6. Monte Carlo Simulation and Integration

  1. Dr. Dierk Raabe1,2

Published Online: 24 MAR 2004

DOI: 10.1002/3527601945.ch6

Computational Materials Science: The Simulation of Materials, Microstructures and Properties

Computational Materials Science: The Simulation of Materials, Microstructures and Properties

How to Cite

Raabe, D. (1998) Monte Carlo Simulation and Integration, in Computational Materials Science: The Simulation of Materials, Microstructures and Properties, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527601945.ch6

Author Information

  1. 1

    Department for Materials Science & Engineering, Carnegie Mellon University, Room 3317, Wean Hall, Pittsburgh, PA 15213-3890, USA

  2. 2

    Institut für Metallkunde und Metallphysik, RWTH Aachen, Kopernikusstraße 14, 52056 Aachen, Germany

Publication History

  1. Published Online: 24 MAR 2004
  2. Published Print: 1 JUN 1998

ISBN Information

Print ISBN: 9783527295418

Online ISBN: 9783527601943

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Keywords:

  • Monte Carlo simulation;
  • random numbers;
  • random walk simulation;
  • random sampling integration;
  • Monte Carlo integration;
  • Metropolis Monte Carlo method;
  • canonical ensembles;
  • spin Monte Carlo models;
  • surface segregation;
  • thin film deposition

Summary

This chapter contains sections titled:

  • Introduction and Fundamentals

  • Some Historical Remarks

  • Random Numbers

  • Random Walk Simulation

  • Hit-or-Miss Random Sampling Integration

  • Simple or Naive Sampling — Nonweighted Monte Carlo Integration

  • Importance Sampling — Weighted Monte Carlo Integration

  • The Metropolis Monte Carlo Method

    • Fundamentals of the Algorithm

    • The Metropolis Method for Canonical and Microcanonical Ensembles

    • The Metropolis Method for Grandcanonical Ensembles

  • Spin Monte Carlo Models

    • Introduction

    • ½ Spin Ising Model

    • Heisenberg Spin Model

    • Lattice Gas Spin Model

    • q-State Potts Spin Model

    • Ising-Related Spin Models — the MFA, CVM, and BWG Models

  • Lattice Types

  • Errors of Monte Carlo Methods

  • Application of the Monte Carlo Method in Materials Science

  • Examples of the Monte Carlo Method in Materials Science

    • Simulation of Surface Segregation

    • Simulation of Phase Transition in Polymers

    • Simulation of Thin Film Deposition