This book aims to provide an example-based education in numerical methods for atomistic and continuum simulations of systems at and away from equilibrium. The focus is on nonequilibrium systems, stressing the use of tools from dynamical systems theory for their analysis. Lyapunov instability and fractal dimensionality are introduced and algorithms for their analysis are detailed. The book is intended to be self-contained and accessible to students who are comfortable with calculus and differential equations.
The wide range of topics covered will provide students, researchers and academics with effective tools for formulating and solving interesting problems, both atomistic and continuum. The detailed description of the use of thermostats to control nonequilibrium systems will help readers in writing their own programs rather than being saddled with packaged software.
Contents: - Mechanics, Molecular Dynamics, and Gibbs' Statistical Mechanics
- Numerical Integration and Error Analysis
- Molecular Dynamics with Thermostats
- Simple Systems with Thermal Constraints
- Ergodicity and Its Importance in Small Systems
- Equilibrium Thermodynamics + Nonequilibrium Hydrodynamics
- Statistical Mechanics of Small Systems
- Microscopic Reversibility, Macroscopic Irreversibility
- Lyapunov Instability, Fractals, and Chaos I
- Lyapunov Instability, Fractals, and Chaos II
- Smooth-Particle Continuum Mechanics
- Epilogue
Readership: Undergraduate, graduate students, researchers focusing on statistical mechanics and numerical simulation.
Keywords:Numerical Methods;Simulation;Nonequilibrium;Molecular Dynamics;Continuum Mechanics;Statistical Mechanics;Chaos;Lyapunov Instability;Hydrodynamics;ThermodynamicsReview:
Key Features:- Three useful areas covered — treatment of control variables such as thermostats and ergostats, dynamical system analysis and the use of smooth particle techniques for analyzing molecular dynamics, and the solution of continuum problems
