﬁeld is directing towards these areas, it can be utilized for vehicle control. Here, we present artiﬁcial potential models for the road and dynamic objects and show a gradient based automated control. This has been tested in a simulation and will be implemented in a vehicle.

Martin Wengenmayr.
“Molekulardynamiksimulation mit IBIsCO”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Aug. 2013.
IBIsCO [1] ist ein Programmpaket für die Molekulardynamiksimulation vergröberter Systeme. Es enthält implementierte Werkzeuge zur Entwicklung effektiver Wechselwirkungspotentiale zwischen den vergröberten Wechselwirkungseinheiten über die iterative Boltzmann-Inversion. Es wird ein Arbeitsablauf für die gewöhnlichen Molekulardynamiksimulationsmethoden von IBIsCO entwickelt. Dazu werden atomistische Simulationen mit Isopren und Polyisopren durchgeführt. Die erhaltene Struktur wird auf das vergröberte Modell übertragen und in Form von Verteilungsfuntionen der Bindungslängen, der Bindungswinkel und der radialen Verteilungsfunktionen analysiert. Sie bilden die Zielfunktionen für die iterative Boltzmann-Inversion, die mit IBIsCO durchgeführt wird. Die erhaltene Struktur wird analysiert und diskutiert. Ziel der Arbeit ist es, anhand der mit IBIsCO gesammelten Erfahrungen eine Entscheidungsgrundlage für die Nutzung des Programmes im Projekt Zwillingspolymerisation zu schaffen. Der neuartige Prozess der Zwillingspolymerisation soll mit einem vergröberten Modell simuliert werden, um die Strukturbildung auf der Nanometer-Skala zu analysieren.

Martin Winter.
“Image Alignment”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Aug. 2013.
Aligning two images is a hard optimization problem. We will abstract it to a point correspondence problem and use a modiﬁed extremal optimization algorithm as a high performance stochastic optimization method to ﬁnd the global minimum of a adequate deﬁned cost function. We will introduce new concepts of ﬁtness and closeness and determine values for the free parameters to maximize the success rate of the algorithm.

Frank Boldt, Karl Heinz Hoffmann, Peter Salamon, and Ronnie Kosloff.
“Time-optimal processes for interacting spin systems”.
In: Europhys. Lett. 99 (2012), pp. 40002–1–5.
doi: 10.1209/0295-5079/99/40002.

Karl Heinz Hoffmann, Christopher Essex, and Janett Prehl.
“A uniﬁed approach to resolving the entropy production paradox”.
In: J. Non-Equilib. Thermodyn. 37.4 (2012), pp. 393–412.
doi: 10.1515/jnetdy-2012-0008.
Bridging the regime between fully irreversible and fully reversible dynamics as represented by the two paradigmatic evolution equations for diffusion and wave propagation became possible by the use of fractional diffusion equations based on time- or space-fractional differential operators. These bridges are each characterized by a one-parameter family of distribution functions. In both cases one encounters a counter-intuitive behavior: the closer one gets to the reversible case, the larger the entropy production becomes. This feature is known as the entropy production paradox, and could be partly resolved for the time-fractional case by using the distribution mean as a way to characterize the internal quickness of the process, while for the space-fractional case a special location parameter was used. Here we are able to present a uniﬁed approach based on the distribution modes as the appropriate measure for the internal quickness of the processes.

Marwan S. Mousa, Andreas Fischer, and Khalil O. Mussa.
“Metallic and Composite Micropoint Cathodes: Aging Effect & Electronic and Spatial Characteristics”.
In: The Jordanian Journal of Physics 5.1 (2012), pp. 21–26.
Composite micro-emitters consisting of a tungsten core coated with different dielectric materials were prepared. Various properties of these emitters were measured including the current-voltage (IV) characteristics and spatial current distributions. We compared coated and uncoated tips and determined differences between both types. It could be proven that coated emitters are superior to uncoated ones in terms of the current stability and the emission current obtained for the same applied voltages. After these samples have been stored under atmospheric conditions for a period of 10 to 20 years from the ﬁrst time being characterized, they were tested again. The IV characteristics and spatial current distributions in addition to stability measurements were recorded. Various similarities as well as some differences compared to the initial characterization have been found. It is interesting to note that after one and a half decades these composite emitters are still functioning effectively without being subjected to ﬁeld desorption processes. The dielectric layers built on the tungsten cores were still in shape and stable. Some theoretical analysis of the tip properties and their change during storage time is included. Particular attention is paid to the deviations from the ideal Fowler-Nordheim (FN) behavior as well as the related slope and intercept correction factors.

Khalil O. Mussa, Andreas Fischer, and Marwan S. Mousa.
“Characterizing a new composite material: Effect of NaOH coating of variable thickness on the properties of a tungsten microemitter”.
In: The Jordanian Journal of Physics 5.1 (2012), pp. 27–31.

Janett Prehl, Christopher Essex, and Karl Heinz Hoffmann.
“Tsallis Relative Entropy and Anomalous Diffusion”.
In: Entropy 14 (2012). open access, pp. 701–716.
doi: 10.3390/e1404701.

Peter Salamon, Karl Heinz Hoffmann, and Anatoly Tsirlin.
“Optimal control in a quantum cooling problem”.
In: Appl. Math. Lett. 25.10 (2012), pp. 1263–1266.
doi: 10.1016/j.aml.2011.11.020.
The optimal control for cooling a quantum harmonic oscillator by controlling its frequency is considered. It is shown that this singular problem may be transformed with the proper choice of coordinates to an equivalent problem which is no longer singular. The coordinates used are sufficiently simple that a graphical solution is possible and eliminates the need to use a Weierstrass-like approach to show optimality. The optimal control of this problem is of signiﬁcance in connection with cooling physical systems to low temperatures. It is also mathematically signiﬁcant in showing the power and limitations of coordinate transformations for attacking apparently singular problems.

Anne-Lene Sax.
“Entwurf und Realisierung eines Neuronalen Netzes zur Vorhersage von Nutzereingaben”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Aug. 2012.
The bachelor thesis focuses on the development of an artiﬁcial Neural Network, which makes predictions of letter-inputs entered by users. Basis of the Neural Network is a simple feed-forward model consisting of two layers, one Input- and one Output-layer. The Network adjusts the connection weights between Input- and Output-Units using the basic Hebb-learning rule with dependence on patterns in the letter-inputs. For the prediction of the proximate letter the previous ten inputs were regarded. In total the Network was tested on the basis of inputs of 20 subjects. To determine a potential effect of the letter arrangement on the keyboard, three distinct letter combinations ”q w e”, ”c z m” and ”a d l” were tested. For each letter combination respectively two different games took place: one with real-time feedback and the other without real-time feedback of the prediction performance. Hence each subject was tested within six different conditions with each condition consisting of 500 inputs. Using the proportion of right predictions to the total number of predictions as performance value, the total mean performance amounts 45,568%. There were no effects found for the letter arrangement and feedback conditions. Further analysis particularly refer to the optimization of the prediction power, especially by gradually extending the number of Network layers.

Kim Schmidt.
“Analyse mehrdimensionaler Zeitreihen eines Fahrsimulators”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Sept. 2012.
This master thesis is about the analysis of lane change in car traffic. The basis for this is data generated by a study from chair of Cognitive and Engineering Psychology of Chemnitz University of Technology. The data was divided into the groups experience, velocity of perceptation, carefulness, safety, sensation seeking, results of an intelligenz test and gender of the drivers and into groups with different initial knowledge of the driving simulator. The lane changes of these groups were analysed in terms of lateral position on the street, changes in velocity, behavior of using the indicator, development of distance to drivers ahead and heading behavior.

Benedikt Willberg.
“Abstandsmesssensoren bei Adaptive Cruise Control (ACC)”.
in German.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Dec. 2012.
Die vorliegende Arbeit bietet einen Überblick über die beiden verfügbaren Sensortechniken bei der Abstandsmessung im Adaptive Cruise Control (ACC), einem Fahrassistenzsystem, das die Fahrgeschwindigkeit eines Kraftfahrzeugs automatisch an den vorausfahrenden Verkehr anpasst. Der Radarsensor, der elektromagnetische Wellen im Millimeterwellen-Bereich einsetzt, bietet eine direkte Messung der Relativgeschwindigkeit, hat aber Schwächen bei der lateralen Auﬂ̈osung. Der Lidarsensor, der im Ultraviolett- bis Infrarot-Bereich operiert, hat eine gute laterale Auﬂ̈osung, ermittelt die Relativgeschwindigkeit aber nur indirekt und ist bei Nebel und Sprühwasser unzuverlässig. Wegen der überlegenen Witterungsbeständigkeit ist der Radarsensor trotz des höheren Preises noch weiter verbreitet, der Lidarsensor hat aber durch technologische Verbesserungen bei der Geschwindigkeitsmessung aufgeholt. Für die Lidar-Technik ergibt sich das Potenzial zus̈atzlicher Fahrassistenzanwendungen aufgrund der sensorspeziﬁschen Realisierbarkeit von Sichtweitenmessung, Nebelerkennung und Tag/Nacht-Erkennung. Beim aktuellen Technologietrend der Sensorfusion werden Abstandsmesssensoren wie Radar und Lidar entweder mit Sensoren desselben Prinzips oder mit zus̈atzlichen Sensoren wie Videoeinheiten kombiniert. Dadurch können Schwächen wie die mangelhafte laterale Auﬂ̈osung des Radarsensors ausgeglichen, die Leistungsfähigkeit von ACC erhöht und neue Anwendungsbereiche wie die automatische Querführung des Fahrzeugserschlossen werden.

Bjarne Andresen, Karl Heinz Hoffmann, James Nulton, Anatoly Tsirlin, and Peter Salamon.
“Optimal control of the parametric oscillator”.
In: Eur. J. Phys. 32.3 (2011), pp. 827–843.
doi: 10.1088/0143-0807/32/3/018.

Lars Bonitz.
“Anomalous Diffusion in 3D Fractal Structures”.
Master Thesis. Chemnitz: Technische Universität Chemnitz, Dec. 2011.
In this thesis we will take an in depth look on the Dasgupta algorithm. We show restrictions implied with this method and ways to overcome them. Furthermore, we are going to extend this algorithm to simulate three dimensional fractals as well. Additionally, we will investigate the side effects that come along with this stereoscopic approach. To simulate diffusion within the fractals of our generating algorithm we compare the random walk method with the master equation approach and decide which of them ﬁts better into our ﬁnal program. Lastly we turn our attention to the runtimes of the resulting program. We will discover on which parts of the code most computation time is spent and try to shorten the duration of each execution with different approaches.

Andreas Fischer, Karl Heinz Hoffmann, and J. Christian Schön.
“Competitive trapping in complex state spaces”.
In: J. Phys. A: Math. Gen. 44.7 (2011), pp. 1–15.
doi: 10.1088/1751-8113/44/7/075101.
In complex state space dynamics at ﬁnite time scales, the trapping in certain regions of state space is of great importance, e.g. in the ﬁeld of protein folding or in the application of stochastic global optimization algorithms. Here, we analyze the inﬂuence of the density of states on the features of the trapping process. In particular, we compare the trapping power of a valley with a power-law density of states to one with an exponentially growing density of states. The outcome of this competition crucially depends on the annealing speed and shows that the clear difference between these two paradigmatic densities of states observed at very slow (near-equilibrium) annealing is lost for fast non-equilibrium processes, and that the outcome of the relaxation can strongly depend on the time scale of the process and subtle features of the density of states.

Karl Heinz Hoffmann, Michael Hofmann, Jens Lang, Gudula Rünger, and Steffen Seeger.
“Accelerating Physical Simulations Using Graphics Processing Units”.
In: it 53.2 (2011), pp. 49–59.
doi: 10.1524/itit.2011.0625.
Graphics processors are used in many ﬁelds of applications that require high computational power. Especially in scientiﬁc computing, the programming of graphics processing units is an active ﬁeld of research. Because of their hardware characteristics, graphics processors are well-suited for regular parallelism, however the implementation of irregular problems requires more advanced strategies. In this article, the hardware architecture of graphics porcessors and different framewords for graphics processor programming, such as CAL, Brook+, CUDA and OpgenCL with their speciﬁc properties, are presented. Additionally, an overview of different physical applications that have been implemented successfully on graphics processors is given. The parallel implementation of a speciﬁc irregular physical application on graphics processors is presented in more detail. This application simulates anomalous diffusion in porous media using random walk on Random Sierpinski Carpets.

Karl Heinz Hoffmann and Peter Salamon.
“Accuracy of coarse grained Markovian dynamics”.
In: Physica A 390 (2011), pp. 3086–3094.
doi: 10.1016/j.physa.2011.04.027.
Markov chain models on a mesoscopic level are a widely used description for complex systems. They are based on the assumption that certain sets of microstates can be coarse grained as their internal dynamics is faster than the time scales considered in the modeling. Here we analyze quantitatively the errors made by using lumping techniques and present the ﬁrst rigorous proof for bounds on such errors. Our bounds express the deviations from a full microscopic description for all subsequent time steps in terms of the deviations in the ﬁrst time step.

Karl Heinz Hoffmann, Peter Salamon, Yair Rezek, and Ronnie Kosloff.
“Time-optimal controls for frictionless cooling in harmonic traps”.
In: Europhys. Lett. 96.6 (2011), pp. 60015–1–6.
doi: 10.1209/0295-5075/96/60015.
Fast adiabatic cooling procedures have important implications for the attainability of absolute zero. While traditionally adiabatically cooling a system is associated with slow thermal processes, for the parametric quantum harmonic oscillator fast frictionless processes are known, which transfer a system from an initial thermal equilibrium at one temperature into thermal equilibrium at another temperature. This makes such systems special tools in analyzing the bounds on fast cooling procedures. Previous discussions of those systems used frictionless cooling assuming real frequencies of the oscillator. Using a control with imaginary frequencies (repulsive potential) revises previous implications for the possible operation of a quantum refrigerator. Here we discuss these requisite revisions in the context of the third law of thermodynamics. In addition to minimum time controls, which are always of the bang-bang form, fast frictionless processes with a continuous variation of the frequency have been presented previously in the literature. Such continuous variation controls have been experimentally veriﬁed by cooling a Bose-Einstein condensate, while minimum time controls still await veriﬁcation. As some implementations may indeed not be able to implement the instantaneous jumps in frequency required by bang-bang controls, constraining the rate of change in the frequency calls for ramped bang-bang solutions. We present such solutions and compare their performance to the continuous controls used in the experiment.

Thomas Streubel.
“Artiﬁcial Potential Fields as a Concept of Environment Modeling for Forward Directed Driver Assistance Systems”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Oct. 2011.
This thesis has been created at the Adam Opel AG in the department Active Safety. It deals with an artiﬁcial potential ﬁeld in the automotive ﬁeld. First already established approaches are introduced. Further, road and obstacle models are developed to create a potential ﬁeld and methods are generated to utilize the gradient. The results are reasonable driveways examined in multiple simulations as well as a pathway in a real driving scene. Hereby, the models are compared and their parameters optimized. Finally, a more realistic simulation was performed by realizing desired driving behavior based on the artiﬁcial potential approach. Overall, the conclusion is that a potential ﬁeld is a reasonable concept to create a representation of the vehicle’s environment leading to a beneﬁt in terms of the gradient pointing away from obstacles. With certain models and corresponding gradient based methods driveways are realizable. This beneﬁt from the potential ﬁeld can be understood according to the famous quote: ”The whole is more than the sum of its parts.” (Aristotle)

Anatoly M. Tsirlin, Peter Salamon, and Karl Heinz Hoffmann.
“Change of state variables in the problems of parametric control of oscillators”.
In: Avtomat. i Telemekh. 8 (2011). Translated in english [188], pp. 53–64.
Решены задачи оптимального параметрического управления одиночным осциллятором и ансамблем квантовых осцилляторов. На их примере продемонстрированы возможности метода перехода к новым переменным пространства состояний управляемой системы.

Anatoly M. Tsirlin, Peter Salamon, and Karl Heinz Hoffmann.
“Change of State Variables in the Problems of Parametric Control of Oscillators”.
In: Automat. Remote Control 72.8 (2011), pp. 1627–1638.
doi: 10.1134/S0005117911080030.
The problems of optimal parametric control of a single oscillator and an assembly of quantum oscillators were solved and used by way of example to demonstrate the potentialities of the method of transition to the new variables of the state space of the controlled system.

Do Hoang Ngoc Anh.
“Anomalous diffusion and Random walks on random fractals”.
URL: http://nbn-resolving.d/urn:nbn:de:bsz:ch1-201000151.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Feb. 2010.

Karen Friedrich, Steffen Wilbrandt, Olaf Stenzel, Norbert Kaiser, and Karl Heinz Hoffmann.
“Computational manufacturing of optical interference coatings: method, simulation results, and comparison with experiment”.
In: Appl. Opt. 49.16 (2010), pp. 3150–3162.
doi: 10.1364/AO.49.003150.
Virtual depostion runs have been performed to estimate the procuction yield of selected oxide optical interference coatings when plasma ion-assisted deposition with an advanced plasma source is applied. Therby, depostion of each layer can be terminated either by broadband optical monitoring or quertz crystal monitoring. Numerous deposition runs of single-layer coatings have been performed to investigate the reproducibility of coating properties and to quantifydeposition errors for the simulation. Variations of the following parameters are considered in the simulation: refractive index, extinction coefficient, and ﬁlm thickness. The refractive index and the extinction coefficient are simulated in terms of the oscillator model. The parameters are varied using an apodized normal distribution with known mean value and standard strategy. Several depositon runs of the selected oxide interference coatings have been performed to verify the simulation results by experimental data.

Karl Heinz Hoffmann, Michael Hofmann, Jens Lang, Gudula Rünger, and Steffen Seeger.
“Simulating anomalous diffusion on graphics processing units”.
In: Proc. of the 11th IEEE International Workshop on Parallel and Distributed Scientiﬁc and Engineering Computing (PDSEC-10).
own, 2010,
Pp. 1–8.
doi: 10.1109/IPDPSW.2010.5470767.
The computational power of modern graphics processing units (GPUs) has become an interesting alternative in high performance computing. The specialized hardware of GPUs delivers a high degree of parallelism and performance. Various applications in scientiﬁc computing have been implemented such that computationally intensive parts are executed on GPUs. In this article, we present a GPU implementation of an application for the simulation of diffusion processes using random fractal structures. It is shown how the irregular computational structure that is inherent to the application can be implemented efficiently in the regular computing environment of a GPU. Performance results are shown to demonstrate the beneﬁts of the chosen implementation approaches.

Janett Prehl.
“Diffusion on fractals and space-fractional diffusion equations”.
URL: http://archive.tu-chemnitz.de/pub/2010/0106.
PhD Thesis. Chemnitz, Germany: Technische Universität Chemnitz, July 2010.
The aim of this thesis is the examination of sub- and superdiffusive processes in fractal structures. The focus of the work concentrates on two separate approaches that are chosen and varied according to the corresponding regime. Thus, we obtain new insights about the underlying mechanisms and a more appropriate way of description for both regimes. In the ﬁrst part subdiffusion is considered, which plays a crucial role for transport processes, as in living tissues. First, we model the fractal state space via ﬁnite Sierpinski carpets with absorbing boundary conditions and we solve the master equation to compute the time development of the probability distribution. To characterize the diffusion on regular as well as random carpets we determine the longest decay time of the probability distribution, the mean exit time and the Random walk dimension. Thus, we can verify the inﬂuence of random structures on the diffusive dynamics. In the second part of this thesis superdiffusive processes are studied by means of the diffusion equation. Its second order space derivative is extended to fractional order, which represents the fractal properties of the surrounding media. The resulting space-fractional diffusion equations span a linking regime from the irreversible diffusion equation to the reversible (half) wave equation. The corresponding solutions are analyzed by different entropies, as the Shannon, Tsallis or Rényi entropies and their entropy production rates, which are natural measures of irreversibility. We ﬁnd an entropy production paradox, i.e. an unexpected increase of the entropy production rate by decreasing irreversibility of the processes. Due to an appropriate rescaling of the entropy we are able to resolve the paradox.

Janett Prehl, Christopher Essex, and Karl Heinz Hoffmann.
“The superdiffusion entropy production paradox in the space-fractional case for extended entropies”.
In: Physica A 389.2 (2010), pp. 215–224.
doi: 10.1016/j.physa.2009.09.009.
Contrary to intuition, entropy production rates grow as reversible, wave-like behavior is approached. This paradox was discovered in time-fractional diffusion equations. It was found to persist for extended entropies and for space-fractional diffusion as well. This paper completes the possibilities by showing that the paradox persists for Tsallis and Rényi entropies in the space-fractional case. Complications arising due to the heavy tail solutions of space-fractional diffusion equations are discussed in detail.

Thomas Schönfelder.
“Molecular Dynamics Simulations with Reactive Force Fields Applied to Polymerization Processes from Monomers”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Apr. 2010.
This thesis is intended to review a twin polymerization process using a simulation based on a reactive force ﬁeld. The force ﬁeld itself is trained by results obtained from quantum chemical calculations. A goal of the usage of a reactive force ﬁeld is to allow simulations with far more molecules than pure quantum chemical approaches could handle. From such simulations more insight in the structure formation process is expected and further model simpliﬁcations should be made in order to allow simulations of large domains. The ﬁrst chapter gives an overview of quantum chemical simulation approaches, force ﬁeld based molecular dynamics methods and the basic ideas of simpliﬁed methods. In the next chapter the chemical model is introduced together with the applied reactive force ﬁeld. The third chapter is devoted to the reactions of the twin polymerization process incorporated in the training process. Finally chapter four presents the force ﬁeld training results and the force ﬁeld applications in simulations. Furthermore, starting points for simpliﬁed models are given based on the obtained results.

Bettina Dietzel.
“Entwicklung eines Algorithmus zur Umrechnung der mit Parsum Inline-Partikelsonden gemessenen Sehnenlängenverteilungen in Durchmesserverteilungen”.
in German.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Sept. 2009.

Karl Heinz Hoffmann and Peter Salamon.
“Bounding the lumping error in Markov chain dynamics”.
In: Appl. Math. Lett. 22 (2009), pp. 1471–1475.
doi: 10.1016/j.aml.2009.03.016.
Forming lumped states in a Markov chain is a very useful device leading to a coarser level of description. The Markov chain on these lumped states is often taken as an approximation for the time evolution of the unlumped chain. In the present work we derive a bound on the error in this approximation.

Jörg L̈assig and Karl Heinz Hoffmann.
“On the Structure of a Best Possible Crossover Selection Strategy in Genetic Algorithms”.
In: Research and Development in Intelligent Systems XXVI.
Ed. by M. Bramer, R. Ellis, and M. Petridis.
1.
Springer. own, 2009,
Pp. 263–276.
doi: 10.1007/978-1-84882-983-1_19.
The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover to ﬁnd a solution with high ﬁtnee for a given optimization problem. Many different schemes have been described in the literature as possible strategies for this task but so far comparisons have been predominantly empirical. It is shown that if one wishes to maximize any linear function of the ﬁnal state probabilities, e.g. the ﬁtness of the best individual in the ﬁnal population of the algorithm, then a best probability distribution for selecting an individual in each generation is a rectangular distribution over the individuals sorted in descending sequence by their ﬁtness values. This means uniform probabilities have to be assigned to a group of the best individuals of the population but probabilities equal to zero to individuals from the current population can be chosen independently for each iteration and each individual. This result is then generalized also to typical practically applied performance measures, such as maximizing the expected ﬁtness value of the best individual seen in any generation.

Jörg L̈assig and Karl Heinz Hoffmann.
“Threshold-selecting strategy for best possible ground state detection with genetic algorithms”.
In: Phys. Rev. E 79.4 (2009), pp. 046702–1–8.
doi: 10.1103/PhysRevE.79.046702.

George Alexandru Nemnes and Karl Heinz Hoffmann.
“Spin-box algorithm for low temperature dynamics of short range disordered Ising spin systems”.
In: Comp. Phys. Comm. 180.7 (2009), pp. 1098–1103.
doi: 10.1016/j.cpc.2008.12.038.
An approximate parallel approach was developed to describe efficiently the low temperature dynamics in short range Ising spin systems, based on the dynamically relevant sequence technique. It relates the low temperature dynamics to the structural properties of the state space of spin glasses and disordered ferromagnets, which has been proved to give accurate results for low temperatures. Large samples can be handled, which allows the analysis of domain formation and the discussion of the growth laws. The results are consistent with existing numerical and experimental data.

Yair Rezek, Peter Salamon, Karl Heinz Hoffmann, and Ronnie Kosloff.
“The quantum refrigerator: The quest for absolute zero”.
In: Europhys. Lett. 85 (2009), pp. 30008–1–5.
doi: 10.1209/0295-5057/85/30008.

Peter Salamon, Karl Heinz Hoffmann, Yair Rezek, and Ronnie Kosloff.
“Maximum work in minimum time from a conservative quantum system”.
In: Phys. Chem. Chem. Phys. 11 (2009), pp. 1027–1032.
doi: 10.1039/B816102J.
This paper considers the problem of obtaining maximum work from a conservative quantum system corresponding to a given change in an external parameter in the Hamiltonian. The example we present is a non-interacting collection of harmonic oscillators with a shared frequency o which changes from a given initial to a given ﬁnal value. The example is interesting for its role in experiments at ultra-low temperatures and for probing ﬁnite-time versions of the third law of thermodynamics. It is also the simplest system displaying quantum friction, which represents loss mechanisms in any reversible prelude to a thermal process. The example leads to a new type of availability. It is also the ﬁrst example of a minimum time for transitions between thermal states of a thermodynamic system.

Sabrina Schmiß.
“Untersuchung von Störfaktoren auf den Verkehrsﬂuss mittels zellulärer Automaten”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, June 2009.

Karsten Schwalbe.
“Funktionsorientierte Toleranzanalyse in der Motorenentwicklung”.
in German.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, July 2009.
In dieser Arbeit wird das Verfahren Funktionsorientierte Toleranzanalyse behandelt. Toleranzbehaftete Größen werden als Zufallszahlen eingeführt, die bestimmten Anforderungen (Einhalten von Toleranzgrenzen) gen̈ugen m̈ussen. Anschließend werden die Koordinatensystemketten eingeführt, da mit ihrer Hilfe die räumlichen Abhängigkeiten von Toleranzen dargestellt werden können. Auf diesen M̈oglichkeiten zur Modellierung von Toleranzen aufbauend werden die 3 Bestandteile der Toleranzanalyse - Sensitivitäts-, Statistische und Arithmetische Analyse - vorgestellt. Die Sensitivitätsanalyse beschäftigt sich mit der Linearisierung von Funktionen und zieht daraus Schlussfolgerungen für den Einﬂuss der Parameter auf die abhängigen Größen. Die Statistische Analyse erlaubt es mit Hilfe von Monte-Carlo-Simulationen Aussagen über die Verteilung der abhängigen Größen zu treffen. Schließlich beschäftigt sich die Arithmetische Analyse mit der Ermittlung von Minimal und Maximalwerten dieser Größen. Auf die dafür notwendigen Optimierungsalgorithmen wird kurz eingegangen. Besondere Beachtung bekommt die Berechnung von Prognosewerten, da die Dauer der Monte-Carlo-Simulation bzw. der exakten Optimierung für Toleranzprobleme sehr groß sein kann. Grundlage der Prognosen ist das lineare Modell aus den Sensitivitätsbetrachtungen. Im Anschluss erfolgt die Toleranzanalyse für ein technisches Beispiel. Dabei zeigt sich eine gute Übereinstimmung von Prognosewerten mit den Berechnungsergebnissen.

Steffen Seeger, Karl Heinz Hoffmann, and Christopher Essex.
“Random Walks on random Koch curves”.
In: J. Phys. A: Math. Gen. 42.22 (2009), pp. 225002–1–11.
doi: 10.1088/1751-8113/42/22/225002.
Diffusion processes in porous materials are often modeled as random walks on fractals. In order to capture the randomness of the materials random fractals are employed, which no longer show the deterministic self-similarity of regular fractals. Finding a continuum differential equation describing the diffusion on such fractals has been a long-standing goal, and we address the question of whether the concepts developed for regular fractals are still applicable. We use the random Koch curve as a convenient example as it provides certain technical advantages by its separation of time and space features. While some of the concepts developed for regular fractals can be used unaltered, others have to be modiﬁed. Based on the concept of ﬁbers, we introduce ensemble-averaged density functions which produce a differentiable estimate of probability explicitly and compare it to random walk data.

Thomas Streubel.
“Realisierung einer aktiven, präventiven Bremsleuchte für Personenkraftwagen”.
in German.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, June 2009.
This bachelor thesis has been created at Volkswagen AG - group research in the department driver assistance & integrated safety. The issue is about realizing an active and preventive breaklight. First some fundamentals are observed concerning car accident statistics and in further detail the reaction time. The current statutory basis are also examined to determine if the integration in vehicles is conformable to law. The potentials of such a system were analyzed and different functionalities stated. A mathmatical simulation is performed to investigate the issue of driving in a convoy while one car applys an emergency break. A traffic jam situation is also simulated thru modifying an existing java applet provided by the TU Dresden. Sensor systems are introduced that are allready implemented and are used for the detection of vehicles ahead and behind. Finally an algorithm has been developed as warning system for the following vehicle when approaching at a high rate while the equipped car is about to break.

Andreas Fischer.
“Modelling Complex Systems: Tree Structures”.
URL: http://archiv.tu-chemnitz.de/pub/2008/0012.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Jan. 2008.
The state space is a very important and fundamental concept for the treatment of complex systems. All the system’s properties can be understood by means of its structure. Due to the gigantic extent of a real system’s state space, a coarse grained approach is inevitable for the analysis. In this work, based on the well established model of hierarchical trees, particular aspects of complex systems have been studied, while at the same time several extensions to the model have been made. In the ﬁrst part of this research work the features of the probability ﬂow are treated in detail at a single saddle point in the energy landscape. Inﬂuences of various parameters like energetic depth, density of states and connectivity are studied isolated and in their interaction. In the second part a whole system showing complex behavior is being considered, especially its energy exchange with the surroundings. It can be demonstrated that the hierarchical relaxation behavior observed in other realizations of complex systems is intrinsically covered by the tree model. Beside energy landscape based systems turbulent diffusion processes possess hierarchical structures, too. In the third part the tree structure has been used to model a turbulent superdiffusion process. The diffusion behavior observed there has been compared with four well known diffusion equation approaches. The results show that only one of the discussed continuum diffusion equations can model the turbulent transport based on the tree model in acceptable fashion.

Andreas Fischer, Karl Heinz Hoffmann, and Paolo Sibani.
“Intermittent relaxation in hierarchical energy landscapes”.
In: Phys. Rev. E 77.4 (2008), pp. 041120/1–5.
doi: 10.1103/PhysRevE.77.041120.
We numerically simulate a thermalization process in an energy landscape with hierarchically organized metastable states. The initial conﬁguration is chosen to have a large energy excess relative to the thermal equilibrium value at the running temperature. We show that the initial energy surplus is dissipated in a series of intermittent bursts, or quakes, whose rate decreases as the inverse of the age of the system. In addition, one observes energy ﬂuctuations with a zero-centered Gaussian distribution. These pertain to the pseudoequilibrium dynamics within a single metastable state and do not contribute to the energy dissipation. The derivative of the thermal energy with respect to the logarithm of time is asymptotically constant and comprises a temperature-independent part and a part with an Arrhenius temperature dependence. The ﬁndings closely mirror recent numerical simulation results obtained for microscopic glassy models. For these models, record-sized energy ﬂuctuations have been claimed to trigger intermittent events during low-temperature thermalization. In the present model record-sized ﬂuctuations are by construction needed to trigger changes from one metastable state to another. This property thus suffices to explain the statistical property of intermittent energy ﬂow in complex metastable systems.

Robert Grone, Karl Heinz Hoffmann, and Peter Salamon.
“An interlacing theorem for reversible Markov chains”.
In: J. Phys. A: Math. Gen. 41 (2008), pp. 1–7.
doi: 10.1088/1751-8113/41/21/212002.
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix.

René Haber.
“Numerical methods for density of states calculations”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, July 2008.
The parQ method, up to now only capable of calculating the density of states in the canonical ensemble, is extended to the grand canonical ensemble and compared to the Wang-Landau algorithm, a local-update ﬂat-histogram method. Both algorithms have been implemented so that the performance and the respective beneﬁts with increasing simulation time can be determined and compared.

Karl Heinz Hoffmann.
“An introduction to endoreversible thermodynamics”.
In: AAPP - Physical, Mathematical, and Natural Sciences 86.1 (2008), pp. 1–19.
doi: 10.1478/C1S0801011.
Reversible thermodynamic processes are convenient abstractions of real processes, which are always irreversible. Approaching the reversible regime means to become more and more quasistatic, letting behind processes which achieve any kind of ﬁnite transformation rate for the quantities studied. On the other hand studying processes with ﬁnite transformation rates means to deal with irreversibilities and in many cases these irreversibilities must be included in a realistic description of such processes. Endoreversible thermodynamics is a non-equilibrium approach in this direction by viewing a system as a network or internally reversible (endoreversible) subsystems exchanging energy in an irreversible fashion. This material provides an introduction to the subject.

Karl Heinz Hoffmann and Janett Prehl.
“Anomalous Transport in Disordered Fractals”.
In: Anomalous Transport - Foundations and Applications.
Ed. by R. Klages, G. Radons, and I. M. Sokolov.
1st ed.
Weinheim: Wiley-VCH, 2008.
Chap. 14, pp. 397–427.
This multi-author reference work provides a unique introduction to the currently emerging, highly interdisciplinary ﬁeld of those transport processes that cannot be described by using standard methods of statistical mechanics. It comprehensively summarizes topics ranging from mathematical foundations of anomalous dynamics to the most recent experiments in this ﬁeld. In so doing, this monograph extracts and emphasizes common principles and methods from many different disciplines while providing up-to-date coverage of this new ﬁeld of research, considering such diverse applications as plasma physics, glassy material, cell science, and socio-economic aspects. The book will be of interest to both theorists and experimentalists in nonlinear dynamics, statistical physics and stochastic processes. It also forms an ideal starting point for graduate students moving into this area. 18 chapters written by internationally recognized experts in this ﬁeld provide in-depth introductions to the following fundamental aspects of anomalous transport: Fractional calculus and stochastic theory; Dynamical systems and deterministic transport; Anomalous transport in disordered systems; Applications to complex systems and experimental results.

Jörg L̈assig, Karl Heinz Hoffmann, and Mihaela Enachescu.
“Threshold Selecting: Best Possible Probability Distribution for Crossover Selection in Genetic Algorithms”.
In: Genetic and Evolutionary Computation Conference.
own, July 2008.
doi: 10.1145/1388969.1389044.
The paper considers the problem of selecting individuals in the current population in genetic algorithms for crossover to ﬁnd a solution of high ﬁtness of a given combinatorial optimization problem. Many different schemes have been considered in literature as possible crossover selection strategies, such as windowing, exponential reduction, linear transformation or normalization and binary tournament selection. It is shown that if one wishes to maximize any linear function of the ﬁnal state probabilities, e.g. the ﬁtness of the best individual of the ﬁnal population of the algorithm, then the best probability distribution for selecting individuals in each generation is a rectangular distribution over the individuals sorted by their ﬁtness values. This means uniform probabilities have to be assigned to a group of the best individuals of the population but probabilities equal to zero to individuals with ﬁtness ranks higher than a ﬁxed cutoff, which is equal to a certain rank in the sorted ﬁtness vector. The considered strategy is called threshold selecting. The proof applies basic arguments of Markov chains and linear optimization and requires only a few assumptions on the underlying principles and hence applies to a large class of genetic algorithms.

George Alexandru Nemnes.
“Sampling procedures for low temperature dynamics on complex energy landscapes”.
PhD Thesis. Chemnitz: Technische Universität Chemnitz, May 2008.
The present work deals with relaxation dynamics on complex energy landscapes. The state space of a complex system possesses, as a hallmark, the multitude of local minima separated by higher states, called barrier states. This feature gives rise to a host of non-equilibrium phenomena. From case to case, for different complex systems, ranging from atomic clusters, spin glasses and proteins to neural networks or ﬁnancial markets, the key quantities like energy and temperature may have different meanings, though their functionality is the same. The numerical handling of relaxational dynamics in such complex systems, even for relatively small sizes, poses a tough challenge if the entire state space is to be considered. Here, state space sampling procedures are introduced that provide an accurate enough description for the low temperature dynamics, using small subsets from the original state space. As test cases, short range Ising spin systems were considered. The samples - depending on the way they are constructed - provide either lower bounds for the largest relaxation timescales in a quasi-ergodic component of the state space or the isothermal relaxation of the mean energy, like in the proposed DRS method. Upon the latter procedure, a parallel heuristic is built which gives the possibility of handling large samples. The collected structural data provides information of the state space topology in systems with different levels of frustration, like disordered ferromagnets and spin glasses. It provides insights into the focusing/anti-focusing types of landscapes, which give rise to different ground state accessibilities. For the large samples, the domain formation and growth has been analysed and compared with existing experimental and numerical data in literature. The algorithms proposed here become more and more accurate as the temperature is decreased and therefore they can provide an alternative to the classical Monte Carlo approach for this temperature range.

George Alexandru Nemnes and Karl Heinz Hoffmann.
“Dynamically relevant structural properties of short-range spin glasses and disordered ferromagnets”.
In: Phys. Rev. B 77 (2008), p. 172410.
Structural properties relevant for the low-temperature dynamics of short-range Ising systems are comparatively analyzed for spin glasses and disordered ferromagnets. The key elements, disorder and frustration, induce different topologies in the state space, going from funnel-like landscapes in the case of disordered ferromagnets to trapping landscapes for spin glasses. An efficient tool, dynamically relevant sequence, is introduced, which directly extracts the low-temperature dynamics.

Janett Prehl, Karl Heinz Hoffmann, Michael Hofmann, Gudula Rünger, and Sujata Tarafdar.
“Anomalous diffusion in porous media”.
In: Thermal Nonequilibrium - Lecture Notes of the 8th International Meeting on Thermodiffusion.
Ed. by S. Wiegand, W. Köhler, and J. K. G. Dhont.
Vol. 3.
Schriftenreihe des Forschungszentrums J̈ulich.
J̈ulich: Forschungszentrum J̈ulich GmbH, 2008,
Pp. 243–248.

Supti Sadhukhan, Janett Prehl, Peter Blaudeck, Karl Heinz Hoffmann, Tapati Dutta, and Sujata Tarafdar.
“Desiccation of a clay ﬁlm: Cracking versus peeling”.
In: Eur. Phys. J. E 27.4 (2008), pp. 391–295.
doi: 10.1140/epje/i2008-10401-9.

Katharina Wagner.
“A graphic based interface to Endoreversible Thermodynamics”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Aug. 2008.
The object of this thesis is a graphic based interface to endoreversible thermodynamics. It is meant to enable the user to visually create endoreversible systems and add the properties of the system by choosing features from a list and in form of equations. Then an equation system is built and the power output and efficiency of the endoreversible system is calculated and plotted. To illustrate the functions of the interface, some examples of heat and chemical engines are discussed.

Do Hoang Ngoc Anh, Peter Blaudeck, Karl Heinz Hoffmann, Janett Prehl, and Sujata Tarafdar.
“Anomalous diffusion on random fractal composites”.
In: J. Phys. A: Math. Gen. 40.38 (2007), pp. 11453–11465.
doi: 10.1088/1751-8113/40/38/002.
Stochastic fractals, generated from combinations of deterministic fractals, have the advantage of being tractable to some extent, but also being closer to real materials, since they are partially disordered. In the present work, we focus our attention on the remarkable nonlinear mixing behavior exhibited by fractals generated as random combinations of two different Sierpinski carpet generators. When patterns with different anomalous diffusion exponents and the same or different fractal dimensions are combined together, the effective diffusion exponent cannot in general be expressed as a linear weighted average of the diffusion exponents of the constituents. The effective exponent may show a maximum or minimum for certain compositions. An explanation of this interesting phenomenon is offered on the basis of details of the carpet generator, particularly on the number and position of ‘connection points’, which determine the connectivity of the ‘fractal composite’.

Andreas Fischer, Steffen Seeger, Karl Heinz Hoffmann, Chistopher Essex, and Matt Davison.
“Modeling anomalous superdiffusion”.
In: J. Phys. A: Math. Gen. 40.38 (2007), pp. 11441–11452.
doi: 10.1088/1751-8113/40/38/001.
Continuous models for anomalous diffusion have previously been tested in the subdiffusive case by making comparisons to diffusion on a Sierpinski gasket. This paper extends this discussion to the superdiffusive case by comparing performance to diffusion on a tree model. Although there is reasonable agreement within limited regimes for all four models, one model, due to Compte and Jou, stands out as being consistently sound over all regimes studied.

Karl Heinz Hoffmann.
“Quantifying Dissipation”.
In: Comm. SIMAI Cong. 2 (2007), pp. 1–12.
doi: 10.1685/CSC06171.
Reversible thermodynamic processes are convenient abstractions of real processes, which are always irreversible. Approaching the reversible regime means to become more and more quasistatic, letting behind processes which achieve any kind of ﬁnite transformation rate for the quantities studied. On the other hand studying processes with ﬁnite transformation rates means to deal with irreversibilities and in many cases these irreversibilities must be included in a realistic description of such processes. There are various approaches how to not negelect ﬁnite times and rates while not being slain by the real worlds complexity. Endoreversible thermodynamics is a non-equilibrium approach in this direction by viewing a system as a network of internally reversible (endoreversible) subsystem exchanging energy in an irreversible fashion.

Karl Heinz Hoffmann, Beltran Rodriguez-Brito, Mya Breitbart, David Bangor, Florent Angly, Ben Felts, James Nulton, Forest Rohwer, and Peter Salamon.
“Power law rank-abundance models for marine phage communities”.
In: FEMS Mircobiol. Lett. 273 (2007), pp. 224–228.
doi: 10.1111/j.1574-6968.2007.00790.x.
Metagenomic analyses suggest that the rank-abundance curve for marine phage communities follows a power law distribution. A new type of power law dependence based on a simple model in which a modiﬁed version of Lotka-Volterra predator-prey dynamics is sampled uniformly in time is presented. Biologically, the model embodies a kill the winner hypothesis and a neutral evolution hypothesis. The model can match observed power law distributions and uses very few parameters that are readily identiﬁable and characterize phage ecosystems. The model makes new untested predictions: (1) it is unlikely that the most abundant phage genotype will be the same at different time points and (2) the long-term decay of isolated phage populations follows a power law.

Markus Schaller.
“Numerically Optimized Diabatic Distillation Columns”.
PhD Thesis. Chemnitz: Technische Universität Chemnitz, May 2007.
Im Gegensatz zur konventionellen adiabatischen Destillation erfolgt bei der diabatischen Destillation Ẅarmeaustausch nicht nur am Kondensator und Verdampfer, sondern auch innerhalb der Kolonne an den einzelnen Siebb̈oden, was die Entropieproduktion (=Exergieverlust) des Destillationsprozesses stark reduziert. In dieser Arbeit werden Modellsysteme zur diabatischen Destillation von idealen binären Gemischen mittels numerischer Optimierung untersucht. Das Ausgangsmodell beschränkt sich auf die Minimierung der Entropieproduktion verursacht durch Ẅarme- und Massentransport im Inneren der diabatischen Destillationskolonne. Im zweiten Modell wird das diabatische Modell um die Irreversibilität bedingt durch den Ẅarmeaustausch mit der Umgebung erweitert. Im dritten Modellsystem wird anstelle der bis dahin voneinander unabhängig geregelten Bodentemperaturen eine diabatische Implementierung mit seriellen Ẅarmetauschern untersucht, die nur mehr vier Kontrollvariablen besitzt und besonders zur praktischen Anwendung geeignet ist. Für alle diabatischen Modelle werden die minimale Entropieproduktion und optimalen Betriebsproﬁle numerisch ermittelt, und mit konventionellen Destillationskolonnen verglichen. Alle Ergebnisse zeigen eine deutlich Reduktion der Entropieproduktion für den diabatische Fall, besonders bei Kolonnen mit vielen B̈oden.

Ralph Schlosser.
“Diffusion on Fractals”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, July 2007.
Many real world phenomena and objects exhibit fractal structures, some at least on certain length scales. One such phenomenon, anomalous diffusion, can be studied from a fractal point of view. In this work, a computer program is developed to simulate anomalous diffusion on a class of fractal lattices – SIERPINSKI carpets – by employing the blind ant random walk approach. The program is used to calculate an important quantity in random walks: The random walk dimension $d w$ . Subsequently, the question is investigated whether the resulting value of $d w$ depends on the random walk origin $(x i 0, y i 0)$ within the SIERPINSKI carpet lattice, or not. To answer this questions, series of simulations are run with ﬁxed origins and randomly selected origins, respectively. An analysis of the results obtained and comparision of this works results to previous works suggests that there is in fact a strong dependence of $d w$ from the origin, at least for a certain number of simulation steps.

Robert Schulz.
“The Investigation of The parQ-Method for Continuous Systems”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Apr. 2007.
To analyze the thermodynamical quantities of canonical systems the parQ-method has been introduced [1]. After testing this method for spin glasses [1, 2], this paper veriﬁes that the parQ-method is also applicable to obtain the density of states of continuous systems, for example ﬂuids, with the periodic boundary condition. Speciﬁcally, the energy transitions of a random walk through state space are observed. Therefore, the necessary methods and system conﬁgurations are introduced and examined. Furthermore, several potential error sources are investigated. The resulting data is compared to [3] where the density of states of a Lennard-Jones ﬂuid is computed using the Wang-Landau scheme [4].

Janett Balg.
“Diffusion on Fractals”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Mar. 2006.

Michael Bauer.
Simulation diskreter Markov-Prozesse zweiter Stufe.
Bachelor Thesis.
09107 Chemnitz, Feb. 2006.
Simulationen von Markov-Prozessen erster Stufe sind in vielen Anwendungsbereichen bekannt, Erkenntnisse ̈uber die Eigenschaften von Prozessen zweiter Markov-Stufe sind jedoch rar. Wichtige Merkmale sollen durch die Simulation diskreter Markov-Prozesse zweiter Stufe herausgearbeitet werden. An erster Stelle steht dabei die Entwicklung eines einfachen Modells zur Simulation von Markov-Prozessen zweiter Stufe mittels eines Random Walkers, der über ein Ged̈achtnis verfügt. Das Modell bildet dabei zeit- und ortsdiskrete Prozesse ab und hält die M̈oglichkeit zur Simulation ̈außerer Kräfte offen. Im Weiteren geben Untersuchungen der zeitlichen Entwicklung der Ortsverteilung und des Entropieverlaufs an so simulierten Zufallswanderern Aufschluss über ̈Ahnlichkeiten und Unterschiede zu Markov-Prozessen erster Stufe. Dabei werden analytische Abschätzungen zur Bestätigung der simulierten Daten genutzt und das Langzeitverhalten der Prozesse untersucht und mit dem von Markov-Prozessen erster Stufe verglichen. Weiterhin wird die Abhängigkeit der Stärke des Ged̈achtnisses auf das Verhalten der Zufallswanderer genauer betrachtet.

Peter Blaudeck and Karl Heinz Hoffmann.
“Optimizing simulated annealing schedules for amorphous carbons”.
In: Parallel algorithms and cluster computing.
Ed. by K. H. Hoffmann and A. Meyer.
Berlin Heidelberg: Springer-Verlag, 2006,
P. 227.
doi: 10.1007/3-540-33541-2_12.
Annealing, carried out in simulation, has taken on an existence of its own as a tool to solve optimization problems of many kinds [1–3]. One of many important applications is to ﬁnd local minima for the potential energy of atomic structures, as in this paper, in particular structures of amorphous carbon at room temperature. Carbon is one of the most promising chemical elements for molecular structure design in nature. An inﬁnite richness of different structures with an incredibly wide variety of physical properties can be produced. Apart from the huge variety of organic substances, even the two crystalline inorganic modiﬁcations, graphite and diamond, show diametrically opposite physical properties. Amorphous carbon continues to attract researchers for both the fundamental understanding of the microstructure and stability of the material and the increasing interest in various applications as a high performance coating material as well as in electronic devices.

Peter Blaudeck, Steffen Seeger, Christian Schulzky, Karl Heinz Hoffmann, Tapati Dutta, and Sujata Tarafdar.
“The coastline and lake shores on a fractal island”.
In: J. Phys. A: Math. Gen. 39 (2006), pp. 1609–1618.
doi: 10.1088/0305-4470/39/7/006.
We compute the fractal dimensions of the ”hulls” or external boundary and the boundaries of the internal cavities in several deterministic as well as random fractal structures. Our conclusion is that the two fractal dimensions are in fact identical. The deterministic fractals we study are Sierpinski carpets (SC) in a two-dimensional space and the random fractals are percolation clusters at criticality. As an intermediate case, we present results on some randomized SC. In the random structures, statistics of the area and perimeters of all internal cavities or holes are taken and the fractal dimension of the hull borderline is computed. Two different deﬁnitions of the borderline are used, considering nearest neighbours as well as nearest and second nearest neighbours as connected. The conclusion is valid for both cases.

Astrid Franz, Christian Schulzky, Ngoc Anh Do Hoang, Steffen Seeger, Janett Balg, and Karl Heinz Hoffmann.
“Random walks on fractals”.
In: Parallel algorithms and cluster computing.
Ed. by Karl Heinz Hoffmann and A. Meyer.
Berlin Heidelberg: Springer-Verlag, 2006,
P. 303.
doi: 10.1007/3-540-33541-2_17.
Porous materials such as aerogel, porous rocks or cements exhibit a fractal structure for a range of length scales [1]. Diffusion processes in such disordered media are widely studied in the physical literature [2, 3]. They exhibit an anomalous behavior in terms of the asymptotic time scaling of the mean square displacement of the diffusive particles.

René Haber.
“Diffusion on Menger Sponges”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, July 2006.

Karl Heinz Hoffmann, Andreas Fischer, Sven Schubert, and Thomas Streibert.
“Modelling aging experiments in spin glasses”.
In: Parallel algorithms and cluster computing.
Ed. by Karl Heinz Hoffmann and A. Meyer.
Berlin Heidelberg: Springer-Verlag, 2006,
P. 281.
doi: 10.1007/3-540-33541-2_16.
Spin glasses are a paradigm for complex systems. They show a wealth of different phenomena including metastability and aging. Especially in the low temperature regime they reveal a very complex dynamical behaviour. For temperatures below the spin glass transition temperature one ﬁnds a variety of features connected to the inability of the systems to attain thermodynamic equilibrium with the ambient conditions on the observation time scale: aging and memory effects have been observed in many experiments [1–11]. Spin glasses are good model systems as their magnetism provides an easy and very accurate experimental probe into their dynamic behavior. In order to investigate such features different experimental techniques have been applied. Complicated setups including temperature and ﬁeld changes with subsequent relaxation phases lead to more interesting effects such as age reinitialization and freezing [12, 13].

Karl Heinz Hoffmann, Michael Hofmann, Gudula Rünger, and Steffen Seeger.
“Task Pool Teams Implementation of the Master Equation Approach for Random Sierpinski Carpets”.
In: Proc. of the 12th International Euro-Par Conference.
Vol. 4128/2006.
Lecture Notes in Computer Science.
Berlin, Heidelberg: Springer, 2006,
Pp. 1043–1052.
doi: 10.1007/11823285\_110.
We consider the use of task pool teams in implementation of the master equation on random Sierpinski carpets. Though the basic idea of dynamic storage of the probability density reported earlier applies straightforward to random carpets, the randomized construction breaks up most of the simpliﬁcations possible for regular carpets. In addition, parallel implementations show highly irregular communication patterns. We compare four implementations on three different Beowulf-Cluster architectures, mainly differing in throughput and latency of their interconnection networks. It appears that task pool teams provide a powerful programming paradigm for handling the irregular communication patterns that arise in our application and show a promising approach to efficiently handle the problems that appear with such randomized structures. This will allow for highly improved modelling of anomalous diffusion in porous media, taking the random structure of real materials into account.

Karl Heinz Hoffmann and Arnd Meyer, eds.
Parallel algorithms and cluster computing - implementations, algorithms, and applications.
Berlin Heidelberg: Springer-Verlag, 2006.
doi: 10.1007/3-540-33541-2.

Wolfgang Muschik and Karl Heinz Hoffmann.
“Endoreversible Thermodynamics: A Tool for Simulating and Comparing Processes of Discrete Systems”.
In: J. Non-Equilib. Thermodyn. 31.3 (2006), pp. 293–317.
doi: 10.1515/JNETDY.2006.013.
Endoreversible thermodynamics is concerned with reversible sub-systems which are in irreversible interaction with each other. Consequently, endoreversible thermodynamics represents the analogue for discrete systems to the local equilibrium hypothesis in continuum thermodynamics. Here a real cyclic 2-reservoir process is simulated by endoreversible model processes. Simulation means, that the simulating process has the same net heat exchanges, cycle time, power, entropy production, and efficiency as the original one. By introducing process-independent heat conduction coefficients as a constraint for the irreversible interaction, a family of comparative endoreversible processes is generated including the simulation of the original process. This procedure allows to compare process parameters of the family of comparative processes to those of the original one. The fraction ”power of the real process over the maximal power inbetween the comparative family” is introduced as a parameter describing the process excellence.

Sven Schubert and Karl Heinz Hoffmann.
“The structure of enumerated spin glass state spaces”.
In: Comp. Phys. Comm. 174 (2006), pp. 191–197.
doi: 10.1016/j.cpc.2004.02.019.
We enumerate the low energy part of the state space of an Ising spin glass using an e cient branch-and-bound algorithm. A coarse graining algorithm (NB-clustering) is employed to condense the inherent information to a system size which is treatable in computer simulations. The reduced state space still incorporates all ingredients necessary to simulate aging e ects. We investigate its structure in detail and ﬁnd that certain assumptions made in heuristical state space models which have been presented in the past to reproduce aging phenomena in spin glass experiments are indeed compatible with the data from the observed state spaces.

Steffen Seeger, Karl Heinz Hoffmann, and Arndt Meyer.
“The cumulant method for gas dynamics”.
In: Parallel algorithms and cluster computing.
Ed. by Karl Heinz Hoffmann and Arndt Meyer.
Berlin Heidelberg: Springer-Verlag, 2006,
Pp. 335–360.
doi: 10.1007/3-540-33541-2_19.

Katharina Wagner.
“Image Alignment”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, May 2006.

S. A. Amelkin, B. Andresen, J. M. Burzler, K. H. Hoffmann, and A. M. Tsirlin.
“Thermo-mechanical systems with several heat reservoirs: maximum power processes”.
In: J. Non-Equilib. Thermodyn. 30.1 (2005), pp. 67–80.
doi: 10.1515/JNETDY.2005.005.
While endoreversible heat-to-power conversion systems operating between two heat reservoirs have been intensely studied, systems with several reservoirs have attracted little attention. Here we analyse the maximum power processes of such systems with stationary temperature reservoirs. We nd that independent of the number of reservoirs the working uid uses only two isotherms and two in nitely fast isentropes/ adiabats. One surprising result is that there may be reservoirs that are never used. This feature is explained for a simple system with three heat reservoirs.

Do Hoang Ngoc Anh, Karl Heinz Hoffmann, Steffen Seeger, and Sujata Tarafdar.
“Diffusion in disordered Fractals”.
In: Europhys. Lett. 70.1 (2005), pp. 109–115.
doi: 10.1209/epl/i2005-10002-x.

Silvia Bertuglia, Alfonso Limon, Bjarne Andresen, Karl Heinz Hoffmann, Chistopher Essex, and Peter Salamon.
“Transport of O $2$ from arterioles”.
In: J. Non-Equilib. Thermodyn. 30.2 (2005), pp. 151–162.
doi: 10.1515/JNETDY.2005.011.
url: http://www.extenza-eps.com/extenza/loadHTML?objectIDValue=64450&type=abstract.
Oxygen delivery to the tissues is crucial to survival but our understanding of the processes involved in the transport of oxygen from blood to tissue is incomplete. The aim of the present work is to illustrate a long-standing paradox regarding such transport by reporting new state-of-the-art measurements and by analyzing the results in several ways, thereby exploring possible resolutions of the paradox. Our model calculations show that slight extensions of system parameters are sufficient to overcome the apparent inconsistencies. Alternatively, so far unappreciated mild effects like ﬂow-assisted diffusion in the interstitium will explain the supernormal diffusion of oxygen.

Frank Heilmann.
“The State Space of Complex Systems”.
PhD Thesis. 09107 Chemnitz: Technische Universität Chemnitz, July 2005.
In dieser Arbeit wird eine Beschreibung von Monte-Carlo-Verfahren zur L̈osung komplexer Optimierungsaufgaben mit Hilfe von Markov-Ketten durchgefuhrt. Nach einer kurzen Einfuhrung werden L̈osungsmenge solcher Aufgaben und der physikalische Zustandsraum komplexer Systeme identiﬁziert. Zunächst wird die Dynamik von Zufallswanderern im Zustandsraum mit Hilfe von Master-Gleichungen modelliert. Durch Einfuhrung von Performanzkriterien können verschiedene Optimierungsstrategien quantitativ miteinander verglichen werden. Insbesondere wird das Verfahren Extremal Optimization vorgestellt, das ebenfalls als Markov-Prozess verstanden werden kann. Es wird bewiesen, dass eine im Sinne der genannten Kriterien beste Implementierung existiert. Da diese von einem sogenannten Fitness Schedule abhängt, wird dieser fur kleine Beispielsysteme explizit berechnet. Daran anschließend wird die Zustandsdichte komplexer Systeme betrachtet. Nach einem kurzen Überblick ̈uber vorhandene Methoden folgt eine detaillierte Untersuchung des Verfahrens von Wang und Landau. Numerische und analytische Hinweise werden gegeben, nach denen dieser Algorithmus innerhalb seiner Klasse wahrscheinlich der Optimale ist. Eine neue Methode zur Approximation der Zustandsdichte wird vorgestellt, die insbesondere für die Untersuchung komplexer Systeme geeignet ist. Abschließend wird ein Ausblick auf zuk̈unftige Arbeiten gegeben.

Frank Heilmann and Karl Heinz Hoffmann.
“ParQ – high-precision calculation of the density of states”.
In: Europhys. Lett. 70.2 (2005), pp. 155–161.
doi: 10.1209/epl/i2004-10486-8.
We present a highly effective, parallelized random-walk-based algorithm to calculate the density of states of complex physical systems. Random walkers’ attempted moves from one energy level to another are represented in a stochastic matrix, giving estimates for the transition matrix at inﬁnite temperature. The eigenvector corresponding to the largest eigenvalue is the density of states up to a normalization. We verify the performance on selected examples of Ising spin systems with random coupling constants drawn uniformly from [-1,1], of which the exact density of states have been calculated by a branch-and-bound approach.

Karl Heinz Hoffmann, Rodriguez-Brito, Mya Breitbart, David Bangor, Florent Angly, Ben Felts, James Nulton, Forest Rohwer, and Peter Salamon.
“The structure of marine phage populations”.
In: Proceedings of ECOS 2005, the 18th International Conference on Efficiency, Cost, Optimization, Simulation, and Environmental Impact of Energy Systems: Trondheim, Norway, June 20 - 22, 2005.
Ed. by Signe Kyelstrup and Norges Forskningsr̊ad.
2.
Norges Teknisk-Naturvitenskapelige Universitet. Tapir Academic Press, 2005,
Pp. 711–715.
Phage are the most abundant biological entities in the biosphere, with an estimated $1031$ particles on the planet. They also play a major role in carbon cycling; at least 25% of ﬁxed carbon passes through phage. Their roles as predators of bacteria have important implications for possible marine CO $2$ sequestration. Metagenomic analyses show that the rank-abundance curve for marine phage communities follows a power law distribution. This distribution is consistent with a proposed, modiﬁed version of Lotka-Volterra predator-prey dynamics, where blooms of a speciﬁc microbial species lead to blooms of their corresponding phage and a subsequent decrease in abundance. The model predicts that the majority of phage genotypes in a population will be rare and it is unlikely that the most abundant phage genotype will be the same at different time points. The model is based on spatial-temporal heterogeneity and a power law phage decay, which are both supported by empirical data.

Karl Heinz Hoffmann and J. Christian Schön.
“Kinetic Features of Preferential Trapping on Energy Landscapes”.
In: Found. Phys. Lett. 18.2 (2005), pp. 171–182.
doi: 10.1007/s10702-005-3960-8.
url: http://springerlink.metapress.com/app/home/contribution.asp?wasp=f5c13b54845140fab06dde9ac8c92b27&referrer=parent&backto=issue,5,7;journal,1,46;searchpublicationsresults,1,1;.
The dynamics of complex systems can be mapped onto trajectories on their energy landscape. The properties of such trajectories as a function of temperature, and thus the chances of the system to enter certain regions of the state space, can be understood in terms of such energy landscapes. Here we show that their kinetic features are of equal importance as the previously discussed energetic and entropic features. Especially for barrier-crossing movements on mountainous landscapes, we observe competing effects between these three aspects, which can lead to surprising inversions in the chances to ﬁnd certain states such as local minima in the systems.

Michael Hofmann.
“Verwendung von Task Pool Team Konzepten zur parallelen Implementierung von Diffusionsprozessen auf Fraktalen”.
Studienarbeit. 09107 Chemnitz: Technische Universität Chemnitz, Feb. 2005.

André John.
“Diffusion on Fractals”.
Master Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Oct. 2005.

Arnulf M̈obius, Karl Heinz Hoffmann, and Christian Schön.
“Optimization by thermal cycling”.
In: Complexity, Metastability and Nonextensitivity.
Ed. by C. Beck, G. Benedek, A. Rapisarda, and C. Tsallis.
copy: World Scientiﬁc, Feb. 2005,
Pp. 215–219.
Thermal cycling is an heuristic optimization algorithm which consists of cyclically heating and quenching by Metropolis and local search procedures, respectively, where the amplitude slowly decreases. In recent years, it has been successfully applied to two combinatorial optimization tasks, the traveling salesman problem and the search for low-energy states of the Coulomb glass. In these cases, the algorithm is far more efficient than usual simulated annealing. In its original form the algorithm was designed only for the case of discrete variables. Its basic ideas are applicable also to a problem with continuous variables, the search for low-energy states of Lennard-Jones clusters.

G. A. Nemnes, U. Wulf, and P. N. Racec.
“Nonlinear $I$ - $V$ characteristics of nanotransistors in the Landauer–B̈uttiker formalism”.
In: J. Appl. Phys. 98 (2005), pp. 1–8.
doi: 10.1063/1.2113413.
We present the nonlinear $I$ - $V$ characteristics of a nanoscale metal-oxide-semiconductor ﬁeld-effect transistor in the Landauer-B̈uttikker formalism. In our three-dimensional ballistic model the gate, source, and drain contacts are treated on an equal footing. As in the drift-diffusion regime for ballistic transport a saturation of the drain current results. We demonstrate the quantum mechanism for the ballistic drain current saturation. As a speciﬁc signature of ballistic transport we ﬁnd a speciﬁc threshold characteristic with a close-to-linear dependence of the drain current on the drain voltage. This threshold characterisitc separates the ON-state regime from a quasi-OFF-state regime in which the device works as a tunneling transistor. Long- and short-channel effects are analyzed in both regimes and compared qualitatively with existing experimental data by Intel [B. Doyle et al., Intel Technol. J. $6$ , 42 (2002)].

Mandes Schönherr.
“Simulation von Diffusion auf Fraktalen”.
in German.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Sept. 2005.
Diffusion auf k̈unstlichen oder natürlichen Strukturen kann durch Bewegung von Random Walkern auf Fraktalen untersucht werden. Diese Simulation wird fast nur numerisch durchgeführt. Um ungeordnete Strukturen zu untersuchen, kann das hier untersuchte auch zufällig zusammengesetzte Fraktale aus verschiedenen vorgegebenen Generatoren mit bestimmten Mischungsverhältnissen, in verschiedenen Iterationstiefen, betrachten. Das Verhalten der ausgegebenen Random-Walk-Dimension kann so über der Variation des Mischungsverhältnisses beobachtet werden. Verschiedene Ergebnisse wurden mit Werten aus der Theorie und anderen Arbeiten verglichen.

Robert Schulz.
“Diffusion on Fractals”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Sept. 2005.
In this work a Sierpinski carpet with several randomly mixed generators is examined. A regular Sierpinski carpet is a self-similar fractal object fully determined by a recurrent pattern. In a random Sierpinski carpet, in order to model the irregularity of natural porous materials, several generators are mixed during the construction of the carpet. Furthermore it will be examined how the random walk dimension depends on the mixture ratio of two generators. This is explored with a numerical implementation of the master equation.

Steffen Seeger and Karl Heinz Hoffmann.
“On symbolic derivation of the cumulant equations”.
In: Comp. Phys. Comm. 168.3 (2005), pp. 165–176.
doi: 10.1016/j.cpc.2005.03.106.
url: http://authors.elsevier.com/sd/article/S001046550500233X.
We discuss the application of Mathematica for automated, symbolic calculation of the cumulant equations of arbitrary order. Like moment equations, these partial differential equations-describing ﬂuid motion on a mesoscopic scale-may be considered an approximation to the Boltzmann equation, a highly nonlinear integro-differential equation that describes the motion of gases at a microscopic scale. Though the cumulant method provides a simple and compact presentation of the theory, actual calculation of very high order equations turns out to be a challenging task.

Steffen Seeger and Karl Heinz Hoffmann.
“On the Domain of Hyperbolicity of the Cumulant Equations”.
In: J. Stat. Phys. 121.1–2 (2005), pp. 75–90.
doi: 10.1007/s10955-005-6969-2.
url: http://www.springerlink.com/openurl.asp?genre=journal&issn=0022-4715.
In this article we consider the inﬂuence of non-equilibirum values of classical variables on the eigenvalues of the advection part of the cumulant equations. Real and ﬁnite eigenvalues are a neccessary condition for the cumulant equations to be hyperbolic which can be used to obtain estimates on admissible deviations from equilibrium for a model of particular order still to be valid. We ﬁnd that this condition puts no constraints on velocity and shear stress values, but speciﬁc energy must be positive, normal stress must be bounded by speciﬁc energy and heat ﬂux not be too large.

Steffen Seeger and Karl Heinz Hoffmann.
“The cumulant method for the space-homogeneous Boltzmann equation”.
In: Continuum Mech. Thermodyn. 17.1 (2005), pp. 51–60.
doi: 10.1007/s00161-004-0187-z.
url: http://www.springerlink.com/app/home/contribution.asp?wasp=c3920916e0174a16a4c2da1e5aeb662b&backto=issue,5,7;journal,3,60;linkingpublicationresults,1:100469,1.
In this work we give a comparison of the exact Bobylev/Krook-Wu solution to the space-homogeneous Boltzmann equation and numerical results obtained by a implementation of the cumulant method for the space-homogeneous case. We ﬁnd excellent agreement of the numerical solution to the cumulant equations with the exact solution of the space-homogeneous Boltzmann equation as long as the exact, non-linear production terms are used. If a linearized variant of the production terms is used, relaxation rates may be underestimated due to convergence to the solution of the linearized equations.

Benoit Sicre, Andreas B̈uhring, Bernd Platzer, and Karl Heinz Hoffmann.
“Energy and cost assessment of micro-CHP plants in high-performance residential buildings”.
In: Proceedings of ECOS 2005, the 18th International Conference on Efficiency, Cost, Optimization, Simulation, and Environmental Impact of Energy Systems: Trondheim, Norway, June 20 - 22, 2005.
Ed. by S. Kjelstrup.
Vol. 2.
Tapir Academic Press, 2005,
Pp. 1063–1071.
Lately, efforts were made to scale-down some Combined Heat and Power (CHP) technologies, sch as fuel cell, gas turbine or organic Rankine cycle power plants in order to suit well for residential applications. The driving force for this is the high overall thermal efficiency and the low associated GHG emmissions. Beside this, distributed power generation is exected to alleviate partially the issue related to the general rise of electricity demand. However, as micro-CHP habe only modest electrical conversion efficiencies, the effective exploitation of the thermal output is critical to realising high levels of energy efficiency and the associated environmental beneﬁts, Heat to power ratio of currently available micro-CHP devices (in the best case approx. 3 to 1) ﬁts poorly with the heat to power ratio of high-performance buildings (in an average 1 to 1 according to recent construction practises). The present paper considers the building and the HVAC system (including the micro-CHP) and the resident’s heat and power patterns as a whole, taking into account their inherent interactions. It describes ﬁrst new simulation tools which were developed to balance in terms of energy and of costs the production and the consumption of both heat and electricity. Computation based on SOFC fuel cells and Stirling engines are discussed. Second, these technologies such as condensing gas boilers. Third, the role of the apropriate level of thermal insulation for the building as a compromise between building heat losses and overall primary energy efficiency, including electricity supply, is discussed.

Sergei A. Amelkin, Bjarne Andresen, Josef Maximilian Burzler, Karl Heinz Hoffmann, and Anatoliy Mikhailovich Tsirlin.
“Maximum power processes for multi-source endoreversible heat engines”.
In: J. Phys. D: Appl. Phys. 37.9 (2004), pp. 1400–1404.
doi: 10.1088/0022-3727/37/9/015.
The maximum power processes of multi-source endoreversible engines with stationary temperature reservoirs are investigated. We prove that the optimal solution is always time independent with a single hot and a cold engine contact temperature. The heat reservoirs fall into three groups: The hot reservoirs which are connected at all times for heat delivery, the cold reservoi rs which are connected at all times for heat drain, and possibly a group of reservoirs at intermediate temperatures which are unused. This phenomenon is demonstrated for a three-source system. We ﬁnd that for a commonly used class of heat transfer functions, including Newtonian, Fourier and radiative heat transport, the efficiencies at maximum power are the same as for two-reservoir engines with appropriately chosen properties.

Janett Balg.
“Anwendung der Methode der gewichteten Residuen auf die eindimensionale Boltzmanngleichung”.
Bachelor Thesis. 09107 Chemnitz: Technische Universität Chemnitz, Aug. 2004.

Josef Maximilian Burzler, Sergej A. Amelkin, Anatoliy Mikhailovich Tsirlin, and Karl Heinz Hoffmann.
“Optimal Allocation of Heat Exchanger Investment”.
In: Open Sys. and Information Dyn. 11.3 (2004), pp. 291–306.
doi: 10.1023/B:OPSY.0000047572.63034.66.
The optimal allocation of a given investment capital to the heat exchanging inventory is studied for heat engines, refrigerators and heat pumps. The study is based on an endoreversible model operating between two constant temperature heat reservoirs at optimal thermodynamic performance, which is either minimal entropy production or maximum power production. The analysis accounts for the fact that the actual costs of heat exchangers equipment is subject to the material, design and operating conditions of the heat exchangers so that the dependency between the costs and heat transfer coe cients generally needs to be considered as nonlinear and di erent for the hot and cold side of the system. Contrary to existing results showing no di erence between cyclic and stationary operation for Newtonian heat transfer we ﬁnd a distinct di erence. This result also pertains to non-Newtonian heat transfer.

Andreas Fischer and Karl Heinz Hoffmann.
“Can a quantitative simulation of an Otto engine be accurately rendered by a simple Novikov model with heat leak?”
In: J. Non-Equilib. Thermodyn. 29.1 (2004), pp. 9–28.
doi: 10.1515/JNETDY.2004.002.
In this case study a complex Otto engine simulation provides data including, but not limited to, effects from losses due to heat conduction, exhaust losses and frictional losses. This data is used as a benchmark to test whether the Novikov engine with heat leak, a simple endoreversible model, can reproduce the complex engine behavior quantitatively by an appropriate choice of model parameters. The reproduction obtained proves to be of high quality.

Frank Heilmann, Karl Heinz Hoffmann, and Peter Salamon.
“Best possible probability distribution over Extremal Optimization ranks”.
In: Europhys. Lett. 66.3 (2004), pp. 305–310.
doi: 10.1209/epl/i2004-10011-3.
We consider the problem of selecting the next degree of freedom (DoF) for update in an Extremal Optimization algorithm designed to ﬁnd the ground state of a sy stem with a complex energy landscape. We show that in order to minimize any linear function of the state probabilities, e.g., the expectation value of the ﬁnal energy, there exists a best distribution for selecting the next DoF. We dub the algorithm using this best distribution Fitness Threshold Accepting.

Karl Heinz Hoffmann, Frank Heilmann, and Peter Salamon.
“Fitness Threshold Accepting over extremal optimization ranks”.
In: Phys. Rev. E 70.4 (2004), pp. 046704–1 –046704–6.
doi: 10.1103/PhysRevE.70.046704.
We treat the problem of selecting the next degree of freedom for update in an extremal optimization algorithm designed to ﬁnd the ground state of a system with a complex energy landscape. We show that there exists a best distribution for selecting the next degree of freedom in order to optimize any linear function of the state probabilities, e.g., the expected number of visits to the ground state. We dub the class of algorithms using this best distribution in conjunction with extremal optimization ﬁtness threshold accepting. In addition, we construct an extended random walk and use it to show that ﬁtness threshold accepting is optimal also for several other measures of algorithm performance, such as maximizing the expected probability of seeing the ground state and minimizing the expected value of the lowest energy seen.

Edward Steven Jimenez, Peter Salamon, Ricardo Rivero, Consuelo Rendon, and Karl Heinz Hoffmann.
“Optimal allocation of Heat Exchanger Inventory in a Serial Type Diabatic Distillation Column”.
In: Proceedings of ECOS 2004.
Ed. by R. Rivero, L. Monroy, R. Pulido, and G. Tsatsaronis.
IMP. Mexico: Instituto Mexicano del Petroleo, 2004,
Pp. 179–187.
Diabatic distillation is a separation process in which heat is transferred on the trays inside the column . We have previously shown (Jimenez et al. 2003) that optimal operation of serial heat exchangers can capture most of the wasted exergy. In the present work we explore the effect of locating a ﬁxed total heat exchanger area in different trays and calculate the optimal allocation of a given heat exchanger inventory.

Steven Jimenez, Peter Salamon, Ricardo Rivero, Consuelo Rendon, Karl Heinz Hoffmann, Markus Schaller, and Bjarne Andresen.
“Optimization of a Diabatic Distillation Column with Sequential Heat Exchangers”.
In: Ind. Eng. Chem. Res. 43.23 (2004), pp. 7566–7571.
doi: 10.1021/ie0495933.
Diabatic distillation is a separation process in which heat is transferred on the trays inside the column as opposed to classical adiabatic columns where heat is only supplied to the reboiler and extracted from the condenser. Such diabatic columns dramatically reduce the exergy needed to perform the separation. One implementation, particularly suitable for retroﬁtting applications, uses a single heating ﬂuid circulating in series from one tray to the next below the feed tray and a single cooling ﬂuid circulating in series above the feed tray. The optimal design of these sequential heat exchangers, minimizing the overall rate of entropy production in the separation process, is a difficult optimization problem because traditional algorithms for optimization invariably get stuck. However, an algorithm based on physical intuition for adjusting the temperature proﬁle can ﬁnd the optimum. The resulting column operation is compared to the optimal operation with independent heat transfer to each tray (the completely controlled diabatic column) and to a conventional adiabatic column. In the former comparison, we ﬁnd how much exergy is lost by circulating a ﬂuid in series rather than using independently adjustable heat exchanges. In the latter, we ﬁnd the possible savings available by retroﬁtting. The comparisons show that most of the potential exergy savings can be captured by diabatization using heat exchangers in series. The potential impact of this technology on the chemical and process industry is enormous because distillation is the single largest energy degrading unit operation worldwide.

Sven Schubert and Karl Heinz Hoffmann.
“Aging in enumerated spin glass state spaces”.
In: Europhys. Lett. 66.1 (2004), pp. 118–124.
doi: 10.1209/epl/i2003-10142-y.
Aging phenomena are observed in many spin class experiments. Heuristic state space models were presented in the past to reproduce these effects. We here start the investigation by considering the real state space of an Ising spin glass Hamiltonian. A branch-and-bound algorithm is used to ﬁnd the low-energy part of the state space. We solve the problem of the still huge size of the state space by employing a special coarse graining algorithm. The system can be reduced to a computational treatable size. We demonstrate that these systems still contain all properties necessary for aging effects.

S. Seeger and K. H. Hoffmann.
“Erratum: The cumulant method applied to a mixture of Maxwell gases”.
In: Continuum Mech. Thermodyn. 16.5 (2004), p. 515.

Sergei A. Amelkin, Anatoliy Mikhailovich Tsirlin, Josef Maximilian Burzler, Sven Schubert, and Karl Heinz Hoffmann.
“Minimal Work for Separation Processes of Binary Mixtures”.
In: Open Sys. and Information Dyn. 10.4 (2003), pp. 335–349.
doi: 10.1023/B:OPSY.0000009555.63816.86.
The work expenditures for both perfect and imperfect separation processes are well known for the reversible case; yet such a description is often far from reality. Real processes operate at ﬁnite times and non-zero rates leading to an additional, irreversible energy expenditure. This paper employs an idealized van t’Hoff chamber as a theoretical model to derive lower bounds for the irreversible work in real separation processes such as membrane separation. Methods of optimal control for open systems and nonlinear programming of averaged problems are used to calculate the optimal mass transfer kinetics for the ﬁnite-time separation of binary mixtures of ideal gases.

Viorel Badescu and Benoit Sicre.
“Renewable energy for passive house heating. Part I: Building Description”.
In: Energ. Buildings 35.11 (2003), pp. 1077–1084.
doi: 10.1016/j.enbuild.2003.10.001.

Viorel Badescu and Benoit Sicre.
“Renewable energy for passive house heating: Part II: Model”.
In: Energ. Buildings 35.11 (2003), pp. 1085–1096.
doi: 10.1016/j.enbuild.2003.09.004.

Peter Blaudeck and Karl Heinz Hoffmann.
“Ground states for condensed amorphous systems: Optimizing annealing schemes”.
In: Comp. Phys. Comm. 150 (2003), pp. 293–299.
doi: 10.1016/S0010-4655(02)00688-4.
Using optimized Simulated Annealing allows ﬁnding distinctly lower minima for the potential energy of amorphous systems. A new scheme resulting in an optimal annealing schedule has been found that can be readily applied to the simulation of molecules, clusters and condensed systems with any atomic composition. The scheme remains applicable if, due to the complexity of the system and its interatomic potentials, the conﬁguration space cannot be explored in more detail.

Josef Maximilian Burzler.
“Performance Optima for Endoreversible Systems”.
PhD Thesis. Technische Universität Chemnitz, Jan. 2003.
Theoretical bounds for performance measures of thermodynamical systems are investigated under conditions of ﬁnite times and rates of processes using endoreversible models. These models consist of reversible operating sub-systems which exchange energy via generally irreversible interactions. Analytical and numerical calculations are performed to obtain performance optima and respective optimized process and design parameters for four model systems. A heat engine where the heat transfer between the working ﬂuid and heat reservoirs is described by generalized, polytropic process is optimized for maximum work output. Thermal efficiencies, optimal values for temperatures and process times of the heat transfer processes are determined. A model of a generalized system suited to describe the operation of heat engines, refrigerators, and heat pumps is optimized with respect to thermal efficiency. Several examples illustrate how the results of the analysis are used to allocate ﬁnancial resources to the heat exchanger inventory in an optimal way. A power-producing thermal system which exchanges heat with several heat reservoirs via irreversible heat transfer processes is analyzed to ﬁnd the optimal contact times between the working ﬂuid and each of the reservoirs. The piston motion of a Diesel engine is optimized to achieve maximum work for a given amount of fuel. The endoreversible model of the Diesel engine accounts for the temporal variations of the heat produced by the combustion process, the basic ﬂow pattern within the engine’s cylinder, the temperature dependence of the viscosity, thermal conductivity, and heat capacity of the working ﬂuid and losses due to friction and heat leak through the cylinder walls.

Josef Maximilian Burzler, Karl Heinz Hoffmann, Sergey Anatolievich Amelkin, and Anatoliy Mikhailovich Tsirlin.
“Optimal Endoreversible Heat Engines with Polytropic Branches”.
In: Int. J. Appl. Thermodyn. 6.2 (2003), pp. 69–78.
Endoreversible engine cycles with two adiabatic and two heat transfer branches are investigated and optimized for maximum work output. The heat transfer branches are described as general polytropic processes which include common standard branches, like isotherms, isobars and isometrics, as special cases. The study considers the ﬁnite heat capacity of the working ﬂuid and the ﬁnite-time character of the heat transfer processes, determines the optimal allocation of branch times, and derives analytic expressions for the maximized work output. The efficiency at maximum work is found to coincide with the Curzon-Ahlborn efficiency for endoreversible Carnot engines and does not depend on design parameters of the engine if the degree of the polytropic processes is equal in both heat transfer branches.

A. A. Dragos, Viorel Badescu, Karl Heinz Hoffmann, and Benoit Sicre.
“Passive houses to reduce the utilization of classical fuels for space heating”.
In: Conferinta nationala pentru dezvoltare durabila.
copy, 2003,
Pp. 227–232.
In the scope of this work, a passive house is a cost efficient building that can manage througout the heating period, due to its speciﬁc construction design, with more than ten times less heat energy that the same building designed to standards presently applicable accross Europe. Its extended thermal insulation and enhanced air tightness removes the need for temperatures higher than 50 degrees Celsius what makes renewable energy sources particularly suitable for heating, cooling and DHW. Description of the ventilation/heating system of an existing passive house is the topic of this paper.

Astrid Franz and Karl Heinz Hoffmann.
“Threshold accepting as limit case for a modiﬁed Tsallis statistics”.
In: Appl. Math. Lett. 16.1 (2003), pp. 27–31.
doi: 10.1016/S0893-9659(02)00140-4.

Karl Heinz Hoffmann, Josef Maximilian Burzler, Andreas Fischer, Markus Schaller, and Sven Schubert.
“Optimal Process Paths for Endoreversible Systems”.
In: J. Non-Equilib. Thermodyn. 28.3 (2003), pp. 233–268.
doi: 10.1515/JNETDY.2003.015.
All energy transformation processes occurring in reality are irreversible and in many cases these irreversibilities must be included in a realistic description of such processes. Endoreversible thermodynamics is a non-equilibrium approach in this direction by viewing a system as a network of internally reversible (endoreversible) subsystems exchanging energy in an irreversible fashion. All irreversibilities are conﬁned to the interaction between the subsystems. This review is dedicated to the dynamical investigation of such endoreversible systems. First the general framework for the endoreversible description of a system is brieﬂy introduced, and then the necessary mathematical tools to determine optimal process paths for such systems are presented. These are complemented by simple examples for the application of the different methods. Then the optimal paths for endoreversible processes of increasing complexity are discussed: ﬁrst the processes between given equilibrium states, and then cyclic processes. These are followed by a review of internal combustion engines and by a number of further selected applications. We conclude with an outlook to other areas of irreversible thermodynamics where path optimization methods have been successfully used.

Xiaorang Li, Christopher Essex, Matt Davison, Karl Heinz Hoffmann, and Christian Schulzky.
“Fractional Diffusion, Irreversibility and Entropy”.
In: J. Non-Equilib. Thermodyn. 28.3 (2003), pp. 279–291.
doi: 10.1515/JNETDY.2003.017.
Three types of equations linking the diffusion equation and the wave equation are studied: the time fractional diffusion equation, the space fractional diffusion equation and the telegrapher’s equation. For each type, the entropy production is calculated and compared. It is found that the two fractional diffusions, considered as linking bridges between reversible and irreversible processes, possess counter-intuitive properties: as the equation becomes more reversible, the entropy production increases. The telegrapher’s equation does not have the same counter-intuitive behavior. It is suggested that the different behaviors of these equations might be related to the velocities of the corresponding random walkers.

Steffen Seeger.
“The Cumulant Method”.
http://archiv.tu-chemnitz.de/pub/2003/0120.
PhD Thesis. Chemnitz: Technische Universität Chemnitz, Sept. 2003.
In this work, a new method to reduce Boltzmann equation to a system of partial differential equations is discussed. After a short introduction to kinetic theory of an inert mixture of gases an overview of the various moment methods known from literature is given. The cumulant method, presented in the following, is based on the assumption that due to the collision processes in a gas correlations of higher order decay more rapidly than correlations of lower order. Based on this assumption the eautions of motion for the cumulants are derived and the production terms of the resulting balance equations are calculated for a mixture of inter Maxwell gases are calculated. Examination of the relexation to an equilibrium state allows to relate these equations to models known from continuum mechanics and shows the validity of the assumption made for this case. In the second part results of numerical experiments are presented, where simulations with various boundary conditions are carried out for Couette and Poiseulle ﬂows. Depending on the particular boundary conditions applied, both characteristic properties of reareﬁed gases but also of Navier-Stokes ﬂows are observed. The last part of this work discusses moment equations as a particular form of the method of weighted residuals applied to the Boltzmann equation, giving an outlook to future work.

Hermann Diering, Steffen Seeger, and Karl Heinz Hoffmann.
Durch Zufall schneller ans Ziel: Anwendung eines stochastischen Optimierungsalgorithmus auf das Problem des Handlungsreisenden.
Besondere Lernleistung.
copy, Feb. 2002.

Astrid Franz and Karl Heinz Hoffmann.
“Optimal Annealing Schedules for a Modiﬁed Tsallis Statistics”.
In: J. Comput. Phys. 176.1 (2002), pp. 196–204.
doi: 10.1006/jcph.2001.6975.

Astrid Franz, Christian Schulzky, and Karl Heinz Hoffmann.
“Using Computer Algebra Methods to Determine the Chemical Dimension of Finitely Ramiﬁed Sierpinski Carpets”.
In: SIGSAM Bulletin 36.2 (2002), pp. 18–30.
doi: 10.1145/581316.581318.

Astrid Franz, Christian Schulzky, Steffen Seeger, and Karl Heinz Hoffmann.
“Diffusion on Fractals – Efficient algorithms to compute the random walk dimension”.
In: Fractal Geometry: Mathematical Methods, Algorithms, Applications.
Ed. by Jonathan M. Blackledge, Allan K. Evans, and Martin J. Turner.
IMA Conference Proceedings.
Horwood Publishing Ltd., Chichester, West Sussex, 2002,
Pp. 52–67.
doi: 10.1533/9780857099594.52.

Karl Heinz Hoffmann.
“Recent Developments in Finite Time Thermodynamics”.
In: Techn. Mech. 22.1 (2002), pp. 14–25.
Finite time thermodynamics is a non-equilibrium theory. Its aim is to provide performance bounds and extremes for irreversible thermodynamics processes. Recent developments in different areas of this theory are presented. First it is shown how irreversible processes between reversible systems can be described by the endoreversible theory. Then maximum power an minimum entropy production processes are introduced. And ﬁnally the extensions of ﬁnite time thermodynamics to the realm of quantum theory is demonstrated.

Karl Heinz Hoffmann.
“The Statistical Physics of Energy Landscapes: From Spin Glasses to Optimization”.
In: Computational Statistical Physics.
Ed. by K. H. Hoffmann and M. Schreiber.
Berlin: Springer Verlag, 2002.
Chap. 4, pp. 57–76.
doi: 10.1007/978-3-662-04804-7_4.
The concept of energy ”landscapes” leads to a uniﬁed understanding of phenomena in a number of different complex physical systems. All these systems are characterized by an energy function which possesses many local minima separated by barriers as a function of the state variables. If graphically depicted such energy function looks very much like a mountainous landscape. Typical examples of such complex systems are spin glasses which show a wealth of interesting relaxation phenomena, but also a number of industrially important minimization problems, which have a mountainous cost function landscape. These problems are intimately connected by the thermally activated relaxation dynamics on complex energy landscapes.

Karl Heinz Hoffmann, Astrid Franz, and Peter Salamon.
“Structure of best possible strategies for ﬁnding ground states”.
In: Phys. Rev. E 66.4 (2002), pp. 046706/1–046706/7.
doi: 10.1103/PhysRevE.66.046706.
Finding the ground state of a system with a complex energy landscape is important for many physical problems including protein folding, spin glasses, chemical clusters, and neural networks. Such problems are usually solved by heuristic search methods whose efficacy is judged by empirical performance on selected examples. We present a proof that for a wide range of objective functions threshold accepting is the best possible strategy within a large class of algorithms that simulate random walks on the landscape. In particular, it can perform better than simulated annealing, Tsallis and Glauber statistics.

Karl Heinz Hoffmann and Michael Schreiber, eds.
Computational Statistical Physics.
Berlin: Springer Verlag, 2002.
In recent years statistical physics has made signiﬁcant progress as a result of advances in numerical techniques. While good textbooks exist on the general aspects of statistical physics, the numerical methods and the new developments based on large-scale computing are not usually adequately presented. In this book 16 experts describe the application of methods of statistical physics to various areas in physics such as disordered materials, quasicrystals, semiconductors, and also to other areas beyond physics, such as ﬁnancial markets, game theory, evolution, and traffic planning, in which statistical physics has recently become signiﬁcant. In this way the universality of the underlying concepts and methods such as fractals, random matrix theory, time series, neural networks, evolutionary algorithms, becomes clear. The topics are covered by introductory, tutorial presentations.

Gelein M. Koeijer, Signe Kjelstrup, Peter Salamon, Gino Siragusa, Markus Schaller, and Karl Heinz Hoffmann.
“Comparison of Entropy Production Rate Minimization Methods for Binary Diabatic Distillation”.
In: Ind. Eng. Chem. Res. 41.23 (2002), pp. 5826–5834.
doi: 10.1021/ie010872p.
The purpose of this study is to compare two analytical methods with two numerical methods for minimizing the entropy production rate in diabatic distillation columns (i.e., with heat exchangers on all trays). The ﬁrst analytical method is the equal thermodynamic distance method. The second uses Lagrange minimization on a model derived from irreversible thermodynamics. The numerical methods use Powell s and a Monte Carlo algorithm and gave the same results. Both analytical methods agreed well with the numerical ones for two columns with low separation per tray, while they did not agree well for a column with large separation per tray.

Markus Schaller, Karl Heinz Hoffmann, R. Rivero, Bjarne Andresen, and Peter Salamon.
“The Inﬂuence of Heat Transfer Irreversibilities on the Optimal Performance of Diabatic Distillation Columns”.
In: J. Non-Equilib. Thermodyn. 27.3 (2002), pp. 257–256.
doi: 10.1515/JNETDY.2002.015.
A distillation column with the possibility of heat exchange on every tray (a fully diabatic column) is optimized in the sense of minimizing its total entropy production. This entropy production counts the interior losses due to heat and mass ﬂow as well as the entropy generated in the heat exchangers. It is observed that the optimal heating distribution, i.e. the heat exchange required on each tray, is essentially the same for all trays in the stripping and rectiﬁcation sections, respectively. This makes a column design with consecutive interior heat exchanger and only one exterior supply for each of the two sections very appealing. The result is only slightly dependent on the heat transfer law considered. In the limit of an inﬁnite number of trays even this column with resistance to transfer of heat becomes reversible.

Steffen Seeger and Karl Heinz Hoffmann.
“The cumulant method applied to a mixture of Maxwell gases”.
In: Continuum Mech. Thermodyn. 14.2 (2002). see also Erratum: CMT 16(5):515, 2004, pp. 321–335.
doi: 10.1007/s001610100067.
We apply the recently proposed cumulant method to derive the production terms for a mixture of gases of Maxwell-molecules in two and three dimensions. For the single component Maxwell gas we introduce a linear approximation of the production terms and give an analytical solution for the (space-)homogeneous case. We ﬁnd that the eigenvariables of the linearized productions appear in three different kinds and the ﬁrst few can be related to classical thermodynamic quantities.

Sergei A. Amelkin, Josef Maximilian Burzler, Karl Heinz Hoffmann, and Anatoliy Mikhailovich Tsirlin.
“Estimates of Limiting Possibilities of Separation Processes”.
In: Theor. Found. Chem. Eng. 35.3 (2001). in Russian, pp. 223–238.
doi: 10.1023/A:1010485906403.
url: http://www.springerlink.com/app/home/contribution.asp?wasp=7b8f8675310e414c8f6ecb3258b4d638&referrer=parent&backto=searcharticlesresults,1,1;journal,1,1;linkingpublicationresults,1:106294,1.
The problem of ﬁnding the minimum work to be done to separate a mixture at a ﬁxed process duration or at a given process capacity is considered. The estimates of the work done in an irreversible process substantially exceed those of the work done in reversible separation, and the work done in irreversible separation of depleted mixtures is ﬁnite even when the concentration of the minor component is arbitrarily close to zero. A method is proposed for extending these estimates to separation processes consuming heat rather than mechanical energy.

Sergei A. Amelkin, Josef Maximilian Burzler, Karl Heinz Hoffmann, and Anatoliy Mikhailovich Tsirlin.
“Evaluating the Efficiency Frontier of Separation Processes”.
In: Theor. Found. Chem. Eng. 35.3 (2001), pp. 217–223.
doi: 10.1023/A:1010485906403.
url: http://www.springerlink.com/app/home/contribution.asp?wasp=7b8f8675310e414c8f6ecb3258b4d638&referrer=parent&backto=searcharticlesresults,1,1;journal,1,1;linkingpublicationresults,1:106294,1.
The problem of ﬁnding the minimum work to be done to separate a mixture at a ﬁxed process duration or at a given process capacity is considered. The estimates of the work done in an irreversible process substantially exceed those of the work done in reversible separation, and the work done in irreversible separation of depleted mixtures is ﬁnite even when the concentration of the minor component is arbitrarily close to zero. A method is proposed for extending these estimates to separation processes consuming heat rather than mechanical energy.

Matt Davison, Christopher Essex, Christian Schulzky, Astrid Franz, and Karl Heinz Hoffmann.
“Clouds, ﬁbres and echoes: a new approach to studying random walks on fractals”.
In: J. Phys. A: Math. Gen. 34.20 (2001), pp. L289–L296.
doi: 10.1088/0305-4470/34/20/101.
Up to now the general approach of constructing evolution differential equations to describe random walks on fractals has not succeeded. Is this because the true probability density function is inherently fractal? When plotted in the appropriate similarity variable, we ﬁnd a cloud which is not too smooth. Further investigation shows that this cloud has a structure that might be overlooked if one is looking for the usual single-valued probability density function. The cloud is composed of an inﬁnite family of smooth ﬁbres, each of which describes the behaviour of the walk on an inﬁnite echo point class. The ﬁbres are individually smooth and so are naturally amenable to analysis with differential equations.

Christopher Essex, Matt Davison, Christian Schulzky, Astrid Franz, and Karl Heinz Hoffmann.
“The Differential Equation Describing Random Walks on the Koch Curve”.
In: J. Phys. A: Math. Gen. 34.41 (2001), pp. 8397–8406.
doi: 10.1088/0305-4470/34/41/301.
Consider a particle which is released at some point on a fractal and which moves about the fractal at random. Along standing goal has been to determine a differential equation governing the probability density function which describes this walk. As well as being interesting in its own right, this problem is thought to provide an insight into the problem of anomalous diffusion. Many attempts to derive such an equation have been made, all with limited success, perhaps because of the tension between smoothness required by differential equation tools and the lack of smoothness inherent in fractals. Here we present, for the ﬁrst time, the equation governing the random walk on a simple fractalthe Koch curve. We show that this equation makes computation of the probability density function for this problem a simple matter.

André Fachat.
“A Comparison of Random Walks with Different Types of Acceptance Probabilities”.
PhD Thesis. Chemnitz: Technische Universität Chemnitz, Mar. 2001.
In this thesis random walks similar to the Metropolis algorithm are investigated. Special emphasis is laid on different types of acceptance probabilities, namely Metropolis, Tsallis and Threshold Accepting. Equilibrium and relaxation properties as well as performance aspects in stochastic optimization are investigated. Analytical investigation of a simple system mimicking an harmonic oscillator yields that a variety of acceptance probabilities, including the abovementioned, result in an equilibrium distribution that is widely dominated by an exponential function. In the last chapter an optimal optimization schedule for the Tsallis acceptance probability for the idealized barrier is investigated.

Astrid Franz, Karl Heinz Hoffmann, and Peter Salamon.
“Best Possible Strategy for Finding Ground States”.
In: Phys. Rev. Lett. 86.23 (2001), pp. 5219–5222.
doi: 10.1103/PhysRevLett.86.5219.
Finding the ground state of a system with a complex energy landscape is important for many physical problems including protein folding, spin glasses, chemical clusters, and neural networks. Such problems are usually solved by heuristic search methods whose efficacy is judged by empirical performance on selected examples. We present a proof that, within the large class of algorithms that simulate a random walk on the landscape, threshold accepting is the best possible strategy. In particular, it can perform better than simulated annealing and Tsallis statistics. Our proof is the ﬁrst example of a provably optimal strategy in this area.

Astrid Franz, Christian Schulzky, and Karl Heinz Hoffmann.
“The Einstein relation for ﬁnitely ramiﬁed Sierpinski carpets”.
In: Nonlinearity 14.5 (2001), pp. 1411–1418.
doi: 10.1088/0951-7715/14/5/324.
Based on an analogy consideration between random walks and resistor networks it is shown that for a wide class of random walks on graphs resulting from ﬁnitely ramiﬁed Sierpinski carpets the Einstein relation is satisﬁed, which is an important equation relating conductivity and diffusivity. On fractal graphs this relation means, for instance, that a wide class of random walk algorithms including the blind and myopic ant random walks have the same random walk dimension.

Astrid Franz, Christian Schulzky, Sujata Tarafdar, and Karl Heinz Hoffmann.
“The pore structure of Sierpinski carpets”.
In: J. Phys. A: Math. Gen. 34.42 (2001), pp. 8751–8765.
doi: 10.1088/0305-4470/34/42/303.
In this paper, a new method is developed to investigate the pore structure of ﬁnitely and even inﬁnitely ramiﬁed Sierpinski carpets. The holes in every iteration stage of the carpet are described by a hole-counting polynomial. This polynomial can be computed iteratively for all carpet stages and contains information about the distribution of holes with different areas and perimeters, from which dimensions governing the scaling of these quantities can be determined. Whereas the hole area is known to be two dimensional, the dimension of the hole perimeter may be related to the random walk dimension.

Karl Heinz Hoffmann.
“Quantum thermodynamics”.
In: Ann. Physik 10.1–2 (2001), pp. 79–88.
doi: 10.1002/1521-3889(200102)10:1/2<79::AID-ANDP79>3.0.CO;2-3.
Quantum theory and thermodynamics are two important corner stones in our understanding of nature. In this paper we discuss a number of interesting topics where both ﬁelds interact starting from Max Planck’s introduction of the energy quantum to todays open questions about the validity of the second law in the quantum regime.

Karl Heinz Hoffmann and Michael Schreiber, eds.
Computational Physics.
Chinese Edition.
Berlin: Springer-Verlag, 2001.

Uwe Ḧubner, Steffen Seeger, and Karsten Petersen.
“Das CLiC-Projekt – Planung und Inbetriebnahme eines PC-Clusters”.
In: Praxis d. Inf. u. Komm. 24.2 (2001), pp. 75–84.
doi: 10.1515/PIKO.2001.75.

Gelein de Koeijer, Signe Kjelstrup, Peter Salamon, Gino Siragusa, Markus Schaller, and Karl Heinz Hoffmann.
“Comparison of Entropy Production Rate Minimization Methods for Binary Diabatic Tray Distillation”.
In: Proceedings of ECOS’01.
Ed. by A. ̈ Oztürk and Y. A. G̈og¯u¸s.
Istanbul, 2001,
Pp. 667–677.
doi: 10.1021/ie010872p.
The purpose of this study is to compare two analytical methods with two numerical methods for minimizing the entropy production rate in diabatic distillation columns (i.e. with heat exchangers on all trays). The ﬁrst analytical method is the Equal-Thermodynamic-Distance method. The second uses Lagrange minimization on a model derived from irreversible thermodynamics. The numerical methods use Powell’s and a Monte-Carlo algorithm and gave the same results. Both analytical methods agreed well with the numerical ones for two columns with low separation per tray, while they did not agree well for a column with large separation per tray.

Peter Salamon, Karl Heinz Hoffmann, Sven Schubert, R. Stephen Berry, and Bjarne Andresen.
“What conditions make minimum entropy production equivalent to maximum power production”.
In: J. Non-Equilib. Thermodyn. 26.1 (2001), pp. 73–83.
doi: 10.1515/JNETDY.2001.006.
Optimization of processes can yield a variety of answers, depending not only on the objective of the optimization but also on the constraints that deﬁne the problem. Within the context of thermodynamic optimization, the role of the constraints is particularly important because, among other things, their choice can make some objectives either equivalent or inequivalent, and can limit or broaden the possible kinds of processes one might choose. After a general discussion of the principles, a speciﬁc example of a model power plant is analyzed to see how the constraints govern the possible solutions.

Markus Schaller, Karl Heinz Hoffmann, Gino Siragusa, Peter Salamon, and Bjarne Andresen.
“Numerically optimized performance of diabatic distillation columns”.
In: Comput. Chem. Eng. 25.11–12 (2001), pp. 1537–1548.
doi: 10.1016/S0098-1354(01)00717-7.

Steffen Seeger, Astrid Franz, Christian Schulzky, and Karl Heinz Hoffmann.
“Random Walks on Finitely Ramiﬁed Sierpinski Carpets”.
In: Comp. Phys. Comm. 134.3 (2001), pp. 307–316.
doi: 10.1016/S0010-4655(00)00208-3.
A new algorithm is presented that allows an efficient computer simulation of random walks on ﬁnitely ramiﬁed Sierpinski carpets. Instead of using a bitmap of the n-th iteration of the carpet to determine allowed neighbour sites, neighbourhood relations are stored in small lookup tables and a hierarchical coordinate notation is used to give the random walker position. The resulting algorithm has low memory requirements, shows no surface effects even for extremely long walks and is well suited for modern computer architectures.

Sujata Tarafdar, Astrid Franz, Christian Schulzky, and Karl Heinz Hoffmann.
“Modelling porous structures by repeated Sierpinski carpets”.
In: Physica A 292.1-4 (2001), pp. 1–8.
doi: 10.1016/S0378-4371(00)00573-2.

Sergey A. Amelkin, Karl Heinz Hoffmann, Benoit Sicre, and Anatoly M. Tsirlin.
“Extreme performance of heat exchangers of various hydrodynamic models of ﬂows”.
In: Periodica Polytechnica Ser. Chem. Eng. 44.1 (2000), pp. 3–16.
The problem of minimization of entropy production is considered for one-pass heat exchangers of various types of description of hydrodynamic characteristics of the ﬂows. Two models of the ﬂows are considered, namely models of ideal mixing and ideal exclusion. The solution of the problem at issue allows one to construct a measure of thermodynamic perfectness of the heat exchanger taking into account the irreversibility of the heat exchange process.

Josef Maximilian Burzler, Peter Blaudeck, and Karl Heinz Hoffmann.
“Optimal Piston Paths for Diesel Engines”.
In: Thermodynamics of Energy Conversion and Transport.
Ed. by S. Stanislaw Sieniutycz and A. de Vos.
Berlin: Springer, 2000,
Pp. 173–198.
doi: 10.1007/978-1-4612-1286-7.
The performance of a Diesel engine is analysed for a model which includes losses due to mechanical friction and heat losses through the cylinder walls. Using the work output of the Diesel engine as an objective the optimal piston trajectories for the compression and power stroke are determined simultaneously. Results for a linear approximation of the heat leakage are compared to a more realistic, empirical heat transfer law due to Annand. Optimal operating conditions are found and discussed and signiﬁcant improvements in the engine’s efficiency relative to conventionally designed engines are obtained.

Chistohper Essex, Matt Davison, and Christian Schulzky.
“Numerical Monsters”.
In: SIGSAM Bulletin 34.4 (2000). snapshot in issue 134, pp. 16–32.
doi: 10.1145/377626.377635.

Christopher Essex, Christian Schulzky, Astrid Franz, and Karl Heinz Hoffmann.
“Tsallis and Rényi Entropies in Fractional Diffusion and Entropy Production”.
In: Physica A 284.1-4 (2000), pp. 299–308.
doi: 10.1016/S0378-4371(00)00174-6.

André Fachat, Karl Heinz Hoffmann, and Astrid Franz.
“Simulated annealing with Threshold Accepting or Tsallis statistics”.
In: Comp. Phys. Comm. 132.3 (2000), pp. 232–240.
doi: 10.1016/S0010-4655(00)00153-3.
Threshold Accepting and Tsallis statistics have shown good results when applied to optimization problems. In contrast to the Metropolis acceptance probability these two algorithms do not have detailed balance and also may have broken ergodicity. This makes it impossible to compute the equilibrium distribution analytically for general state spaces and neighborhood relations. In this paper we investigate the equilibrium properties of Threshold Accepting and Tsallis statistics numerically. For simple problems as a ladder of states both algorithms yield exponential functions as equilibrium probability distributions. However, as detailed balance does not hold, the neighborhood relation has an important inﬂuence on the resulting probability distribution. This is most obvious in systems with random energy values and random neighborhood structure.

A. Franz.
“Hausdorff dimension estimates for non-injective maps using the cardinality of the pre-image sets”.
In: Nonlinearity 13.5 (2000), pp. 1425–1438.
doi: 10.1088/0951-7715/13/5/301.

Astrid Franz, Christian Schulzky, Steffen Seeger, and Karl Heinz Hoffmann.
“An Efficient Implementation of the Exact Enumeration Method for Random Walks on Sierpinski Carpets”.
In: Fractals 8.2 (2000), pp. 155–161.
doi: 10.1142/S0218348X00000172.
In the following we present a highly efficient algorithm to iterate the master equation for random walks on effectively inﬁnite Sierpinski carpets, i.e. without surface effects. The resulting probability distribution can, for instance, be used to get an estimate for the random walk dimension, which is determined by the scaling exponent of the mean square displacement versus time. The advantage of this algorithm is a dynamic data structure for storing the fractal. It covers only a little bit more than the points of the fractal with positive probability and is enlarged when needed. Thus the size of the considered part of the Sierpinski carpet has not to be ﬁxed at the beginning of the algorithm. It is restricted only by the amount of available computer RAM. Furthermore all the information which is needed in every step to update the probability distribution is stored in tables. The lookup of this information is much faster compared to a repeated calculation. Hence, every time step is speeded up and the total computation time for a given number of time steps is decreased.

Christian Schulzky.
“Anomalous Diffusion and Random Walks on Fractals”.
http://archiv.tu-chemnitz.de/pub/2000/0070.
PhD Thesis. Chemnitz: Technische Universität Chemnitz, Aug. 2000.
In dieser Arbeit werden verschieden Ans̈atze diskutiert, die zum Verständnis und zur Beschreibung anomalen Diffusionsverhaltens beitragen, wobei insbesondere zwei unterschiedliche Aspekte hervorgehoben werden. Zum einen wird das Entropieproduktions-Paradoxon beschrieben, welches bei der Analyse der Entropieproduktion bei der anomalen Diffusion, beschrieben durch fraktionale Diffusionsgleichungen auftritt. Andererseits wird ein detaillierter Vergleich zwischen L̈osungen verallgemeinerter Diffusionsgleichungen mit numerischen Daten präsentiert, die durch Iteration der Mastergleichung auf verschiedenen Fraktalen produziert worden sind. Die Entropieproduktionsrate für superdiffusive Prozesse wird berechnet und zeigt einen unerwarteten Anstieg beim Übergang von dissipativer Diffusion zur reversiblen Wellenausbreitung. Dieses Entropieproduktions-Paradoxon ist die direkte Konsequenz einer anwachsenden intrinsischen Rate bei Prozessen mit zunehmendem Wellencharakter. Nach Berücksichtigung dieser Rate zeigt die Entropie den erwarteten monotonen Abfall. Diese Überlegungen werden für generalisierte Entropiedeﬁnitionen, wie die Tsallis- und Renyi-Entropien, fortgefhrt. Der zweite Aspekt bezieht sich auf die anomale Diffusion auf Fraktalen, im Besonderen auf Sierpinski-Dreiecke und -Teppiche. Die entsprechenden Mastergleichungen werden iteriert und die auf diese Weise numerisch gewonnenen Wahrscheinlichkeitsverteilungen werden mit den L̈osungen vier verschiedener verallgemeinerter Diffusionsgleichungen verglichen.

Christian Schulzky, Christopher Essex, Matt Davison, Astrid Franz, and Karl Heinz Hoffmann.
“The similarity group and anomalous diffusion equations”.
In: J. Phys. A: Math. Gen. 33.31 (2000), pp. 5501–5511.
doi: 10.1088/0305-4470/33/31/305.
A number of distinct differential equations, known as generalized diffusion equations, have been proposed to describe the phenomenon of anomalous diffusion on fractal objects. Although all are constructed to correctly reproduce the basic subdiffusive property of this phenomenon, using similarity methods it becomes very clear that this is far from sufficient to conﬁrm their validity. The similarity group that they all have in common is the natural basis for making comparisons between these otherwise different equations, and a practical basis for comparisons between the very different modelling assumptions that their solutions each represent. Similarity induces a natural space in which to compare these solutions both with one another and with data from numerical experiments on fractals. It also reduces the differential equations to (extra-) ordinary ones, which are presented here for the ﬁrst time. It becomes clear here from this approach that the proposed equations cannot agree even qualitatively with either each other or the data, suggesting that a new approach is needed.

Christian Schulzky, Astrid Franz, and Karl Heinz Hoffmann.
“Resistance Scaling and Random Walk Dimensions for Finitely Ramiﬁed Sierpinski Carpets”.
In: SIGSAM Bulletin 34.3 (2000), pp. 1–8.
doi: 10.1145/377604.377608.
We present a new algorithm to calculate the random walk dimension of ﬁnitely ramiﬁed Sierpinski carpets. The fractal structure is interpreted as a resistor network for which the resistance scaling exponent is calculated using Mathematica. A fractal form of the Einstein relation, which connects diffusion with conductivity, is used to give a numerical value for the random walk dimension.

Steffen Seeger and Karl Heinz Hoffmann.
“The cumulant method for computational kinetic theory”.
In: Continuum Mech. Thermodyn. 12 (2000), pp. 403–421.
doi: 10.1007/s001610050145.
We propose a new method for numerical simulation of gas dynamics based on kinetic theory. The method is based on a cumulant-expansion-ansatz for the phase space density, which leads to a set of quasi-linear, hyperbolic partial differential equations. The method is compared to the moment method of Grad. Both methods agree for low-order approximations but the method proposed shows additional non-linear terms for high order approximations. Boundary conditions on the cumulants for an ideally reﬂecting and an ideally rough boundary surface are derived from conditions on the phase space density. A Lax-method is used for numerical analysis of a 2d-BGK ﬂuid, which results in an easy-to-implement algorithm well suited for implementation on massivly parallel computers. The results are found to agree qualitatively with predictions from moment theories.

Peter Michael Sp̈ath.
“Renewed Theory, Interfacing, and Visualization of Thermal Lattice Boltzmann Schemes”.
PhD Thesis. copy Technische Universität Chemnitz, July 2000.
In this document the Lattice Boltzmann scheme, a heuristic method for the simulation of ﬂows in complicated boundaries, is investigated. Its theory is renewed by emphasizing the entropy maximization principle, andnew means for the modeling of geometries (including moving boundaries) and the visual representation of evoluting ﬂows are presented. An object oriented implementation is given with communication between objects realized by an interpreterobject and communication from outside realized via interprocess communication. Within the new theoretical approach the applicability of existing Lattice Boltzmann schemes to model thermal ﬂows for arbitrary temperatures is reexamined.

Karl Heinz Hoffmann.
“Slow relaxation dynamics – from spin glasses to stochastic optimization”.
In: Comp. Phys. Comm. 121-122.1-3 (1999), pp. 30–33.
doi: 10.1016/S0010-4655(99)00272-6.
Metastable systems such as spin glasses show a wealth of interesting relaxation phenomena. Stochastic optimization procedures such as simulated annealing help to solve a number of industrially important minimization problems. Here we show that the two ﬁelds are intimately connected by the thermally activated relaxation dynamics of complex energy landscapes. The numerical as well as the analytical tools to analyze it are discussed. Finally two applications, aging phenomena in spin glasses and adaptive simulated annealing procedures, are presented.

Arnulf M̈obius, Anastasio Diaz-Sanchez, Bernd Freisleben, Michael Schreiber, André Fachat, Karl Heinz Hoffmann, Peter Merz, and A. Neklioudov.
“Two physically motivated algorithms for combinatorial optimization: thermal cycling and iterative partial transcription”.
In: Comp. Phys. Comm. 121–122.1–3 (1999), pp. 34–46.
doi: 10.1016/S0010-4655(99)00273-8.
Among the various heuristic approaches to combinatorial optimization, local-search-based evolutionary algorithms have been particularly successful for the last years. We present two algorithms developed for jumping from local minimum to local minimum: Thermal cycling consists of cyclically heating and quenching by Metropolis and local search procedures, respectively, where the amplitude decreases during the process. Iterative partial transcription acts as a local search in the subspace spanned by the differing components of two approximate solutions corresponding to the relaxation of a spin glass by ﬂipping clusters. The high efficiency of the proposed procedures is illustrated for the traveling salesman problem.

Sven Schubert.
“Random Walks in Complex Systems – Anomalous Relaxation”.
see also http://archiv.tu-chemnitz.de/pub/1999/0017.
PhD Thesis. Chemnitz: Technische Universität Chemnitz, June 1999.
Goal of this work is the examination of the dynamics of complex systems. A central role play random walks, which are used to simulate anomalous relaxation in such systems. The complexity of the systems examined in this work is highly reﬂected in the state-space structure. After an introduction to different complex systems the algorithms are explained that play an important role in the exploration of the sometimes huge state-spaces. For the examination of the low-energy part of complex state-spaces a branch-and-bound algorithm is used. The simulation of dynamics is done by simulating random-walk processes and a statistical description by the master equation. A detailed description of different forms of the master equation and their solution is given. Important applications are simulations of random walks on fractals or hierarchical tree structures. Such simulations allow the comparison of experimental ﬁndings, e.g. for anomalous diffusion or non-equilibrium phenomena in spin-glasses. With such a modelling experimental results can be reproduced and understood. Another important contribution to the understanding of such processes is done by a newly developed algorithm for the coarse-graining of state-spaces.

R. Tafelmayer and Karl Heinz Hoffmann.
“Adaptive Schedules for Ensemble-Based Threshold Accepting”.
In: Appl. Math. Lett. 12.5 (1999), pp. 131–135.
doi: 10.1016/S0893-9659(99)00068-3.
We study numerically an adaptive schedule in the ensemble approach of threshold accepting by considering a traveling salesman problem. We ﬁnd that the probability for ﬁnding low lying minima is higher than in the widely used conventional exponential schedules. The algorithm is well suited for parallel implementations.

André Fachat and Karl Heinz Hoffmann.
Blocking vs. Non-blocking Communication under MPI on a Master-Worker Problem.
Tech. rep. SFB393/98-18.
copy: Technische Universität Chemnitz, 1998.
In this report we describe the conversion of a simple Master-Worker parallel program from global blocking communications to non-blocking communications. The program is MPI-based and has been run on different computer architectures. By moving the communication to the background the processors can use the former waiting time for computation. However we ﬁnd that the computing time increases by the time the communication time decreases in the used MPICH implementation on a cluster of workstations. Also using non-global communication instead of the global communication slows the algorithm down on computers with optimized global communication routines like the Cray T3D.

Astrid Franz.
“Hausdorff dimension estimates for invariant sets with an equivariant tangent bundle splitting”.
In: Nonlinearity 11.4 (1998), pp. 1063–1074.
doi: 10.1088/0951-7715/11/4/017.
Upper bounds for the Hausdorff dimension of compact and invariant sets of diffeomorphisms are given using a singular value function of the tangent map and the topological entropy under the assumption, that there exists an equivariant splitting of the tangent bundle. This improves previous results for compact uniformly hyperbolic sets of diffeomorphisms satisfying an additional pinching condition. Furthermore it is shown that the results can be extended to a special class of non-injective maps.

Karl Heinz Hoffmann, Christopher Essex, and Christian Schulzky.
“Fractional Diffusion and Entropy Production”.
In: J. Non-Equilib. Thermodyn. 23.2 (1998), pp. 166–175.
doi: 10.1515/jnet.1998.23.2.166.
The entropy production rate for fractional diffusion processes is calculated and shows an apparently counter-intuitive increase with the transition from dissipative diffusion behaviour to reversible wave propagation. This is deduced directly from invariant and non-invariant factors of the (probability) density function, arising from a group method applied to the fractional differential equation which exists between the pure wave and diffusion equations. However, the counter-intuitive increase of the entropy production rate within the transition turns out to be a consequence of increasing quickness of processes as the wave case is approached. When this aspect is removed the entropy shows the expected decrease with the approach to the reversible wave limit.

Thomas Klotz, Sven Schubert, and Karl Heinz Hoffmann.
“Coarse Graining of a spin-glass state space”.
In: J. Phys.: Condens. Matter 10.27 (1998), pp. 6127–6134.
doi: 10.1088/0953-8984/10/27/013.
The complex structure of a spin-glass state space can be simpliﬁed by a coarse-graining procedure, i.e. microscopic states being assembled into larger clusters. An algorithm for the coarse graining of the state space of a short-range Ising spin glass is provided, which is the basis of a coarse-grained dynamics. Different ways for modelling the transition rates in the coarse-grained state space are discussed. A comparison with the dynamics of the microscopic system shows that the dynamics in the coarse-grained state space gives an appropriate approximation.

Thomas Klotz, Sven Schubert, and Karl Heinz Hoffmann.
“Qunatitative analysis of the state-space structure in a short-range Ising spin glas”.
In: Rev. Mex. Fis. 44.S1 (1998), pp. 81–84.
The state space structure of a ﬁnite cubic Ising spin glass model with a uniform distribution of short-range interactions is analysed in detail. The global and different measures for the local state density are presented and discussed quantitatively. The comparison of these densities gives an interesting insight in the structure of the state space. In addition the density of local minima and it’s scaling behaviour is considered. The geometry of barriers in the system is investigated.

Thomas Klotz, Sven Schubert, and Karl Heinz Hoffmann.
“The state space of short-range Ising spin glasses: the density of states”.
In: Eur. Phys. J. B 2.3 (1998), pp. 313–317.
doi: 10.1007/s100510050254.
The state space of ﬁnite square and cubic Ising spin glass models is analysed in terms of the global and the local density of states. Systems with uniform and Gaussian probability distribution of interactions are compared. Different measures for the local state density are presented and discussed. In particular, the question whether the local density of states grows exponentially or not is considered. The direct comparison of global and local densities leads to consequences for the structure of the state space.

Ralph E. Kunz, Peter Blaudeck, Karl Heinz Hoffmann, and R. Stephen Berry.
“Atomic clusters and nanoscale particles: From coarse-grained dynamics to optimized annealing schedules”.
In: J. Chem. Phys. 108.6 (1998), pp. 2576–2582.
doi: 10.1063/1.475642.
An adaptive method is presented to optimize schedules for the simulated annealing of clusters and nanoscale particles. The method, based on both molecular-dynamics simulations and a set of master equations, is applied to a model conﬁguration space for which the exact optimal schedule can also be found. The adaptive method is demonstrably suitable for optimizing larger and more realistic systems than can be treated by an exact method, even one based on a statistical-sample master equation.

André Fachat and Karl Heinz Hoffmann.
“Implementation of Ensemble Based Simulated Annealing with Dynamic Load Balancing under MPI”.
In: Comp. Phys. Comm. 107.1–3 (1997), pp. 49–53.
doi: 10.1016/S0010-4655(97)00096-9.
This paper describes an implementation of Ensemble Based Simulated Annealing (EBSA) with dynamic load balancing. It is running under the MPI Message Passing Library allowing parallel execution on various types of computers. The load balancing is used to get maximum use of the available processing power, even on heterogeneous workstation clusters where the machines differ a lot in computing power.

K. H. Hoffmann, Sven Schubert, and Paolo Sibani.
“Age reinitialization in hierarchical relaxation models for spin-glass dynamics”.
In: Europhys. Lett. 38.8 (1997), pp. 613–618.
doi: 10.1209/epl/i1997-00292-4.
We show that thermal relaxation on a tree structure is reinitialized by a temperature pulse, similarly to the experimental behavior of spin-glasses. The models’ behavior originates from fast dynamical modes being excited – a mechanism which goes beyond the usual quasi-equilibrium description of slow relaxation based on the concept of a free-energy landscape. We demonstrate the excellent agreement of the model predictions with the thermoremanent magnetization experiments and discuss some of the implications of the results for the understanding of complex relaxation.

Karl Heinz Hoffmann, Josef Maximilian Burzler, and Sven Schubert.
“Endoreversible Thermodynamics”.
In: J. Non-Equilib. Thermodyn. 22.4 (1997), pp. 311–355.
All energy transformation processes occurring in reality are irreversible and in many cases these irreversibilities must be included in a realistic description of such processes. Endoreversible thermodynamics is a non-equilibrium approach in this direction by viewing a system as a network of internally reversible (endoreversible) subsystems exchanging energy in an irreversible fashion. All irreversibilities are conﬁned to the interaction between the subsystems. In this review a general framework for the endoreversible description of a system is presented, followed by a discussion of the performance of such systems. Thereafter the scope of the review is narrowed to time-independent stationary or cyclicly operating systems. We present the endoreversible theory of heat engines, and give an overview over the different heat transfer laws used in the entropy interactions between the subsystems. Also engine cycles different from the Carnot cycle and internal irreversibilities as well as the design optimization for such systems are discussed. These aspects are also important in the description of refrigerators and heat pumps which follows. Then combined and staged systems comprising several subsystems and their performance are reviewed and we conclude with a presentation of selected applications of endoreversible thermodynamics.

Arnulf M̈obius, A. Neklioudov, Anastasio Diaz-Sanchez, Karl Heinz Hoffmann, André Fachat, and Michael Schreiber.
“Optimization by thermal cycling”.
In: Phys. Rev. Lett. 79.22 (1997), pp. 4297–4301.
doi: 10.1103/PhysRevLett.79.4297.
An optimization algorithm is presented which consists of cyclically heating and quenching by Metropolis and local search procedures, respectively. It works partially well when it is applied to an archive of samples instead of to a single one. We demonstrate for the travelling salesman problem that this algorithm is far more efficient than usual simulated annealing; our implementation can compete concerning speed with recent, very fast genetic local search algorithms, and exhibits good scaling properties.

Peter Salamon, Jacob M. Pedersen, Paolo Sibani, and Karl Heinz Hoffmann.
“Ensemble Implementations of Simulated Annealing: A Modelling Approach”.
In: Math. Mod. and Scient. Comp. 7.1 (1997), pp. 28–37.
We address the problem of optimal ensemble size in simulated annealing algorithms by presenting some simple models which give insight into the dynamics of simulated annealing problems. We show that the presence of entrapment in these models leads to the conclusion that, for sufficiently large computational effort, the optimal ensemble size grows linearly with effort.

Paolo Sibani and Karl Heinz Hoffmann.
“Aging and relaxation dynamics in free-energy landscapes with multiple minima”.
In: Physica A 234 (1997), pp. 751–763.
doi: 10.1016/S0378-4371(96)00312-3.
We consider the stochastic dynamics of a system thermally relaxing in a free-energy landscape with multiple attractors, and show that lack of translational homogeneity in this landscape leads to aging effects, e.g. to the dependence of the susceptibilities on the time elapsed from a thermal quench to the imposition of the probing ﬁeld. We then prove an inequality between response and correlation which generalizes the ﬂuctuation dissipation theorem to a situation far from thermodynamical equilibrium. As an application and a check we specialize our formalism in a way which we suggest is appropriate for spin-glass systems: we assume a hierarchical organization of the landscape, and ﬁnd aging behavior in the response curves in good agreement with relevant experimental data. We ﬁnally conclude with a summary and a brief discussion of different approaches to slow relaxation in complex systems.

Karl Heinz Hoffmann.
“Metastable Systems and Stochastic Optimization”.
In: Computational Physics.
Ed. by Karl Heinz Hoffmann and Michael Schreiber.
Berlin, Heidelberg, New-York: Springer-Verlag, 1996,
Pp. 44–63.
doi: 10.1007/978-3-642-85238-1_4.
Metastable systems such as spin glasses show a wealth of interesting relaxation phenomena. Stochastic optimization procedures such as simulated annealing help to solve a number of industrially important minimization problems. Here we show that the two ﬁelds are intimately connected by the thermally activated relaxation dynamics of complex energy landscapes. The numerical as well as the analytical tools to analyse it are discussed. Finally two applications, aging phenomena in spin glasses and adaptive simulated annealing procedures, are presented.

Karl Heinz Hoffmann and Michael Schreiber, eds.
Computational Physics.
Berlin, Heidelberg, New-York: Springer-Verlag, 1996.
doi: 10.1007/978-3-642-85238-1.

Peter Blaudeck and Karl Heinz Hoffmann.
“Optimization of the Power Output for the Compression and Power Stroke of the Diesel Engine”.
In: Efficiency, Costs, Optimization and Environmental Impact of Energy Systems.
Ed. by Y. A. G̈og¯u¸s, A. ̈ Oztürk, and G. Tsatsaronis.
Vol. 2.
Proceedings of the ECOS95 Conference.
International Centre for applied Thermodynamics (ICAT). Istanbul: ICAT, 1995,
P. 754.
For the Diesel engine the compression stroke and the power stroke are optimized to get the maximum power output. Contrary to previous papers the important heat transfer is completely taken into account. For both cases with and without constraints in piston acceleration a signiﬁcant improvement of the efficiency in comparison with the conventional engine is found.

Klaus Ergenzinger, Karl Heinz Hoffmann, and Peter Salamon.
“Optimal Simulated Annealing Schedules for Self Similar Systems”.
In: J. Appl. Phys. 77.11 (1995), pp. 5501–5508.
doi: 10.1063/1.359253.
The successful application of the stochastic optimization method known as simulated annealing can depend very much on the appropriate annealing schedule. While determining optimal schedules for arbitrary complex optimization problems is beyond the current scope, we here determine optimal schedules for a special class of systems with known properties. The state spaces of these special systems have the structure of self similar trees. Using methods of optimal control theory, we are able to predict the optimal schedule analytically for two distinct optimization criteria. These predictions are shown to be in good agreement with numerical results.

R. Tafelmayer and Karl Heinz Hoffmann.
“Scaling features in complex optimization problems”.
In: Comp. Phys. Comm. 86 (1995), pp. 81–90.
doi: 10.1016/0010-4655(95)00004-Y.
We study the scaling behaviour in the ensemble approach of simulated annealing and threshold accepting considering two examples of complex optimization problems, namely the Grötschel’s traveling salesman problem and a spin glass problem with Gaussian distribution of the couplings. If scaling is present it should allow for an estimation of the ground state energy. Our numerical results show a different qualitative behaviour for the two kinds of problems. Whereas scaling is present in the spin glass problem it is widely absent in the traveling salesman problem.

C. Uhlig, Karl Heinz Hoffmann, and Paolo Sibani.
“Relaxation in Self Similar Hierarchies”.
In: Z. Phys. B 96 (1995), pp. 409–416.
doi: 10.1007/BF01313064.
We investigate in some detail the relaxation process in self similar hierarchies. We ﬁnd that the process can be divided in four different time regimes. After an initial phase in which the connectivity of the hierarchy determines the relaxation, the system enters a kind of stationary state, which can be accurately described by a simple analytical sink-picture. At longer times the behavior of the process is correctly described by the idea of quasiequilibrium. In this regime, propagators decay with power-laws. Finally, the global equilibrium state is reached, and the evolution stops.

Karl Heinz Hoffmann.
“Optimal control theory and irreversible thermodynamics”.
In: Period. Polytechn. 2 (1994), p. 15.

Michael Christoph and Karl Heinz Hoffmann.
“Scaling behaviour of optimal simulated annealing schedules”.
In: J. Phys. A: Math. Gen. 26.13 (1993), pp. 3267–3277.
doi: 10.1088/0305-4470/26/13/028.
The success of simulated annealing depends strongly upon the choice of a suitable annealing schedule. For a class of small sample systems the optimal annealing schedules are determined. They show distinct scaling behaviour as a function of the number of Metropolis steps carried out at each temperature of the schedule. This behaviour can be traced back to the inﬂuence of dominating barriers during cooling. Knowing the optimal schedule for a few different total annealing steps allows to predict the optimal annealing schedule for intermediate times.

Karl Heinz Hoffmann.
“Optimizing Irreversible Thermodynamic Processes”.
In: Statistical physics and thermodynamics of nonlinear nonequilibrium systems.
Ed. by W. Ebeling and W. Muschik.
invited contribution.
Singapore: World-Scientiﬁc Publishing Co., 1993,
Pp. 109–120.
Often ideal thermodynamic processes and the limits for process variables derived from them are compared to real industrial processes. But sometimes these are too far from equilibrium to be considered reversible, and thus the irreversibilities have to be taken into account to obtain a more realistic description. Then the question arises whether one can determine process limits and accompanying process paths for these irreversible processes. This paper addresses this question by means of two examples, one using a classical macroscopic thermodynamic description while the other uses statistical concepts: The ﬁrst example deals with internal combustion engines and the second with simulated annealing. For both examples optimal process paths are determined.

Karl Heinz Hoffmann, Thomas Meintrup, C. Uhlig, and Paplo Sibani.
“Linear-Response Theory for Slowly Relaxing Systems”.
In: Europhys. Lett. 22.8 (1993), pp. 565–570.
doi: 10.1209/0295-5075/22/8/002.
Slowly relaxing systems as spin glasses below the transition temperature are far from thermal equilibrium on experimental time scales. Nontheless experiments suggest the applicability of the ﬂuctuation dissipation theorem out of equilibrium. To test this suggestion, we ﬁrst derive the non-equilibrium response and correlation function for a large class of marcovian relaxation dynamics obeying detailed balance. We ﬁnd that there exist no dynamics where the corrections to the FDT vanish exactly. Applying the formalism to a speciﬁc model, we then ﬁnd that the corrections remain small in agreement with the experiments.

Claas De Groot, Diethelm Ẅurtz, and Karl Heinz Hoffmann.
“Low Autocorrelation Binary Sequences: Exact Enumeration and Optimization by Evolution Strategies”.
In: Optimization 23 (1992), pp. 369–384.
doi: 10.1080/02331939208843771.

Claas de Groot, Diethelm Ẅurtz, and Karl Heinz Hoffmann.
“Optimizing Complex Problems by Nature’s Algorithms: Simulated Annealing and Evolution Strategy – a Comparative Study”.
In: Parallel Problem Solving from Nature.
Ed. by H.-P. Schwefel and R. Maenner.
copy, copy of the preprint version: Springer-Verlag, Berlin, 1991,
Pp. 445–454.
doi: 10.1007/BFb0029786.
We compare two optimization algorithms which glean their heuristics from nature: simulated annealing and evolution strategy. These algorithms are applied to difficult optimization problems: ﬁnding binary sequences with low autocorrelation, calculating ground states of certain spin glass Hamiltonians, and giving the optimal tour in a traveling salesman problem. Our ﬁndings show a problem dependence of the quality of the results. Because of fundamental difficulties in the judgement of the algorithms’ quality no ﬁnal conclusions can be drawn, but the comparison gives valuable insight in the behaviour of the algorithms.

Karl Heinz Hoffmann, Michael Christoph, and Martin Hanf.
“Optimizing Simulated Annealing”.
In: Parallel Problem Solving from Nature.
Ed. by H.-P. Schwefel and R. Maenner.
Berlin: Springer-Verlag, 1991,
Pp. 221–225.
doi: 10.1007/BFb0029756.
This paper reviews efforts towards optimizing simulated annealing. In particular we address the question of the optimal schedule and of how estimates of system properties needed in optimizing simulated annealing can be obtained. We describe the ensemble approach to simulated annealing which lends itself readily to the implementation on parallel and vector computers and which thus leads to improved adaptive schedules.

Karl Heinz Hoffmann and Peter Salamon.
“Simulated Annealing for Single Minimum Optimization Problems”.
In: Internat. J. Computer Math. 39 (1991), pp. 193–204.
doi: 10.1080/00207169108803991.
Two examples are presented which show that simulated annealing can perform better than quenching and steepest descent even on problems with a single minimum. An implication for real global optimization problems is that simulated annealing can be useful even on time scales which are short compared to the time required for a greedy algorithm to reach the nearest local minimum.

Karl Heinz Hoffmann, Diethelm Ẅurtz, Class de Groot, and Martin Hanf.
“Concepts in optimizing simulated annealing schedules: an adaptive approach for parallel and vector machines”.
In: Parallel and Distributed Optimization.
Ed. by M. Grauer and D. B. Pressmar.
Berlin, Heidelberg, New-York: Springer-Verlag, 1991,
Pp. 154–175.
doi: 10.1007/978-3-642-95665-2_10.
Simulated Annealing (̌Cemy 1983, Kirkpatrick et al. 1983) is a technique which allows to ﬁnd optimal or near optimal solutions to difficult optimization problems. It has been especially successful in applications to NP-complete or NP-hard problems, which occur in a variety of ﬁelds (Garey and Johnson 1979). These include mathematics with many graph problems (e.g. Brelaz 1979, Bonomi and Lutton 1987, Andresen et al. 1988), condensed matter physics, e.g. with the problem of ﬁnding the ground state of spin glasses (Ettelaie and Moore 1985), with the problem of solving the Ginzberg-Landau equations (Doria et al. 1989), engineering problems with the design of integrated circuits including the partitioning as well as the wiring problem (Vecchi and Kirkpatrick 1983, Sechen and Sangiovanni-Vincentelli 1985, Siarry et al. 1987), the design of binary sequences with low autocorrelation (Beenker et al. 1985, Bernasconi 1987, 1988), image processing (Carnevali et al. 1985), design of X-ray mirrors (Ẅurtz and Schneider 1989), statistics with the application as a learning paradigm in neural network theory (Bernasconi 1990) and economics for instance with the travelling salesman problem (e.g. Bonomi and Lutton 1984, Kirkpatrick and Toulouse 1985, Hanf et al. 1990). Naturally, these are only some selected examples, since it is not possible here to give reference to the few hundred simulated annealing papers which appeared during the last years.

C. Schulze, Karl Heinz Hoffmann, and Paolo Sibani.
“Aging Phenomena in Complex Systems: A Hierarchical Model for Temperature Step Experiments”.
In: Europhys. Lett. 15.3 (1991), pp. 361–366.
doi: 10.1209/0295-5075/15/3/022.
We show that a previously introduced hierarchical model for relaxation in spin glasses and other complex systems, which described successfully the aging behaviour in the time domain, can also account for the effects of temperature changes on the magnetic response of the sample.

Paolo Sibani and Karl Heinz Hoffmann.
“Relaxation in Complex Systems: Local Minima and their Exponents”.
In: Europhys. Lett. 16.5 (1991), p. 423.
doi: 10.1209/0295-5075/16/5/002.

Claas de Groot, Diethelm Ẅurtz, and Karl Heinz Hoffmann.
“Simulated Annealing and Evolution Strategy – a Comparison”.
In: Helv. Phys. Acta 63 (1990), p. 843.
We compare two optimization algorithms which glean their heuristic from nature: simulated annealing and evolution strategy. These algorithms are applied to two different difficult optimization problems which present themselves in a physical context as calculations of ground states with respect to certain Hamitonians. Our two Hamiltonians belong to short range two dimensional spin glasses and an autocorrelation funtion on a linear binary sequence which can be considered as a chain of long range interacting spins. Our results show a problem dependence of the behavior of the algorithms. While simulated annealing performs slightly better in the case of spin glasses, our evolution strategy for the autocorrelation function ﬁnds better results than ever obtained by other stochastic methods.

Martin Hanf, Yves Lehareinger, Diethelm Ẅurtz, Karl Heinz Hoffmann, Claas de Groot, and Max Anliker.
Implementation of a New Adaptive Simulated Annealing Schedule on a Multi Transputer System.
Technical Report 90-13–21.
IPS Research Report.
CH-8092 Z̈urich, Switzerland: IPS, ETH Z̈urich, 1990.
Simulated annealing is known to be a widely applicable optimization procedure from theoretical physics. We present an adaptive algorithm to optimize the annealing schedule using an ensemble approach. This approach is well-suited for a parallel computer. We give details of an implementation on a 32 transputer farm. We also compared this code to results obtained on other machines by applying them to the 532-city travelling salesman problem of Padberg and Rinaldi.

Karl Heinz Hoffmann.
“Optima and Bounds for Irreversible Thermodynamic Processes”.
In: Finite-Time Thermodynamics and Thermoeconomics, Advances in Thermodynamics 4.
Ed. by Stanislaw Sieniutycz and Peter Salamon.
New York: Taylor and Francis, 1990,
Pp. 22–65.
In this paper bounds and optima for irreversible thermodynamic processes and their application in different ﬁelds are discussed. The tools of ﬁnite time thermodynamics are presented and especially optimal control theory is introduced. These methods are applied to heat engines, including models of the Diesel engine and a light-driven engine. Further bounds for irreversible processes are introduced, discussing work deﬁciency and its relation to thermodynamic length. Moreover the problem of dissipation in systems composed of several subsystems is studied. Finally, the methods of ﬁnite time thermodynamics are applied to thermodynamic processes described on a more microscopic level. The process used as an example is simulated annealing. It is shown how optimal control theory is applied to ﬁnd the optimal cooling schedule for this important stochastic optimization method

Karl Heinz Hoffmann and Peter Salamon.
“The Optimal Simulated Annealing Schedule for a Simple Model”.
In: J. Phys. A: Math. Gen. 23 (1990), pp. 3511–3523.
doi: 10.1088/0305-4470/23/15/023.
Used as a tool for large scale global optimization, simulated annealing incurs heavy computational costs. Therefore, choosing an optimal cooling schedule is of great scientiﬁc and economic importance. For the ﬁrst time an analytic as well as a numeric solution to this problem is presented, albeit only for a small example system. The example shows the role of optimal control theory for this problem.

Karl Heinz Hoffmann and Paolo Sibani.
“Relaxation and aging in spin glasses and other complex systems”.
In: Z. Phys. B 80 (1990), pp. 429–438.
doi: 10.1007/BF01323526.
We describe how a hierachical model of spin glass relaxation can display aging behaviour, similarly to what is found in spin glasses and other complex systems out of thermodynamic equilibrium. Since we deal with a nonequilibrium situation, the usualF(luctuation)D(issipation)T(heory) does not apply. We therefore derive a general relation between the linear response function and the non equilibrium propagator of the unperturbed system. The relation is shown to be very similar to the equilibrium FDT under certain conditions, which one can reasonably assume for spin glass systems. Having thus related the linear response of the system to a small external ﬁeld to the autocorrelation function of the magnetization, we calculate the latter quantity by a master equation on a set of states which have the topology of a tree. The model can reproduce the main qualitative features of theZ(ero)F(ield)C(ooled) spin glass experiments, i.e. the maximum in the logarithmic time derivative of the magnetization, with only two free parameters.

Karl Heinz Hoffmann, Paolo Sibani, Jacob M. Pedersen, and Peter Salamon.
“Optimal Ensemble Size for Parallel Implementations of Simulated Annealing”.
In: Appl. Math. Lett. 3.3 (1990), pp. 53–56.
doi: 10.1016/0893-9659(90)90136-Y.
We determine the optimal ensemble size for a simulated annealing based on assumptions about scaling properties of the system dynamics and of the density of states in the low energy regime. The derivations indicate the optimal annealing time for any one ensemble member, thereby providing a stopping criterion and an explanation for the ”brick wall effect”.

Paolo Sibani, Jacob M. Pedersen, Karl Heinz Hoffmann, and Peter Salamon.
“Monte Carlo dynamics of optimization problems: A scaling description”.
In: Phys. Rev. A 42.12 (1990), pp. 7080–7086.
doi: 10.1103/PhysRevA.42.7080.
We show that some hard optimization problems studied by Monte Carlo methods, such as simulated annealing, have features that can be estimated by a statistical analysis of the data, well before being actually observed. This applies, for instance, to the estimation of the ground-state energy of the problem. We start by showing that the density of states and the distribution of extremes of energy seen in a given time interval in the Monte Carlo dynamics of combinatorial optimization problems are strongly related to each other through the ﬁrst-passage-time distribution of the stochastic dynamics of the system. We then introduce a scaling ansatz for this last quantitiy, which allows an estimate of the ground state energy. Finally, we demonstrate the method on a travaling-salesman problem with know ground state energy and apply it to the simulated annealing of a graph-bipartitioning problem.

Karl Heinz Hoffmann, Bjarne Andresen, and Peter Salamon.
“Measures of Dissipation”.
In: Phys. Rev. A 39 (1989), pp. 3618–3621.
doi: 10.1103/PhysRevA.39.3618.

Paolo Sibani and Karl Heinz Hoffmann.
“Hierarchical models for aging and relaxation of spin glasses”.
In: Phys. Rev. Lett. 63.26 (1989), pp. 2853–2856.
doi: 10.1103/PhysRevLett.63.2853.
We show that the aging phenomena found in spin glasses and other complex systems can be reproduced by a hierarchical model of relaxation.

Stanley J. Watowich, Karl Heinz Hoffmann, and R. Stephen Berry.
“Optimal Paths for a Bimolecular, Light-Driven Engine”.
In: Il Nuovo Cim. B 104.2 (1989), pp. 131–147.
doi: 10.1007/BF02906311.

Bjarne Andresen, Karl Heinz Hoffmann, Klaus Mosegaard, Jim Nulton, Jacob M. Pedersen, and Peter Salamon.
“On lumped models for thermodynamic properties of simulated annealing problems”.
In: J. Phys. 49 (1988), pp. 1485–1492.
doi: 10.1051/jphys:019880049090148500.
The paper describes a new method for the estimation of thermodynamic properties for simulated annealing problems using data obtained during a simulated annealing run. The method works by estimating energy-to-energy transition probabilities and is well adapted to simulations such as simulated annealing, in which the system is never in equlibrium.

Karl Heinz Hoffmann.
“Bounds and Optima for Irreversible Thermodynamic Processes and their Application to Simulated Annealing”.
Habilitationsschrift. Heidelberg: Ruprecht-Karls-Universität, Dec. 1988.

Karl Heinz Hoffmann and Paolo Sibani.
“Diffusion in Hierarchies”.
In: Phys. Rev. A 38.8 (1988), pp. 4261–4270.
doi: 10.1103/PhysRevA.38.4261.
In this paper we show that diffusion processes in a ’complex’ phase space with many local minima can be mapped into a random walk problem on a tree structure. We then rigorously solve the latter problem for regular trees, under the quite general assumption about the rates. Finally, we extend our results to the case of inhomogenious trees.

Karl Heinz Hoffmann and Natalia Meshkov.
“A Problem From Empirical Economics II: Determining Uncertainties Arising From Incomplete Data Using Information Theory”.
In: Renewable Energy 9 (1987), pp. 259–273.
doi: 10.1016/0165-0572(87)90005-3.
Information theory is used to extract numerical values for quantities that are not directly available in existing data sources, but occur as linear combinations of other quantities for which data exist. The method uses known data to construct a distribution for the unknown quantities, which minimizes the Shannon information; hence, mean values and mean deviations for the unknowns can also be calculated. The results of an approach based on information theory are compared with the results obtained by another method.

Karl Heinz Hoffmann and Peter Salamon.
“Lower Bounds on Dissipation in Composite Systems”.
In: Phys. Rev. A 35 (1987), pp. 369–373.
doi: 10.1103/PhysRevA.35.369.
The dissipation inherent in the time evolution of a composite system consisting of a number of subsystems is characterized. We present two thermodynamic quantities which serve as general lower bounds to the minimum entropy production in a composite system. These lower bounds are easier to compute than the minimum entropy production and the difference between the bounds and the minimum entropy production quantiﬁes a mismatch in the coevolution of subsystems. This mismatch has important implications for process control and design.

B. Neudecker and Karl Heinz Hoffmann.
“Electrical Potential and current distribution for the quantized Hall effect”.
In: Solid State Commun. 62.3 (1987), pp. 135–139.
doi: 10.1016/0038-1098(87)90177-3.

Paolo Sibani and Karl Heinz Hoffmann.
“Random Walks on Cayley Trees: Temperature-Induced Transience-Recurrence Transition, Small Exponents and Logarithmic Relaxation”.
In: Europhys. Lett. 4.9 (1987), pp. 967–972.
doi: 10.1209/0295-5075/4/9/003.
Random walks on tree structures are as useful tools in physics as they are interesting themselves. Here we show that for a certain class of models they can undergo a transition from being recurrent to being transient depending on the temperature. At the transition the relaxation is logarithmic. The signiﬁcance of the pole in the relaxation exponent is also discussed.

Karl Heinz Hoffmann and B. Neudecker.
“Fractional quantized Hall effect on a model with shortranged interaction in a sphere”.
In: Z. Phys. B 62 (1986), pp. 279–285.
doi: 10.1007/BF01313448.
We consider a model forN electrons conﬁned to the surface of a sphere in a strong radial magnetic ﬁeld. The electron-electron interaction is modelled as a simple hardcore like repulsion. Numerical calculations have been carried out for up to N=6, neglecting contributions from higher Landau levels. Spectral properties of low-lying states are discussed within the quasihole-quasiparticle picture.

Siegfried Grossmann, Franz Wegner, and Karl Heinz Hoffmann.
“Anomalous Diffusion on a Selfsimilar Hierarchical Structure”.
In: J. Phys. Lett. France 46.13 (1985), pp. L575–L583.
doi: 10.1051/jphyslet:019850046013057500.

Karl Heinz Hoffmann, Siegfried Grossmann, and Franz Wegner.
“Random Walk on a Fractal: Eigenvalue Analysis”.
In: Z. Phys. B 60.2-4 (1985), pp. 401–414.
doi: 10.1007/BF01304462.
The eigenvalues of the master equation describing the motion on a nested hierarchy of $d$ -dimensional intervals with selfsimilar scaling of spatial extension as well as of the level dependent transition rates are derived. Based on this spectrum the diffusion behaviour is obtained, which is anomalous, either exponential or obeying a power law with various exponents. Emphasis is put on the insight into the mechanism of the anomalous diffusion, in particular the geometrical structure of the decay rate spectrum.

Karl Heinz Hoffmann, Stanley J. Watowich, and R. Stephen Berry.
“Optimal Paths for Thermodynamic Systems: The Ideal Diesel Cycle”.
In: J. Appl. Phys. 58.6 (1985), pp. 2125–2134.
doi: 10.1063/1.335977.
Optimal control theory is used to determine the piston trajectory which yields maximum power output for a model which incorporates the Diesel engine’s major irreversibilities. Optimal trajectories were obtained for the cases of unconstrained piston acceleration. Optimizing the path four our standard engine increased both the net work output per cycle and the net efficiency by about 10%.

Stanley J. Watowich, Karl Heinz Hoffmann, and R. Stephen Berry.
“Intrinsically Irreversible Light-Driven Engine”.
In: J. Appl. Phys. 58 (1985), pp. 2893–2901.
doi: 10.1063/1.336281.
We examine a reciprocating heat engine which necessarily operates far from equilibrium and about an unstable steady state. The piston of the engine is driven by the nonlinear coupling of the working ﬂuid to an external light source which provides high quality heat and to the environment into which waste heat is dumped. We determine the piston trajectories that optimize two different criteria of process performance, the maximization of work output, and the minimization of entropy production. The trajectories optimizing different performance goals are qualitatively different. In engines not dominated by friction losses, the cycle optimizing work output requires that the expansion stroke begins with a slight compression and the temperature of the working ﬂuid increases brieﬂy.

Karl Heinz Hoffmann.
“Die Hopfbifurkation unter dem Einﬂuß von weißem Rauschen”.
in German.
PhD Thesis. RWTH Aachen, 1982.

Karl Heinz Hoffmann.
“The Birkhoff Normalization Procedure and the Reductive Perturbation Approach: Two equivalent Methods to Discuss the Hopf Bifurcation”.
In: Phys. Lett. A 92.4 (1982), pp. 163–164.
doi: 10.1016/0375-9601(82)90522-9.
It is shown that the reductive perturbation approach yields exactly the same dynamical equations for systems with a small deviation of the control parameter from the onset of the Hopf bifurcation as the Birkhoff normalization procedure with an additional expansion with respect to this deviation.

Karl Heinz Hoffmann.
“The Hopf Bifurcation of Twodimensional Systems under the Inﬂuence of One External Noise Source”.
In: Z. Phys. B 49 (1982), pp. 245–252.
doi: 10.1007/BF01313033.
The behaviour of the Hopf bifurcation under the inﬂuence of external noise is investigated by means of a twodimensional model which uses Gaussian white noise as input. The model includes the case of multiplicative and/or additive noise. Applying the Birkhoff transformation the model is transformed to the coordinates normally used to discuss the deterministic Hopf bifurcation. Then the stationary solution of the model is calculated as an expansion for weak noise: The Hopf bifurcation under the inﬂuence of noise exhibits a bifurcation interval with width and position depending on the noise power. Moreover, a class of the systems described by the model can perform noise driven bifurcations.

Karl Heinz Hoffmann.
“Stationäre L̈osungen stochastischer Bewegungsgleichungen und ihr Zusammenhang mit der deterministischen Dynamik”.
in German.
Diplomarbeit. RWTH Aachen, 1979.

Karl Heinz Hoffmann.
“K-Isomorphie und K-̈Aquivalenz von Ordnungen”.
in German.
Diplomarbeit. RWTH Aachen, 1978.