Computational Physics, Softcover reprint of the original 1st ed. 1996 Selected Methods Simple Exercises Serious Applications

Computational Physics. Selected Methods, Simple Exercises,Serious Applications is an overview written by leading researchers of a variety of fields and developments. Selected Methods introduce the reader to current fields, including molecular dynamics, hybrid Monte-Carlo algorithms, and neural networks. Simple Exercises give hands-on advice for effective program solutions from a small number of lines to demonstration programs with elaborate graphics. SeriousApplications show how questions concerning, for example, aging, many-minima optimisation, or phase transitions can be treated by appropriate tools. The source code and demonstration graphics are included on a 3.5" MS-DOS diskette.

Random Number Generation.- 1 Introduction.- 2 The Miracle Number 16807.- 3 Bit Strings of Kirkpatrick-Stoll.- 4 A Modern Example.- 5 Problems.- 6 Summary.- References.- A Few Exercises with Random Numbers.- Monte Carlo Simulations of Spin Systems.- 1 Introduction.- 2 Spin Models and Phase Transitions.- 2.1 Models and Observables.- 2.2 Phase Transitions.- 3 The Monte Carlo Method.- 3.1 Estimators and Autocorrelation Times.- 3.2 Metropolis Algorithm.- 3.3 Cluster Algorithms.- 3.4 Multicanonical Algorithms for First-Order Transitions.- 4 Reweighting Techniques.- 5 Applications to the 3D Heisenberg Model.- 5.1 Simulations for T>Tc.- 5.2 Simulations near Tc.- 6 Concluding Remarks.- Appendix: Program Codes.- References.- Metastable Systems and Stochastic Optimization.- 1 An Introduction to Complex Systems.- 2 Dynamics in Complex Systems.- 2.1 Thermal Relaxation Dynamics: The Metropolis Algorithm.- 2.2 Thermal 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 Tree Dynamics.- 3.3 A Serious Application: Aging Effects in Spin Glasses.- 4 Stochastic Optimization: How to Find the Ground State of Complex Systems.- 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.- 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 Collisional Cooling.- 1.4 Stick-and-Slip Motion and Self-Organized Criticality (with S. Dippel).- 1.5 Segregation, Convection, Heaping (with S. Dippel).- 2 Molecular Dynamics Simulations I: Soft Particles.- 2.1 General Remarks.- 2.2 Normal Force.- 2.3 Tangential Force.- 2.4 Detachment Effect.- 2.5 Brake Failure Effect (with J. Schäfer).- 3 Molecular Dynamic Simulations II: Hard Particles (with J. Schäfer).- 3.1 Event-Driven Simulation.- 3.2 Collision Operator.- 3.3 Limitations.- 4 Contact Dynamics Simulations (with L. Brendel and F. Radjai).- 4.1 General Remarks.- 4.2 Contact Laws and Equations of Motion.- 4.3 Iterative Determination of Forces and Accelerations.- 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.- 1 Introduction.- 2 Concepts and Models.- 3 Techniques.- 4 Results.- References.- Simulations of Chemical Reactions.- 1 Introduction.- 2 The Basic Kinetic Approach.- 3 Numerical and Analytical Approaches for Reactions Under Diffusion.- 4 Reactions in Layered Systems.- 5 Reactions Under Mixing.- 6 Reactions Controlled by Enhanced Diffusion.- References.- Random Walks on Fractals.- 1 Introduction.- 2 Deterministic Fractals.- 2.1 The Koch Curve.- 2.2 The Sierpinski Gasket.- 3 Random Fractals.- 3.1 The Random-Walk Trail.- 3.2 Self-Avoiding Walks.- 3.3 Percolation.- 4 The “Chemical Distance” ?.- 5 Random Walks on Fractals.- 5.1 Root Mean Square Displacement R(t).- 5.2 The Mean Probability Density.- 6 Biased Diffusion.- 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.- 1 Electronic States in Disordered Systems.- 2 The Anderson Model of Localization.- 3 Calculation of the Eigenvectors.- 4 Description of Multifractal Objects.- 5 Multifractal Analysis of the Wave Functions.- 6 Computation of the Multifractal Characteristics.- 7 Topical Results of the Multifractal Analysis.- References.- Transfer-Matrix Methods and Finite-Size Scaling for Disordered Systems.- 1 Introduction.- 2 One-Dimensional Systems.- 2.1 The Transfer Matrix.- 2.2 The Ordered Limit.- 2.3 The Localization Length.- 2.4 Resolvent Method.- 3 Finite-Size Scaling.- 4 Numerical Evaluation of the Anderson Transition.- 4.1 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 185 References.- Quantum Monte Carlo Investigations for the Hubbard Model.- 1 Introduction.- 1.1 The Hubbard Model.- 1.2 What to Compute.- 1.3 Quantum Simulations.- 2 Grand Canonical Quantum Monte Carlo.- 2.1 The Trotter-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 Spin Updates.- 3.2 Numerical Instabilities.- 4 History and Further Reading.- Appendix A: Statistical Monte Carlo Methods.- Appendix B: OCTAVE.- Appendix C: Exercises.- References.- Quantum Dynamics in Nanoscale Devices.- 1 Introduction.- 2 Theory.- 3 Data Analysis.- 4 Implementation.- 5 Application: Quantum Interference of Two Identical Particles.- References.- Quantum Chaos.- 1 Classical and Quantum Chaos.- 2 Quantum Time Evolution.- 3 Quantum State Tomography.- 3.1 Phase-Space Distributions.- 3.2 Phase-Space Entropy.- 4 Case Study: A Driven Anharmonic Quantum Oscillator.- 4.1 Classical Phase-Space Dynamics.- 4.2 Quantum Phase-Space Dynamics.- 4.3 Quasienergy Spectra.- 4.4 Chaotic Tunneling.- 5 Concluding Remarks.- References.- Numerical Simulation in Quantum Field Theory.- 1 Quantum Field Theory and Particle Physics.- 1.1 Particles, Fields, 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 Metropolis Algorithm for ?4.- 4 Summary.- Appendix: FORTRAN Monte Carlo Package for ?4.- References.- Modeling and a Simulation Method for Molecular Systems.- 1 Introduction.- 2 Brief Review of the Simulation Method.- 3 Modeling of Polymer Systems.- 4 Coarse-Graining.- 5 The Monomer Unit.- 6 Bonded Interactions for BPA-PC.- 7 Parallelization of the Polymer System.- References.- Constraints in Molecular Dynamics, Nonequilibrium Processes in Fluids via Computer Simulations.- 1 Introduction.- 2 Basics of Molecular Dynamics.- 2.1 Equations of Motion.- 2.2 Extraction of Data from MD Simulations.- 3 Potentials, Constraints, and Integrators.- 3.1 Interaction Potential and Scaling.- 3.2 Thermostats.- 3.3 Integrators.- 4 Nonequilibrium Phenomena.- 4.1 Relaxation Processes.- 4.2 Plane Couette Flow.- 4.3 Viscosity.- 4.4 Structural Changes.- 4.5 Colloidal Dispersions.- 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.- 1 Introduction.- 2 Simulation Methods.- 3 Total Energies and Interatomic Forces.- 3.1 Classical Concepts.- 3.2 Density-Functional Theory, Car-Parrinello 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-Crystalline and Amorphous Solids.- 6.3 Surfaces and Adsorbates.- 7 Accuracy and Transferability.- 7.1 Small Silicon Clusters, Sin.- 7.2 Molecules, Hydrocarbons.- 7.3 Solid Crystalline Modifications, Silicon.- 8 Applications.- 8.1 Structure and Stability of Polymerized C60.- 8.2 Stability of Highly Tetrahedral Amorphous Carbon, ta-C.- 8.3 Diamond Surface Reconstructions.- 9 Summary.- References.- Finite Element Methods for the Stokes Equation.- 1 Introduction.- 2 Stokes Equation.- 2.1 Conservation Equations.- 2.2 Function Spaces and Variational Formulation.- 2.3 Saddle Point Problem.- 2.4 General Boundary Conditions.- 2.5 Example.- 3 Discretization.- 3.1 General Formulation.- 3.2 Finite Elements for Saddle-Point Problems.- 4 Final Remarks.- References.- Principles of Parallel Computers and Some Impacts on Their Programming Models.- 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.- 1 Introduction.- 2 Programming Models.- 2.1 Definition.- 2.2 Classification.- 3 Programming a Shared Memory Computer.- 3.1 The KSR Programming Model.- 3.2 Levels of Parallelism.- 3.3 Program Implementation.- 3.4 Examples.- 4 Programming a Distributed Memory Computer Using PARIX.- 4.1 What is PARIX.- 4.2 PARIX Hardware 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 What Is Included in MPI?.- 5.4 What Does the Standard Exclude?.- 5.5 MPI Says “Hello World”.- 5.6 Current Available Implementations of MPI.- 6 Summary.- References.

This book introduces the reader to current fields, including molecular dynamics, hybrid Monte-Carlo algorithms, and neural networks. It gives hands-on advice for effective program solutions from a small number of lines to demonstration programs with elaborate graphics. It shows how questions concerning, for example, aging, many-minima optimization, or phase transitions can be treated by appropriate tools. The source code and demonstration graphics are included on a 3î1/2 MS-DOS disk.