Computational statistical physics / Lucas Böttcher, Hans J. Herrmann.

Format:

Book

Author/Creator:

Böttcher, Lucas, author.

Herrmann, Hans J., author.

Language:

English

Subjects (All):

Statistical physics.

Physical Description:

1 online resource (xiii, 257 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

Providing a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications such as percolation, random walks, magnetic systems, machine learning dynamics, and spreading processes on complex networks. A detailed discussion of molecular dynamics simulations is also included, a topic of great importance in biophysics and physical chemistry. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level, and numerous worked examples and end of chapter problems allow students to test their progress and understanding.

Contents:

Cover

Half-title Page

Title Page

Copyright Page

Dedication

Contents

Preface

What is Computational Physics?

Part I Stochastic Methods

1 Random Numbers

1.1 Definition of Random Numbers

1.2 Congruential RNG (Multiplicative)

1.3 Lagged Fibonacci RNG (Additive)

1.4 Available Libraries

1.5 How Good is an RNG?

1.6 Nonuniform Distributions

2 Random-Geometrical Models

2.1 Percolation

2.2 The Sol-Gel Transition

2.3 The Percolation Model

2.4 Fractals

2.5 Walks

2.6 Complex Networks

3 Equilibrium Systems

3.1 Classical Statistical Mechanics

3.2 Ising Model

4 Monte Carlo Methods

4.1 Computation of Integrals

4.2 Integration Errors

4.3 Hard Spheres in a Box

4.4 Markov Chains

4.5 M(RT)[sup(2)] Algorithm

4.6 Glauber Dynamics (Heat Bath Dynamics)

4.7 Binary Mixtures and Kawasaki Dynamics

4.8 Creutz Algorithm

4.9 Boundary Conditions

4.10 Application to Interfaces

5 Phase Transitions

5.1 Temporal Correlations

5.2 Decorrelated Configurations

5.3 Finite-Size Scaling

5.4 Binder Cumulant

5.5 First-Order Transitions

6 Cluster Algorithms

6.1 Potts Model

6.2 The Kasteleyn and Fortuin Theorem

6.3 Coniglio-Klein Clusters

6.4 Swendsen-Wang Algorithm

6.5 Wolff Algorithm

6.6 Continuous Degrees of Freedom: The n-Vector Model

7 Histogram Methods

7.1 Broad Histogram Method

7.2 Flat Histogram Method

7.3 Umbrella Sampling

8 Renormalization Group

8.1 Real Space Renormalization

8.2 Renormalization and Free Energy

8.3 Majority Rule

8.4 Decimation of the One-Dimensional Ising Model

8.5 Generalization

8.6 Monte Carlo Renormalization Group

9 Learning and Optimizing

9.1 Hopfield Network

9.2 Boltzmann Machine Learning

9.3 Simulated Annealing

10 Parallelization

10.1 Multispin Coding.

10.2 Vectorization

10.3 Domain Decomposition

11 Nonequilibrium Systems

11.1 Directed Percolation and Gillespie Algorithms

11.2 Cellular Automata

11.3 Irreversible Growth

Part II Molecular Dynamics

12 Basic Molecular Dynamics

12.1 Introduction

12.2 Equations of Motion

12.3 Contact Time

12.4 Verlet Method

12.5 Leapfrog Method

13 Optimizing Molecular Dynamics

13.1 Verlet Tables

13.2 Linked-Cell Method

14 Dynamics of Composed Particles

14.1 Lagrange Multipliers

14.2 Rigid Bodies

15 Long-Range Potentials

15.1 Ewald Summation

15.2 Particle-Mesh Method

15.3 Reaction Field Method

16 Canonical Ensemble

16.1 Velocity Rescaling

16.2 Constraint Method

16.3 Nosé-Hoover Thermostat

16.4 Stochastic Method

16.5 Constant Pressure

16.6 Parrinello-Rahman Barostat

17 Inelastic Collisions in Molecular Dynamics

17.1 Restitution Coefficient

17.2 Plastic Deformation

17.3 Coulomb Friction and Discrete Element Method

18 Event-Driven Molecular Dynamics

18.1 Event-Driven Procedure

18.2 Lubachevsky Method

18.3 Collision with Perfect Slip

18.4 Collision with Rotation

18.5 Inelastic Collisions

18.6 Inelastic Collapse

19 Nonspherical Particles

19.1 Ellipsoidal Particles

19.2 Polygons

19.3 Spheropolygons

20 Contact Dynamics

20.1 One-Dimensional Contact

20.2 Generalization to N Particles

21 Discrete Fluid Models

21.1 Lattice Gas Automata

21.2 Lattice Boltzmann Method

21.3 Stochastic Rotation Dynamics

21.4 Direct Simulation Monte Carlo

21.5 Dissipative Particle Dynamics

21.6 Smoothed Particle Hydrodynamics

22 Ab Initio Simulations

22.1 Introduction

22.2 Implementation of Wave Functions

22.3 Born-Oppenheimer Approximation

22.4 Hohenberg-Kohn Theorems

22.5 Kohn-Sham Approximation.

22.6 Hellmann-Feynman Theorem

22.7 Car-Parrinello Method

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 24 Aug 2021).

ISBN:

1-108-89665-0

1-108-88231-5

OCLC:

1263705817