6533b834fe1ef96bd129e0f2

RESEARCH PRODUCT

Monte-Carlo Methods

subject

description

The article conbtains sections titled: 1 Introduction and Overview 2 Random-Number Generation 2.1 General Introduction 2.2 Properties That a Random-Number Generator (RNG) Should Have 2.3 Comments about a Few Frequently Used Generators 3 Simple Sampling of Probability Distributions Using Random Numbers 3.1 Numerical Estimation of Known Probability Distributions 3.2 “Importance Sampling” versus “Simple Sampling” 3.3 Monte-Carlo as a Method of Integration 3.4 Infinite Integration Space 3.5 Random Selection of Lattice Sites 3.6 The Self-Avoiding Walk Problem 3.7 Simple Sampling versus Biased Sampling: the Example of SAWs Continued 4 Survey of Applications to Simulation of Transport Processes 4.1 The “Shielding Problem” 4.2 Diffusion-Limited Aggregation (DLA) 5 Monte-Carlo Methods in Statistical Thermodynamics: Importance Sampling 5.1 The General Idea of the Metropolis Importance-Sampling Method 5.2 Comments on the Formulation of a Monte-Carlo Algorithm 5.3 The Dynamic Interpretation of the Monte-Carlo Method 5.4 Monte-Carlo Study of the Dynamics of Fluctuations Near Equilibrium and of the Approach toward Equilibrium 5.5 The Choice of Statistical Ensembles 6 Accuracy Problems: Finite-Size Problems, Dynamic Correlation of Errors, Boundary Conditions 6.1 Finite-Size–Induced Rounding and Shifting of Phase Transitions 6.2 Different Boundary Conditions: Simulation of Surfaces and Interfaces 6.3 Estimation of Statistical Errors 7 Sampling of Free Energies and Free Energy Barriers 7.1 Bulk Free Energies 7.2 Interfacial Free Energies 7.3 Transition Path Sampling 8 Quantum Monte-Carlo Techniques 8.1 General Remarks 8.2 Path-Integral Monte-Carlo Methods 8.3 A Classical Application: the Momentum Distribution of Fluid He 8.4 A Few Qualitative Comments on Fermion Problems 9 Lattice Gauge Theory 9.1 Some Basic Ideas of Lattice Gauge Theory 9.2 A Famous Application 10 Selected Applications in Classical Statistical Mechanics of Condensed Matter 10.1 Metallurgy and Materials Science 10.2 Polymer Science 10.3 Surface Physics 11 Concluding Remarks Glossary Keywords: self-averaging; attrition problem; sweep step; statistical inefficiency; quenched approximation; random-number generator