计算物理学（英文本）

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