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Cellular Automata Modeling of Physical Systems [Kõva köide]

(Université de Genève), (Université de Genève)
  • Formaat: Hardback, 353 pages, kõrgus x laius x paksus: 255x180x24 mm, kaal: 750 g, Worked examples or Exercises; 86 Halftones, unspecified; 85 Line drawings, unspecified
  • Sari: Collection Alea-Saclay: Monographs and Texts in Statistical Physics
  • Ilmumisaeg: 10-Dec-1998
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521461685
  • ISBN-13: 9780521461689
Teised raamatud teemal:
Cellular Automata Modeling of Physical SystemsSuurem pilt
  • Formaat: Hardback, 353 pages, kõrgus x laius x paksus: 255x180x24 mm, kaal: 750 g, Worked examples or Exercises; 86 Halftones, unspecified; 85 Line drawings, unspecified
  • Sari: Collection Alea-Saclay: Monographs and Texts in Statistical Physics
  • Ilmumisaeg: 10-Dec-1998
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521461685
  • ISBN-13: 9780521461689
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780521461689.html
Märksõnad:
Self-contained, pedagogic introduction to powerful techniques for graduate students and researchers in physics and computer science.

This book provides an introduction to cellular automata and lattice Boltzmann techniques. It begins with a chapter introducing the basic concepts of this developing field; a second chapter describes methods used in cellular automata modeling. Following chapters discuss the statistical mechanics of lattice gases, diffusion phenomena, reaction-diffusion processes and nonequilibrium phase transitions. A final chapter looks at other models and applications, such as wave propagation and multiparticle fluids. With a pedagogic approach, the volume focuses on the use of cellular automata in the framework of equilibrium and nonequilibrium statistical physics, emphasizing application-oriented problems such as fluid dynamics and pattern formation. The book contains many examples and problems as well as a glossary and a detailed bibliography. This will be a valuable book for graduate students and researchers working in statistical physics, solid state physics, chemical physics and computer science.

Arvustused

'The book should become a standard reference for anyone interested in cellular automata modelling.' A. Bovier, Zentralblatt für Mathematik

Muu info

Self-contained, pedagogic introduction to powerful techniques for graduate students and researchers in physics and computer science.
Preface xi
1 Introduction
1(20)
1.1 Brief history
1(7)
1.1.1 Self-reproducing systems
1(2)
1.1.2 Simple dynamical systems
3(1)
1.1.3 A synthetic universe
4(1)
1.1.4 Modeling physical systems
5(2)
1.1.5 Beyond the cellular automata dynamics: lattice Boltzmann methods and multiparticle models
7(1)
1.2 A simple cellular automation: the parity rule
8(4)
1.3 Definitions
12(6)
1.3.1 Cellular automata
12(2)
1.3.2 Neighborhood
14(1)
1.3.3 Boundary conditions
15(1)
1.3.4 Some remarks
16(2)
1.4 Problems
18(3)
2 Cellular automata modeling
21(45)
2.1 Why cellular automata are useful in physics
21(7)
2.1.1 Cellular automata as simple dynamical systems
21(3)
2.1.2 Cellular automata as spatially extended systems
24(2)
2.1.3 Several levels of reality
26(1)
2.1.4 A fictitious microscopic world
27(1)
2.2 Modeling of simple systems: a sampler of rules
28(33)
2.2.1 The rule 184 as a model for surface growth
29(1)
2.2.2 Probabilistic cellular automata rules
29(4)
2.2.3 The Q2R rule
33(4)
2.2.4 The annealing rule
37(1)
2.2.5 The HPP rule
38(4)
2.2.6 The sand pile rule
42(4)
2.2.7 The ant rule
46(5)
2.2.8 The road traffic rule
51(5)
2.2.9 The solid body motion rule
56(5)
2.3 Problems
61(5)
3 Statistical mechanics of lattice gas
66(72)
3.1 The one-dimensional diffusion automaton
66(9)
3.1.1 A random walk automaton
67(1)
3.1.2 The macroscopic limit
68(3)
3.1.3 The Chapman--Enskog expansion
71(3)
3.1.4 Spurious invariants
74(1)
3.2 The FHP model
75(37)
3.2.1 The collision rule
75(3)
3.2.2 The microdynamics
78(2)
3.2.3 From microdynamics to macrodynamics
80(25)
3.2.4 The collision matrix and semi-detailed balance
105(2)
3.2.5 The FHP-III model
107(3)
3.2.6 Examples of fluid flows
110(2)
3.2.7 Three-dimensional lattice gas models
112(1)
3.3 Thermal lattice gas automata
112(5)
3.3.1 Multispeed models
112(3)
3.3.2 Thermo-hydrodynamical equations
115(1)
3.3.3 Thermal FHP lattice gases
116(1)
3.4 The staggered invariants
117(5)
3.5 Lattice Boltzmann models
122(13)
3.5.1 Introduction
122(3)
3.5.2 A simple two-dimensional lattice Boltzmann fluid
125(9)
3.5.3 Lattice Boltzmann flows
134(1)
3.6 Problems
135(3)
4 Diffusion phenomena
138(40)
4.1 Introduction
138(1)
4.2 The diffusion model
139(11)
4.2.1 Microdynamics of the diffusion process
140(7)
4.2.2 The mean square displacement and the Green--Kubo formula
147(2)
4.2.3 The three-dimensional case
149(1)
4.3 Finite systems
150(13)
4.3.1 The stationary source--sink problem
151(2)
4.3.2 Telegraphist equation
153(4)
4.3.3 The discrete Boltzmann equation in 2D
157(2)
4.3.4 Semi-infinite strip
159(4)
4.4 Applications of the diffusion rule
163(12)
4.4.1 Study of the diffusion front
163(3)
4.4.2 Diffusion-limited aggregation
166(5)
4.4.3 Diffusion-limited surface adsorption
171(4)
4.5 Problems
175(3)
5 Reaction-diffusion processes
178(54)
5.1 Introduction
178(1)
5.2 A model for excitable media
179(2)
5.3 Lattice gas microdynamics
181(6)
5.3.1 From microdynamics to rate equations
184(3)
5.4 Anomalous kinetics
187(6)
5.4.1 The homogeneous A + B --> (Phi) process
188(2)
5.4.2 Cellular automata or lattice Boltzmann modeling
190(1)
5.4.3 Simulation results
191(2)
5.5 Reaction front in the A + B --> (Phi) process
193(5)
5.5.1 The scaling solution
195(3)
5.6 Liesegang patterns
198(11)
5.6.1 What are Liesegang patterns
198(3)
5.6.2 The lattice gas automata model
201(1)
5.6.3 Cellular automata bands and rings
202(4)
5.6.4 The lattice Boltzmann model
206(2)
5.6.5 Lattice Boltzmann rings and spirals
208(1)
5.7 Multiparticle models
209(10)
5.7.1 Multiparticle diffusion model
210(2)
5.7.2 Numerical implementation
212(2)
5.7.3 The reaction algorithm
214(2)
5.7.4 Rate equation approximation
216(1)
5.7.5 Turing patterns
217(2)
5.8 From cellular automata to field theory
219(9)
5.9 Problems
228(4)
6 Nonequilibrium phase transitions
232(24)
6.1 Introduction
232(2)
6.2 Simple interacting particle systems
234(8)
6.2.1 The A model
234(7)
6.2.2 The contact process model (CPM)
241(1)
6.3 Simple models of catalytic surfaces
242(7)
6.3.1 The Ziff model
242(6)
6.3.2 More complicated models
248(1)
6.4 Critical behavior
249(5)
6.4.1 Localization of the critical point
250(2)
6.4.2 Critical exponents and universality classes
252(2)
6.5 Problems
254(2)
7 Other models and applications
256(57)
7.1 Wave propagation
256(24)
7.1.1 One-dimensional waves
256(2)
7.1.2 Two-dimensional waves
258(9)
7.1.3 The lattice BGK formulation of the wave model
267(11)
7.1.4 An application to wave propagation in urban environments
278(2)
7.2 Wetting, spreading and two-phase fluids
280(18)
7.2.1 Multiphase flows
280(2)
7.2.2 The problem of wetting
282(2)
7.2.3 An FHP model with surface tension
284(3)
7.2.4 Mapping of the hexagonal lattice on a square lattice
287(2)
7.2.5 Simulations of wetting phenomena
289(3)
7.2.6 Another force rule
292(1)
7.2.7 An Ising cellular automata fluid
293(5)
7.3 Multiparticle fluids
298(7)
7.3.1 The multiparticle collision rule
299(3)
7.3.2 Multiparticle fluid simulations
302(2)
7.4 Modeling snow transport by wind
305(8)
7.4.1 The wind model
305(3)
7.4.2 The snow model
308(4)
7.4.3 Simulations of snow transport
312(1)
References 313(14)
Glossary 327(10)
Index 337