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E-raamat: Computational Statistical Physics

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 26-Aug-2021
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108896658
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Computational Statistical PhysicsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 26-Aug-2021
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108896658
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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.

Detailed and pedagogical account of computational statistical physics, this book covers both theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level.

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Detailed account of computational statistical physics, including theoretical foundations and modern, computational applications.
Preface xi
What is Computational Physics? xiii
Part I Stochastic Methods
1(146)
1 Random Numbers
3(14)
1.1 Definition of Random Numbers
3(1)
1.2 Congruential RNG (Multiplicative)
4(3)
1.3 Lagged Fibonacci RNG (Additive)
7(1)
1.4 Available Libraries
8(1)
1.5 How Good is an RNG?
9(2)
1.6 Nonuniform Distributions
11(6)
2 Random-Geometrical Models
17(38)
2.1 Percolation
17(1)
2.2 The Sol--Gel Transition
17(2)
2.3 The Percolation Model
19(15)
2.4 Fractals
34(8)
2.5 Walks
42(8)
2.6 Complex Networks
50(5)
3 Equilibrium Systems
55(12)
3.1 Classical Statistical Mechanics
55(4)
3.2 Ising Model
59(8)
4 Monte Carlo Methods
67(18)
4.1 Computation of Integrals
67(1)
4.2 Integration Errors
68(3)
4.3 Hard Spheres in a Box
71(3)
4.4 Markov Chains
74(2)
4.5 M(RT)2 Algorithm
76(3)
4.6 Glauber Dynamics (Heat Bath Dynamics)
79(1)
4.7 Binary Mixtures and Kawasaki Dynamics
80(1)
4.8 Creutz Algorithm
81(2)
4.9 Boundary Conditions
83(1)
4.10 Application to Interfaces
83(2)
5 Phase Transitions
85(8)
5.1 Temporal Correlations
85(2)
5.2 Decorrelated Configurations
87(1)
5.3 Finite-Size Scaling
87(2)
5.4 Binder Cumulant
89(1)
5.5 First-Order Transitions
90(3)
6 Cluster Algorithms
93(7)
6.1 Potts Model
93(1)
6.2 The Kasteleyn and Fortuin Theorem
94(1)
6.3 Coniglio--Klein Clusters
95(1)
6.4 Swendsen--Wang Algorithm
96(1)
6.5 Wolff Algorithm
97(1)
6.6 Continuous Degrees of Freedom: The n-Vector Model
98(2)
7 Histogram Methods
100(5)
7.1 Broad Histogram Method
101(1)
7.2 Flat Histogram Method
102(1)
7.3 Umbrella Sampling
103(2)
8 Renormalization Group
105(7)
8.1 Real Space Renormalization
105(1)
8.2 Renormalization and Free Energy
105(1)
8.3 Majority Rule
106(1)
8.4 Decimation of the One-Dimensional Ising Model
107(2)
8.5 Generalization
109(2)
8.6 Monte Carlo Renormalization Group
111(1)
9 Learning and Optimizing
112(10)
9.1 Hopfield Network
112(2)
9.2 Boltzmann Machine Learning
114(5)
9.3 Simulated Annealing
119(3)
10 Parallelization
122(5)
10.1 Multispin Coding
122(2)
10.2 Vectorization
124(1)
10.3 Domain Decomposition
125(2)
11 Nonequilibrium Systems
127(20)
11.1 Directed Percolation and Gillespie Algorithms
127(6)
11.2 Cellular Automata
133(4)
11.3 Irreversible Growth
137(10)
Part II Molecular Dynamics
147(85)
12 Basic Molecular Dynamics
149(8)
12.1 Introduction
149(1)
12.2 Equations of Motion
150(2)
12.3 Contact Time
152(1)
12.4 Verlet Method
153(1)
12.5 Leapfrog Method
154(3)
13 Optimizing Molecular Dynamics
157(4)
13.1 Verlet Tables
158(1)
13.2 Linked-Cell Method
158(3)
14 Dynamics of Composed Particles
161(8)
14.1 Lagrange Multipliers
161(2)
14.2 Rigid Bodies
163(6)
15 Long-Range Potentials
169(8)
15.1 Ewald Summation
169(2)
15.2 Particle-Mesh Method
171(4)
15.3 Reaction Field Method
175(2)
16 Canonical Ensemble
177(10)
16.1 Velocity Rescaling
178(1)
16.2 Constraint Method
179(1)
16.3 Nose-Hoover Thermostat
179(4)
16.4 Stochastic Method
183(1)
16.5 Constant Pressure
184(1)
16.6 Parrinello--Rahman Barostat
185(2)
17 Inelastic Collisions in Molecular Dynamics
187(5)
17.1 Restitution Coefficient
187(1)
17.2 Plastic Deformation
188(2)
17.3 Coulomb Friction and Discrete Element Method
190(2)
18 Event-Driven Molecular Dynamics
192(10)
18.1 Event-Driven Procedure
192(2)
18.2 Lubachevsky Method
194(1)
18.3 Collision with Perfect Slip
195(1)
18.4 Collision with Rotation
196(1)
18.5 Inelastic Collisions
197(1)
18.6 Inelastic Collapse
198(4)
19 Nonspherical Particles
202(6)
19.1 Ellipsoidal Particles
202(3)
19.2 Polygons
205(1)
19.3 Spheropolygons
205(3)
20 Contact Dynamics
208(7)
20.1 One-Dimensional Contact
208(4)
20.2 Generalization to N Particles
212(3)
21 Discrete Fluid Models
215(7)
21.1 Lattice Gas Automata
215(1)
21.2 Lattice Boltzmann Method
215(3)
21.3 Stochastic Rotation Dynamics
218(1)
21.4 Direct Simulation Monte Carlo
219(1)
21.5 Dissipative Particle Dynamics
220(1)
21.6 Smoothed Particle Hydrodynamics
221(1)
22 Ab Initio Simulations
222(10)
22.1 Introduction
222(3)
22.2 Implementation of Wave Functions
225(1)
22.3 Born--Oppenheimer Approximation
225(1)
22.4 Hohenberg--Kohn Theorems
226(2)
22.5 Kohn--Sham Approximation
228(1)
22.6 Hellmann--Feynman Theorem
229(1)
22.7 Car--Parrinello Method
230(2)
References 232(20)
Index 252
Lucas Böttcher is Assistant Professor of Computational Social Science at Frankfurt School of Finance and Management and Research Scientist at UCLA's Department of Computational Medicine. His research areas include statistical physics, applied mathematics, complex systems science, and computational physics. He is interested in the application of concepts and models from statistical physics to other disciplines, including biology, ecology, and sociology. Hans J. Herrmann is Directeur de Recherche at CNRS in Paris, visiting Professor at the Federal University of Ceará in Brazil and Emeritus of ETH Zürich. He is a Guggenheim Fellow (1986), member of the Brazilian Academy of Science, and a Fellow of the American Physical Society. He has been the recipient of numerous prestigious awards including the Max-Planck Prize (2002), the Gentner-Kastler prize (2005), the Aneesur Rahman prize (2018), and an IBM Faculty Award (2009), and he has received an ERC Advanced Grant (2012). He is Managing Editor of International Journal of Modern Physics C and of Granular Matter. He has coauthored over 700 publications and coedited 13 books.
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