Computer Simulation in Physics and Engineering

Preface

1. Introduction to Computer Simulation
1.1 Historical Background
1.2 Theory, Modeling and Simulation in Physics
1.3 Reductionism in Physics
1.4 Basics of Ordinary and Partial Differential Equations in Physics
1.5 Numerical Solution of Differential Equations: Mesh-Based vs. Particle Methods
1.6 The Role of Algorithms in Scientific Computing
1.7 Remarks on Software Design
1.8 Summary

2. Fundamentals of Statistical Physics
2.1 Introduction
2.2 Elementary Statistics
2.3 Introduction to Classical Statistical Mechanics
2.4 Introduction to Thermodynamics
2.5 Summary

3. Inter- and Intramolecular Short-Range Potentials
3.1 Introduction
3.2 Quantum Mechanical Basis of Intermolecular Interactions
3.2.1 Perturbation Theory
3.3 Classical Theories of Intermolecular Interactions
3.4 Potential Functions
3.5 Molecular Systems
3.6 Summary

4. Molecular Dynamics Simulation
4.1 Introduction
4.2 Basic Ideas of MD
4.3 Algorithms for Calculating Trajectories
4.4 Link between MD and Quantum Mechanics
4.5 Basic MD Algorithm: Implementation Details
4.6 Boundary Conditions
4.7 The Cutoff Radius for Short-Range Potentials
4.8 Neighbor Lists: The Linked-Cell Algorithm
4.9 The Method of Ghost Particles
4.10 Implementation Details of the Ghost Particle Method
4.11 Making Measurements
4.12 Ensembles and Thermostats
4.13 Case Study: Impact of Two Different Bodies
4.14 Case Study: Rayleigh-Taylor Instability
4.15 Case Study: Liquid-Solid Phase Transition of Argon

5. Advanced MD Simulation
5.1 Introduction
5.2 Parallelization
5.3 More Complex Potentials and Molecules
5.4 Many Body Potentials
5.5 Coarse Grained MD for Mesoscopic Systems

6. Outlook on Monte Carlo Simulations
6.1 Introduction
6.2 The Metropolis Monte-Carlo Method
6.2.1 Calculation of Volumina and Surfaces
6.2.2 Percolation Theory
6.3 Basic MC Algorithm: Implementation Details
6.3.1 Case Study: The 2D Ising Magnet
6.3.2 Trial

Martin Steinhauser, Fraunhofer-Institute for High-Speed Dynamics, Ernst-Mach-Institut, EMI, Freiburg, Germany.