Schüttler Computer Simulation Studies in Condensed-Matter Physics XVII

Proceedings of the Seventeenth Workshop, Athens, GA, USA, February 16-20, 2004
1. Auflage 2006
ISBN: 978-3-540-26565-8
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 277 Seiten

Over ?fteen years ago, because of the tremendous increase in the power and utility of computer simulations, The University of Georgia formed the ?rst institutional unit devoted to the use of simulations in research and teaching: The Center for Simulational Physics. As the international simulations c- munityexpandedfurther,wesensedaneedforameetingplaceforbothex- riencedsimulatorsandneophytestodiscussnewtechniquesandrecentresults in an environment which promoted lively discussion. As a consequence, the Center for Simulational Physics established an annual workshop on Recent DevelopmentsinComputerSimulationStudiesinCondensedMatterPhysics. This year's workshop was the seventeenth in this series, and the continued interest shown by the scienti?c community demonstrates quite clearly the useful purpose that these meetings have served. The latest workshop was held at The University of Georgia, February 16-20, 2004, and these proce- ings provide a 'status report' on a number of important topics. This volume is published with the goal of timely dissemination of the material to a wider audience. We wish to o?er a special thanks to IBM and to SGI for partial support of this year's workshop. This volume contains both invited papers and contributed presentations on problems in both classical and quantum condensed matter physics. We hope that each reader will bene?t from specialized results as well as pro?t from exposure to new algorithms, methods of analysis, and conceptual dev- opments.

Autoren/Hrsg.

Schüttler, Heinz-Bernd

Inhaltsverzeichnis

1;Preface;6
2;Contents;7
3;Systems out of Equilibrium;11
4;1 Computer Simulation Studies in Condensed Matter Physics: An Introduction;12
5;Part I Systems out of Equilibrium;18
5.1;2 Shake, Rattle or Roll: Things to do with a Granular Mixture on a Computer;18
5.1.1;2.1 Introduction;18
5.1.2;2.2 Simulation Methodology;19
5.1.3;2.3 Chute Flow;21
5.1.4;2.4 Brazil-Nut E.ect;22
5.1.5;2.5 Granular Ratchet;23
5.1.6;2.6 Rotating Cylinder – Axial Segregation;25
5.1.7;2.7 Rotating Cylinder – Radial Segregation;27
5.1.8;2.8 Horizontally vibrated layer;27
5.1.9;2.9 Conclusion;29
5.1.10;References;29
5.2;3 A New Method of Investigating Equilibrium Properties from Nonequilibrium Work;30
5.2.1;3.1 Introduction;30
5.2.2;3.2 Method;30
5.2.3;3.3 Application for Lennard–Jones System;32
5.2.4;3.4 Summary and Discussion;34
5.2.5;References;35
5.3;4 Numerical Simulations of Critical Dynamics far from Equilibrium;36
5.3.1;4.1 Introduction;36
5.3.2;4.2 Short-Time Dynamic Scaling Form;38
5.3.3;4.3 Applications of Short-Time Dynamic Scaling;41
5.3.4;4.4 Numerical Solutions of Deterministic Dynamics;48
5.3.5;4.5 Conclusions;50
5.3.6;References;51
6;Part II Soft and Disordered Materials;55
6.1;5 Entropy Driven Phase Separation;56
6.1.1;5.1 Introduction;56
6.1.2;5.2 Grand Canonical Monte Carlo;58
6.1.3;5.3 Cluster Moves;60
6.1.4;5.4 Detailed Balance;61
6.1.5;5.5 Ergodicity;64
6.1.6;5.6 Early Rejection Scheme;65
6.1.7;5.7 Application;65
6.1.8;5.8 Conclusions;69
6.1.9;5.9 Appendix: Random Points;69
6.1.10;References;70
6.2;6 Supercooled Liquids under Shear: Computational Approach;72
6.2.1;6.1 Introduction;72
6.2.2;6.2 Simulation Method;73
6.2.3;6.3 Simulation Results;75
6.2.4;6.4 Conclusions;81
6.2.5;References;83
6.3;7 Optimizing Glasses with Extremal Dynamics;85
6.3.1;References;89
6.4;8 Stochastic Collision Molecular Dynamics Simulations for Ion Transfer Across Liquid – Liquid Interfaces;91
6.4.1;8.1 Introduction;91
6.4.2;8.2 Potential-energy Surface;91
6.4.3;8.3 Simulations of Ion Transfer;92
6.4.4;8.4 Conclusions;94
6.4.5;References;95
7;Part III Biological Systems;97
7.1;9 Generalized-Ensemble Simulations of Small Proteins;98
7.1.1;References;100
7.2;10 A Biological Coevolution Model with Correlated Individual- Based Dynamics;101
7.2.1;10.1 Introduction;101
7.2.2;10.2 Model;101
7.2.3;10.3 The Interaction Matrix;102
7.2.4;10.4 Simulation Results;103
7.2.5;References;105
7.3;11 An Image Recognition Algorithm for Automatic Counting of Brain Cells of Fruit Fly;106
7.3.1;11.1 Introduction;106
7.3.2;11.2 Data;107
7.3.3;11.3 Counting Algorithm;107
7.3.4;11.4 Results;109
7.3.5;References;110
7.4;12 Preferred Binding Sites of Gene- Regulatory Proteins Based on the Deterministic Dead-End Elimination Algorithm;111
7.4.1;12.1 Introduction;111
7.4.2;12.2 Numerical Methods;112
7.4.3;12.3 Results and Discussion;114
7.4.4;References;116
8;Part IV Algorithms and Methods;119
8.1;13 Geometric Cluster Algorithm for Interacting Fluids;120
8.1.1;13.1 Introduction and Motivation;120
8.1.2;13.2 Cluster Monte Carlo Algorithms;121
8.1.3;13.3 Generalized Geometric Cluster Algorithm;122
8.1.4;13.4 Performance;126
8.1.5;13.5 Illustration;131
8.1.6;13.6 Conclusion and Outlook;131
8.1.7;References;132
8.2;14 Polymer Simulations with a Flat Histogram Stochastic Growth Algorithm;133
8.2.1;14.1 Introduction;133
8.2.2;14.2 The Algorithm;136
8.2.3;14.3 Simulations;141
8.2.4;14.4 Conclusion and Outlook;146
8.2.5;References;146
8.3;15 Convergence of the Wang – Landau Algorithm and Statistical Error;147
8.3.1;References;152
8.4;16 Wang–Landau Sampling with Cluster Updates;153
8.4.1;16.1 Introduction;153
8.4.2;16.2 Cluster Updates;154
8.4.3;16.3 Performance;155
8.4.4;16.4 Conclusions;155
8.4.5;References;156
8.5;17 Multibaric-Multithermal Simulations for Lennard – Jones Fluids;157
8.5.1;17.1 Introduction;157
8.5.2;17.2 Methods;157
8.5.3;17.3 Computational Details;158
8.5.4;17.4 Results and Discussion;159
8.5.5;17.5 Conclusions;161
8.5.6;References;161
8.6;18 A Successive Umbrella Sampling Algorithm to Sample and Overcome Free Energy Barriers;162
8.6.1;18.1 Introduction;162
8.6.2;18.2 A Coarse-Grained Model for Hexadecane;162
8.6.3;18.3 Successive Umbrella Sampling;164
8.6.4;18.4 Phase Behavior and Interfacial Tension of Hexadecane;164
8.6.5;References;165
9;Part V Computer Tools;167
9.1;19 C++ and Generic Programming for Rapid Development of Monte Carlo Simulations;168
9.1.1;19.1 Introduction;168
9.1.2;19.2 Flexible Energy Calculation;170
9.1.3;19.3 Monte Carlo Concepts;173
9.1.4;19.4 Summary;178
9.1.5;References;179
9.2;20 Visualization of Vector Spin Con.gurations;180
9.2.1;20.1 Introduction;180
9.2.2;20.2 Models;181
9.2.3;20.3 AViz;181
9.2.4;20.4 Visualizing Vector Spins;182
9.2.5;20.5 Three Dimensions;184
9.2.6;References;184
9.3;21 The BlueGene/L Project;185
9.3.1;21.1 Project Background;185
9.3.2;21.2 BlueGene/L Architecture;185
9.3.3;21.3 Project Status Update;188
9.3.4;21.4 Conclusion;189
9.3.5;References;189
10;Part VI Molecules, Clusters and Nanoparticles;191
10.1;22 All-Electron Path Integral Monte Carlo Simulations of Small Atoms and Molecules;192
10.1.1;22.1 Introduction: Path Integral Theory;192
10.1.2;22.2 Recent Path Integral Simulations on Nanostructures;194
10.1.3;22.3 Motivation for Atomic and Molecular Calculations;195
10.1.4;22.4 Monte Carlo Simulation Technique;196
10.1.5;22.5 Examples and Tests for Non-Interacting Fermions;199
10.1.6;22.6 Calculations on Atoms;201
10.1.7;22.7 Calculations on Molecules;203
10.1.8;22.8 Conclusion and Future Work;205
10.1.9;References;206
10.2;23 Projective Dynamics in Realistic Models of Nanomagnets;207
10.2.1;23.1 Introduction;207
10.2.2;23.2 Model and Numerical Results;207
10.2.3;23.3 Summary and Conclusions;210
10.2.4;References;210
10.3;24 Cumulants for an Ising Model for Folded 1- d Small- World Materials;212
10.3.1;24.1 Introduction;212
10.3.2;24.2 Models and Methods;212
10.3.3;24.3 Results;213
10.3.4;24.4 Summary and Conclusions;213
10.3.5;References;215
10.4;25 Embryonic Forms of Nickel and Palladium: A Molecular Dynamics Computer Simulation;216
10.4.1;25.1 Introduction;216
10.4.2;25.2 The Potential Energy Function;217
10.4.3;25.3 Calculations and Discussion;218
10.4.4;25.4 Conclusion;221
10.4.5;References;222
11;Part VII Surfaces and Alloys;225
11.1;26 Usage of Pattern Recognition Scheme in Kinetic Monte Carlo Simulations: Application to Cluster Di . usion on Cu( 111);226
11.1.1;26.1 Introduction;226
11.1.2;26.2 Theoretical Details;228
11.1.3;26.3 Model Systems;232
11.1.4;26.4 Di.usion Processes and Activation Energies;232
11.1.5;26.5 Results;232
11.1.6;26.6 Conclusions;248
11.1.7;References;250
11.2;27 Including Long-Range Interactions in Atomistic Modelling of Di . usional Phase Changes;252
11.2.1;27.1 Introduction;252
11.2.2;27.2 Computational Method;254
11.2.3;27.3 Clustering in the Al-Cu and Al-Cu-Mg Systems;260
11.2.4;27.4 Conclusions;264
11.2.5;References;267
11.3;28 Br Electrodeposition on Au(100): From DFT to Experiment;269
11.3.1;References;275
11.4;29 Simulation of ZnSe, ZnS Coating on CdSe Substrate: The Electronic Structure and Absorption Spectra;276
11.4.1;29.1 Introduction;276
11.4.2;29.2 Calculation Details;277
11.4.3;29.3 Results and Discussion;277
11.4.4;29.4 Conclusion;280
11.4.5;References;280
11.5;30 Simulation of Islands and Vacancy Structures for Si/ Ge- covered Si( 001) Using a Hybrid MC- MD Algorithm;281
11.5.1;30.1 Introduction;281
11.5.2;30.2 Simulation Method;282
11.5.3;30.3 Relaxation of Islands and Step Edges;283
11.5.4;30.4 Formation of Vacancy Structures;284
11.5.5;30.5 Conclusion;286
11.5.6;References;286
11.6;31 Spin-Polarons in the FM Kondo Model;287
11.6.1;References;292
12;List of Contributors;294

Leseproben

8 Stochastic Collision Molecular Dynamics Simulations for Ion Transfer Across Liquid–Liquid Interfaces (p. 80)

S. Frank, and W. Schmickler

1 Abteilung Elektrochemie, Universität Ulm, 89069 Ulm, Germany

2 Current address: Center for Materials Research and Technology and School of Computational Science and Information Technology, Florida State University, Tallahassee, FL 32306-4350, USA

[e-mail], [e-mail]

Abstract.

We compute the potential-energy surface for ion transfer across liquid– liquid interfaces from a lattice gas model and simulate the transfer as a random walk of the ion coupled to a heat bath. The kinetics obey Tafel behavior. The reaction rate is slowed down due to friction, and the friction effect is stronger than for a free particle.

8.1 Introduction

Ion transfer across liquid–liquid interfaces, though of considerable experimental interest, still lacks an established theoretical description. It is not clear whether this process should be viewed as a chemical reaction requiring an activation energy, or simply as a mass transport across a viscous boundary. Molecular dynamics simulations have shown a continuous increase of the chemical part of the free energy of ion transfer and no barrier (see, e.g., [1]).

However, the simulations were performed in the presence of a high field driving the ion across the interface, and in the absence of space charge regions. Thus, an essential part of the interaction energy of the transferring ion has been missing. In a model proposed by Schmickler [2], it is the combination of several interactions that constitutes a barrier at the interface. Here, we follow Schmickler’s ideas and treat ion transfer as a chemical reaction. The reaction coordinate – simply the distance from the average interface position – is singled out, and all the other degrees of freedom are represented as a heat bath, the same approach as in Kramers’ theory [3]. With this simplification, we can observe the reaction directly in a simulation.

8.2 Potential-energy Surface

We calculate the potential-energy surface of a transferring ion as the con.gurational energy of a positively charged test particle with fixed position in a simple cubic lattice gas, as a function of the distance z from the average interface position. Our model contains two solvents S1 and S2 and a different base electrolyte in each phase, and each lattice site is occupied by one particle.

The configurational energy is given by the sum over all nearestneighbor interactions, plus for ions the energy in the instantaneous electrostatic potential caused by all ions in the system. We calculate the equilibrium properties of this model using the Metropolis Monte Carlo algorithm. Details are given elsewhere [4]. The system is polarizable in a certain potential window, and the absolute value of the free energy of ion transfer, which is governed by a single interaction parameter ±r for the interaction with the two solvents, must be low enough for the ion to be transferable within this window.