This work is a needed reference for widely used techniques and methods of computer simulation in physics and other disciplines, such as materials science. Molecular dynamics computes a molecule's reactions and dynamics based on physical models; Monte Carlo uses random numbers to image a system's behaviour when there are different possible outcomes with related probabilities. The work conveys both the theoretical foundations as well as applications and "tricks of the trade", that often are scattered across various papers. Thus it will meet a need and fill a gap for every scientist who needs computer simulations for his/her task at hand. In addition to being a reference, case studies and exercises for use as course reading are included.
|Product dimensions:||6.69(w) x 9.45(h) x (d)|
|Age Range:||18 Years|
About the Author
Martin Oliver Steinhauser, Fraunhofer-Institute for High-Speed Dynamics, Ernst-Mach-Institute, EMI, Freiburg, Germany.
Table of Contents
1. Introduction to Computer Simulation1.1 Historical Background1.2 Theory, Modeling and Simulation in Physics1.3 Reductionism in Physics1.4 Basics of Ordinary and Partial Differential Equations in Physics1.5 Numerical Solution of Differential Equations: Mesh-Based vs. Particle Methods1.6 The Role of Algorithms in Scientific Computing1.7 Remarks on Software Design1.8 Summary
2. Fundamentals of Statistical Physics2.1 Introduction2.2 Elementary Statistics2.3 Introduction to Classical Statistical Mechanics2.4 Introduction to Thermodynamics2.5 Summary
3. Inter- and Intramolecular Short-Range Potentials3.1 Introduction3.2 Quantum Mechanical Basis of Intermolecular Interactions3.2.1 Perturbation Theory3.3 Classical Theories of Intermolecular Interactions3.4 Potential Functions3.5 Molecular Systems3.6 Summary
4. Molecular Dynamics Simulation4.1 Introduction4.2 Basic Ideas of MD4.3 Algorithms for Calculating Trajectories4.4 Link between MD and Quantum Mechanics4.5 Basic MD Algorithm: Implementation Details4.6 Boundary Conditions4.7 The Cutoff Radius for Short-Range Potentials4.8 Neighbor Lists: The Linked-Cell Algorithm4.9 The Method of Ghost Particles4.10 Implementation Details of the Ghost Particle Method4.11 Making Measurements4.12 Ensembles and Thermostats4.13 Case Study: Impact of Two Different Bodies4.14 Case Study: Rayleigh-Taylor Instability4.15 Case Study: Liquid-Solid Phase Transition of Argon
5. Advanced MD Simulation5.1 Introduction5.2 Parallelization5.3 More Complex Potentials and Molecules5.4 Many Body Potentials5.5 Coarse Grained MD for Mesoscopic Systems
6. Outlook on Monte Carlo Simulations6.1 Introduction6.2 The Metropolis Monte-Carlo Method6.2.1 Calculation of Volumina and Surfaces6.2.2 Percolation Theory6.3 Basic MC Algorithm: Implementation Details6.3.1 Case Study: The 2D Ising Magnet6.3.2 Trial Moves and Pivot Moves6.3.3 Case Study: Combined MD and MC for Equilibrating a Gaussian Chain6.3.4 Case Study: MC of Hard Disks6.3.5 Case Study: MC of Hard Disk Dumbbells in 2D6.3.6 Case Study: Equation of State for the Lennard-Jones Fluid6.4 Rosenbluth and Rosenbluth Method6.5 Bond Fluctuation Model6.6 Monte Carlo Simulations in Different Ensembles6.7 Random Numbers Are Hard to Find
7. Applications from Soft Matter and Shock Wave Physics7.1 Biomembranes7.2 Scaling Properties of Polymers7.3 Polymer Melts7.4 Polymer Networks as a Model for the Cytoskeleton of Cells7.5 Shock Wave Impact in Brittle Solids
8. Concluding Remarks
A AppendixA.1 Quantum Statistics of Ideal GasesA.2 Maxwell-Boltzmann, Bose-Einstein- and Fermi-Dirac StatisticsA.3 Stirling’s FormulaA.4 Useful Integrals in Statistical PhysicsA.3 Useful Conventions for Implementing Simulation ProgramsA.4 Quicksort and Heapsort AlgorithmsA.4 Selected Solutions to ExercisesAbbreviationsBibliographyIndex