Random Number Generation* Dietrich Stauffer 1 Introduction 2 TheMiracleNumber 16807 3 Bit Strings of Kirkpatrick-Stoll 4 A Modern Example 5 Problems 6 Summary References A Few Exercises with Random Numbers Peter Blaudeck Monte Carlo Simulations of Spin Systems* Wolfuard Janke 1 Introduction 2 Spin Models and Phase Transitions 2.1 ModelsandObservables 2.2 Phase Transitions 3 TheMonte CarloMethod 3.1 Estimators and Autocorrelation Times 3.2 Metropolis Algorithm 3.3 Cluster Algorithms 3.4 Multicanonical Algorithms fOr First-Order Transitions 4 ReweightingTechniques 5 Applications to the 3D Heisenberg Model 5 1 Simulation8forT>Tc 5.2 SimulationsnearTc 6 Concluding Remaxks Appendix: Program Codes Metastable Systems and Stochastic Optimization* Karl Heinz Hoffmann 1 An Introduction to Complex Systems 2 Dynamics in Complex Systems 2.1 Thermal Relaxation Dynamics: The Metropolis Algorithm 2.2 ThermaJ Relaxation Dynamics: A Marcov Process 2.3 Thermal Relaxation Dynamics: A Simple Example 3 Modeling Constant-Temperature Thermal Relaxation 3.1 Coarse-Graining a Complex State Space 3.2 TheeDynaJnics 3.3 A Serious Application: Aging Effects in Spin Glasses 4 Stochastic Optimization: How to Find the Ground State of ComplexSystems 4.1 Simulated Annealing 4 2 Optimal Simulated Annealing Schedules: A Simple Example. 4.3 AdaPtive Annealing Schedules and the Ensemble Approach to Simulated Annealing 5 Summary Appendix: Examples and Exercises (with S. Schubert) References Modelling and Computer Simulation of Granular Media Dietrich E.Wolf 1 The Physics of Granular Media 1.1 What are Granular Media? 1.2 Stress Distribution in Granular Packing: Arching 1.3 Dilatancy, Fluidization and CollisionaJ Cooling 1.4 Stickand-Slip Motion and Self Organized Criticality (withS.Dippel) 1.5 Segregation, Convection, HeaPing (with S. Dippel) 2 Molecular Dynamics Simulations I: Soft Particles 2.1 General Remaxks 2.2 Normal Force 2.3 Tangelltial Force 2.4 Detarhment Effect 2.5 Brake Failure Effect (with J. Scharer) 3 Moleculax Dynamic Simulations II: Haxd Paxticles (with J Scharer) 3.1 Evellt-Driven Simulation 3.2 Collision Operator 3.3 Limitations 4 Contact Dynamics Simulations (with L. Brendel and F. Radai) 4.1 General Remarks 4.2 Contact Laws and Equations of Motion 4.3 Iterative Determination of Forces and Acceler8.tions 4.4 Results 5 The Bottom-to-Top Restructuring Model 5.1 The Algorithm and its Justification (with E. Jobs) 5.2 Simulation of a Rotating Drum (with T. Scheffler and G. Baumann 6 Conclusion References Algorithms for Biological Aging* DietrichStauffer 1 Introduction 2 Concepts and Models 3 Techniques 4 Results References Simulations of Chemical Reactions Alexander Blumen, Igor Sokolov, Gerd Zumofen, and Joseph Klafter . 1 lntroduction 2 TheBasicKineticApproach 3 Numerical and AnalyticaJ Approaches for Reactions Under Diffusion. 4 Reactionsin LayeredSystems 5 ReactionsUnderMiring 6 Reactions Controlled by Enhanced Diffusion references Random Walks on Fractals* Armin Bunde, Julia Drager, and Markus Porto, 1 Introduction 2 Deterministic fractals 2.1 TheKochCurve 2.2 The Sierpinski Gasket 3 Random fractaJs 3.l The Random-Walk trail 3.2 Self Avoiding Walks 3.3 Percolation 4 The "Chemical Distance" e 5 Random Walks on fractals 5.1 Root Mean Square Displacement R(t) 5.2 The Mean Probability Density 6 Biased Diffosion 7 Numerical Approaches 7 1 Generation of Percolation Clusters, 7.2 Simulation of Random Walks 8 Description of the Programs References Multifractal Characteristics of Electronic Wave Functions in Disordered Systems* MichaelSchreiber 1 Electronic States in Disordered Systems 2 The Anderson Model of Localization 3 CaJGulation of the Eigenvectors 4 Description of Multifractal Objects 5 Mu1tifractal AnaJysis of the Wave Functions 6 Computation of the Multifractal Characteristics 7 Topical Results of the Multifractal Analysis References Thansfer-Matrix Methods and Finite-Size Scaling fOr Disordered Systems* BernhardKramer and Michael Schreiber l Introduction 2 One-Dimensional Systems 2.1 Thenansfer Matrix 2.2 TheOrdered Limit 2.3 The Localization Length 2.4 Resolvent Method 3 Finite-Size Scaling 4 Numerical Evaluation of the Anderson Transition 4.l Localization Length of Quasi-1D Systems 4.2 Dependence of the Localization Length on the Cross Section. 4.3 Finite-Size Scaling Numerically 5 Present Status of the Results from Transfer-Matrix Calculations References Quantum Monte Carlo Investigations for the Hubbard Model* Hans-Georg Matuttis and Ingo Morgenstern 1 Introduction 1.1 TheHubbardModel 1.2 WhattoCompute 1.3 QuantumSimulations 2 Grand Canonical Quantum Monte Carlo 2.1 The Thotter--Suzuki Transformation 2.2 The Hubbard--Stratonovich Transformation 2.3 The Partition Function 2.4 The Monte Carlo Weight 3 Equal--Time Greens Functions 3.1 Single SpinUpdates 3.2 Numerical Instabilities 4 Historyand Further Reading Appendix A: Statistical Monte Carlo Methods AppendixB: OCTAVE AppendixC:Exercises References Quantum Dynamics in Nanoscale Devices* Hans De Raedt l Introduction 2 Theory 3 Data AnaJysis 4 Implemelltation 5 Application: Quatum Interference of Two Identical Particles References Quantum Chaos Hans Jhrgen Korsch and Henning Wiescher 1 Classical and Quantum Chaos 2 QuantumTimeEvolution 3 QuantumStateTomograPhy 3.1 Phase-Space Distributions 3.2 Phase-SpaceEntropy 4 Case Study: A Driven Anharmonic Quatum Oscillator 4.1 Classical Phase-Space Dynamics. 4.2 Quatum Phase-Space Dynamics 4.3 Quasienergy Spectra 4 4 ChaoticTUnneling 5 Conc1udingRemarks References Numerical Simulation in Quantum Field Theory* Ulli Wolff 1 Quantum Field Theory and Particle Physics 1.1 Paxticles, FieIds, Standard Model 1 2 Beyond Perturbation Theory 2 Lattice Formulation of Field Theory 2.1 Path Integral, 2.2 Lattice RegUlarization 2.3 Field Theory and Critical Phenomena 2.4 Effective Field Theory 3 Stochastic Evaluation of Path Integrals 3.1 Monte Carlo Method 3.2 MetropolisAlgorithmforW 4 Summary Appendix: FORTRAN Monte Carlo Package for References Modeling and a Simulation Method for Molecular Systems Dieter W.Heermann 1 Introduction 2 Brief Review of the Simulation Method 3 Modeling of Polymer Systems 4 Coarses Graining 5 The Monomer Unit 6 Bonded Interactions for BPA-PC 7 Parallelization of the Polymer System References Constrailits in Molecular Dynarnics, Nonequilibrium Processes in Fluids via ComPuter Simulations SiegfriedHess 1 Introduction 2 Basics of Moleculax Dynamics, 2.1 Equations of Motion 2.2 Extraction of Data from MD Simulations 3 Potentials, Constraints, and Integrators 3.1 Interaction Potelltialand Scaling 3.2 Thermostats 3.3 Integrators 4 Nonequilibrium Phenomena 4.1 Relaxation Processes 4.2 PlaneCouetteFlow 4.3 Viscosity 4.4 StructuralChanges 4.5 ColloidalDispersions 4.6 Mixtures 5 Complex Fluids 5.1 Polymer Melts 5.2 Nematic Liquid Crystals 5.3 Ferrofluids and Magneto-Rheological Fluids References Molecular-Dynamic Simulations of Structure Formation in Complex Materials Thomas ftauenheim, Dirk Porezag, Thomas K5hler, and nank Weich 1 Introduction 2 SimulationMethods 3 Total Energies and Interatomic Forces 3 1 ClassicaJConcepts 3.2 Density-Functional Theory, Car--Paxrinello MD 4 Density-Functional Based Tight-Binding Method 4.1 Creation of the Pseudoatoms 4 2 Calculation of Matrix Elements 4.3 Fitting of Short-Range Repulsive Part 5 Vibrational Properties 6 Simulation Geometries and Regimes 6 1 Clusters,Molecules 6.2 Bulk-CrystaJline and Amorphous Solids 6.3 Surfaces and Adsorbates 7 Accuracy and Thansferability 7 1 SmaJl Silicon Clusters, Si 7.2 Molecules, Hydrocarbons 7.3 Solid Crystalline Modifications, Silicon 8 Applications 8.1 Structure and Stability of Polymerized C6o. 8.2 Stability of Highly TetrahedraJ Amorphous Carbon, ta-C 8.3 Diamond Surface Reconstructions 9 Summary References Finite Element Methods for the Stokes Equation Jochen Reichenbach and Nuri Aksel 1 Introduction 2 Stokes Equation 2.1 Conservation Equations 2.2 Function Spaces and Vaiational Formulation 2.3 SaddlePoilltProblem 2.4 GeneraJ Boundary Conditions 2.5 Example 3 Discretization 3.l GeneralFormulation 3.2 Finite Elements for Saddle-Point Problems 4 Final Remaxks References Principles of Parallel Computers and Some Impacts on Their Programming Models Wolfgang Rehmand Thomas Radke 1 Introduction 2 Overview on Architecture Principles 3 General Classification 4 Multiprocessor Systems 5 Massively Parallel Processor Systems 6 Multiple Shared-Memory Multiprocessors 7 Multithreading Programming Model 8 Message-Passing Programming Model 9 Summary References Parallel Programming Styles: A Brief Overview Andreas Munke, JorgWerner, and WolfgangRehm 1 Introduction 2 ProgrammingModels 2.1 Definition 2.2 ClassifiCation 3 Programming a Shared Memory Computer 3.1 The KSR Programming Model 3.2 Levelsof Parallelism 3.3 Program Implementation 3.4 Examples 4 Programming a Distributed Memory Computer Using PARIX 4.1 Whatis PAmX 4.2 PARIX Haxdware Environment 4 3 Communication and Process Model Under PARIX 4.4 Programming Model 4.5 An Example, PARIX says "Hello World" 5 Programming Heterogenous WOrkstation Clusters Using MPI 5.1 Introduction 5.2 Basic Structure of MPICH 5.3 WhatIsIncluded in MPI? 5.4 What Does the Standard Exclude? 5.5 MPI Says "Hello World" 5 6 Current Avalable Implementations of MPI 6 Summary References Index
京公网安备 11010102004214号