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Statistical Physics of Non-Thermal Phase Transitions: From Foundations to Applications 2015 ed. [Kõva köide]

  • Formaat: Hardback, 497 pages, kõrgus x laius: 235x155 mm, kaal: 8867 g, 2 Illustrations, color; 142 Illustrations, black and white; XIV, 497 p. 144 illus., 2 illus. in color., 1 Hardback
  • Sari: Springer Series in Synergetics
  • Ilmumisaeg: 09-Jun-2015
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319124684
  • ISBN-13: 9783319124681
  • Formaat: Hardback, 497 pages, kõrgus x laius: 235x155 mm, kaal: 8867 g, 2 Illustrations, color; 142 Illustrations, black and white; XIV, 497 p. 144 illus., 2 illus. in color., 1 Hardback
  • Sari: Springer Series in Synergetics
  • Ilmumisaeg: 09-Jun-2015
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319124684
  • ISBN-13: 9783319124681
This book addresses the application of methods used in statistical physics to complex systems—from simple phenomenological analogies to more complex aspects, such as correlations, fluctuation-dissipation theorem, the concept of free energy, renormalization group approach and scaling. Statistical physics contains a well-developed formalism that describes phase transitions. It is useful to apply this formalism for damage phenomena as well. Fractals, the Ising model, percolation, damage mechanics, fluctuations, free energy formalism, renormalization group, and scaling, are some of the topics covered in Statistical Physics of Phase Transitions.

Arvustused

The present book in which one shows that fractals are pervasive everywhere in the Ising model, percolation, damage phenomena, renormalization group and scaling. The chapters are almost self-containing. It is a nice book quite suitable for a personal library. (Guy Jumarie, zbMATH, Vol.1325.82001, 2015)

1 Fractals 1(54)
1.1 The Concepts of Scale Invariance and Self-Similarity
1(3)
1.2 Measure Versus Dimensionality
4(8)
1.3 Self-Similarity (Scale Invariance) as the Origin of the Fractal Dimension
12(2)
1.4 Fractal Trees
14(2)
1.5 Self-Affine Fractals
16(3)
1.6 The Geometrical Support of Multifractals
19(4)
1.7 Multifractals, Examples
23(18)
1.7.1 Definitions
23(2)
1.7.2 The General Case of the Cantor Set
25(1)
1.7.3 Dimensions of the Subsets
26(3)
1.7.4 Lengths of the Subsets
29(5)
1.7.5 Measures of the Subsets
34(5)
1.7.6 Analogy with Statistical Physics
39(1)
1.7.7 Subsets η Versus Subsets α
40(1)
1.7.8 Summary
41(1)
1.8 The General Formalism of Multifractals
41(7)
1.9 Moments of the Measure Distribution
48(4)
References
52(3)
2 Ensemble Theory in Statistical Physics: Free Energy Potential 55(94)
2.1 Basic Definitions
55(2)
2.2 Energy Spectrum
57(6)
2.3 Microcanonical Ensemble
63(6)
2.4 MCE: Fluctuations as Nonequilibrium Probability Distributions
69(11)
2.5 Free Energy Potential of the MCE
80(8)
2.6 MCE: Free Energy Minimization Principle (Entropy Maximization Principle)
88(2)
2.7 Canonical Ensemble
90(5)
2.8 Nonequilibrium Fluctuations of the Canonical Ensemble
95(4)
2.9 Properties of the Probability Distribution of Energy Fluctuations
99(7)
2.10 Method of Steepest Descent
106(10)
2.11 Entropy of the CE. The Equivalence of the MCE and CE
116(2)
2.12 Free Energy Potential of the CE
118(6)
2.13 Free Energy Minimization Principle
124(2)
2.14 Other Ensembles
126(13)
2.15 Fluctuations as the Investigator's Tool
139(3)
2.16 The Action of the Free Energy
142(4)
References
146(3)
3 The Ising Model 149(76)
3.1 Definition of the Model
149(3)
3.2 Microstates, MCE, CE, Order Parameter
152(3)
3.3 Two-Level System Without Pair Spins Interactions
155(4)
3.4 A One-Dimensional Nonideal System with Short-Range Pair Spin Interactions: The Exact Solution
159(6)
3.5 Nonideal System with Pair Spin Interactions: The Mean-Field Approach
165(5)
3.6 Landau Theory
170(30)
3.6.1 The Equation of State
170(2)
3.6.2 The Minimization of Free Energy
172(4)
3.6.3 Stable, Metastable, Unstable States, and Maxwell's Rule
176(4)
3.6.4 Susceptibility
180(2)
3.6.5 Heat Capacity
182(4)
3.6.6 Equilibrium Free Energy
186(2)
3.6.7 Classification of Phase Transitions
188(1)
3.6.8 Critical and Spinodal Slowing Down
189(6)
3.6.9 Heterogeneous System
195(5)
3.7 Mean-Field Approach
200(7)
3.8 Antiferromagnets
207(10)
3.9 Antiferromagnet on a Triangular Lattice. Frustration
217(2)
3.10 Mixed Ferromagnet-Antiferromagnet
219(2)
References
221(4)
4 The Theory of Percolation 225(34)
4.1 The Model of Percolation
226(3)
4.2 One-Dimensional Percolation
229(4)
4.3 Square Lattice
233(4)
4.4 Bethe Lattice
237(10)
4.5 An Arbitrary Lattice
247(6)
4.6 The Moments of the Cluster-Size Distribution
253(3)
References
256(3)
5 Damage Phenomena 259(30)
5.1 The Parameter of Damage
259(2)
5.2 The Fiber-Bundle Model with Quenched Disorder
261(2)
5.3 The Ensemble of Constant Strain
263(4)
5.4 Stresses of Fibers
267(3)
5.5 The Ensemble of Constant Stress
270(7)
5.6 Spinodal Slowing Down
277(4)
5.7 FBM with Annealed Disorder
281(2)
References
283(6)
6 Correlations, Susceptibility, and the Fluctuation-Dissipation Theorem 289(76)
6.1 Correlations: The One-Dimensional Ising Model with Short-Range Interactions
290(6)
6.2 Correlations: The Mean-Field Approach for the Ising Model in Higher Dimensions
296(15)
6.3 Magnetic Systems: The Fluctuation-Dissipation Theorem
311(7)
6.4 Magnetic Systems: The Ginzburg Criterion
318(5)
6.5 Magnetic Systems: Heat Capacity as Susceptibility
323(5)
6.6 Percolation: The Correlation Length
328(5)
6.7 Percolation: Fluctuation-Dissipation Theorem
333(3)
6.8 Percolation: The Hyperscaling Relation and the Scaling of the Order Parameter
336(5)
6.9 Why Percolation Differs from Magnetic Systems
341(2)
6.10 Percolation: The Ensemble of Clusters
343(6)
6.11 The FBM: The Fluctuation-Dissipation Theorem
349(3)
6.12 The Ising Model
352(3)
6.13 The FBM: The epsilon-Ensemble
355(1)
6.14 The FBM: The σ-Ensemble
356(7)
References
363(2)
7 The Renormalization Group 365(56)
7.1 Scaling
366(2)
7.2 RG Approach of a Single Survivor: One-Dimensional Magnetic Systems
368(14)
7.3 RG Approach of a Single Survivor: Two-Dimensional Magnetic Systems
382(4)
7.4 RG Approach of Representation: Two-Dimensional Magnetic Systems in the Absence of Magnetic Field
386(12)
7.5 RG Approach of Representation: Two-Dimensional Magnetic Systems in the Presence of Magnetic Field
398(8)
7.6 Percolation
406(8)
7.7 Damage Phenomena
414(2)
7.8 Why does the RG Transformation Return only Approximate Results?
416(2)
References
418(3)
8 Scaling: The Finite-Size Effect and Crossover Effects 421(74)
8.1 Percolation: Why Is the Cluster-Size Distribution Hypothesis Wrong?
421(7)
8.2 Percolation: The Finite-Size Effect
428(15)
8.3 Magnetic Systems: The Scaling of Landau Theory
443(10)
8.4 Magnetic Systems: Scaling Hypotheses
453(6)
8.5 Magnetic Systems: Superseding Correction
459(5)
8.6 Crossover Effect of Magnetic Field
464(4)
8.7 Magnetic Systems: Crossover Phenomena
468(1)
8.8 Magnetic Systems: The Finite-Size Effect
469(3)
8.9 The Illusory Asymmetry of the Temperature
472(3)
8.10 The Formalism of General Homogeneous Functions
475(3)
8.11 The Renormalization Group as the Source of Scaling
478(12)
8.12 Magnetic Systems: Spinodal Scaling
490(2)
References
492(3)
Index 495