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8. An Introduction to Computer Simulation

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Computer simulation is increasingly used in physics and engineering to predict the probable outcome of experiments and to aid in their interpretation. The methods of simulation are based on a range of numerical techniques for treating ordinary and partial differential equations. Since much of physics can be broken down into a relatively small set of fundamental equations, there is a set of very general methods which can be widely applied. This text aims to give an introduction to those methods suitable for readers at an undergraduate level and those meeting the subject for the first time at postgraduate level. The methods are illustrated with simple programs and problems. The book covers a range of material not available in a simple form in a single text elsewhere.

Table of Contents

List of programs available
1 Models and simulation 1
2 Finite-difference methods 33
3 Simulation with particles 87
4 The Monte Carlo method 129
5 The wave equation 156
6 The finite-element method 179
7 Computational fluid dynamics 211
App. 1 The elements of matrix algebra 259
App. 2 A simple conjugate gradient method 265
App. 3 The virial theorem 268
App. 4 The condition for collisionless PIC 270
App. 5 The coefficients of a half-sine-wave Fourier series 273
App. 6 Numerical quadrature 274
App. 7 Calculation of the four-element solution to (6.11) 284
Problems - solutions and comments 287
References 307
Index 309

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2. The Art of Molecular Dynamics Simulation

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¡¾×÷Õß¡¿Dennis C Rapaport

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     This book describes the extremely powerful technique of molecular dynamics simulation, which involves solving the classical many-body problem in contexts relevant to the study of matter at the atomic level. The method allows the prediction of the static and dynamic properties of substances directly from the underlying interactions between the molecules. Because there is no alternative approach capable of handling such a broad range of problems at the required level of detail, molecular dynamics methods have proved themselves indispensable in both pure and applied research. This volume will be of value to advanced students and researchers in physics, chemistry, polymer science and materials science in universities and industrial laboratories.

Contents
Preface

1 Introduction

2 Basic MD approach
soft-disk fluid, methodology, programming, equilibration, sample results.

3 Simulating simple systems
equations of motion, potential functions, interaction computations, integration methods, initial state, efficiency, trajectory sensitivity.

4 Equilibrium properties of simple fluids
thermodynamics, structure, Voronoi polyhedra, clusters.

5 Dynamical properties of simple fluids
transport coefficients, space-time correlation functions.

6 Alternative ensembles
feedback and constraint methods for constant temperature and pressure.

7 Nonequilibrium dynamics
homogeneous and inhomogeneous systems, sheared flow, heat transport.

8 Rigid molecules
dynamics, molecular construction, water, properties, hydrogen bonds.

9 Flexible molecules
polymer chains, properties.

10 Geometrically constrained molecules
solving the constraint problem, internal forces, alkane chains, properties.

11 Other interactions
long-range forces, three-body potentials, dipole fluid, liquid silicon.

12 Step potentials
computational scheme, events, results, generalizations.

13 Time-dependent phenomena
open systems, thermal convection, obstructed flow.

14 Algorithms for supercomputers
MD algorithms for distributed- and vector-processing computers.

15 The future

Appendices
data management, organizing extensive computations, utility functions, list of variables.

Bibliography

Indices
function index, subject index.

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4. Understanding Molecular Simulation From Algorithms to Applications

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ISBN: 0122673700
Title: Understanding Molecular Simulation: From Algorithms to Applications 1996-08
Author: Daan Frenkel, Berend Smit
Publisher: Academic Press
Publication Date: 1996-08
Number Of Pages: 443
Average Amazon Rating: 4.5
Summary:
Computer simulation techniques have become almost essential in the study of the macro-molecular phenomena and phase behavior on the molecular level. As these techniques become increasingly important, it is necessaryto realize that they are useful tools, but are not the goals of research. With this important distinction in mind, Understanding Molecular Simulation describes simulation techniques along with the physics behind the phenomena that these techniques simulate.
Each chapter is comprised of three components: the general theoretical basis, an outline of the necessary computer code, and a few applications which illustrate the use of the technique demonstrated. The chapters also include examples of the typical practical problems that could be solved using each technique.

Key Features
* Gives a unified presentation of computational tools used to study molecular systems in the equilibrium state
* Describes simulation techniques and physics behind the phenomena simulated
* Emphasizes important topics of phase behavior and computer simulation of macro-molecular (polymer-type) substances
* Includes references to the authors home page where additional information from the authors can be found


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