Phase transition dynamics:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
2014
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXII, 555 S. graph. Darst. |
| ISBN: | 9781461489627 |
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| 245 | 1 | 0 | |a Phase transition dynamics |c Tian Ma ; Shouhong Wang |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2014 | |
| 300 | |a XXII, 555 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804150713555615744 |
|---|---|
| adam_text | Contents
Introduction
.......................................................xvii
1
Introduction
to Dynamic Transitions
............................. 1
1.1
First Principles and Dynamic Models
.......................... 1
1.1.1
Physical Laws and Mathematical Models
................ 1
1.1.2
Rayleigh-Bénard
Convection
.......................... 2
1.1.3
Mathematical Formulation of Physical Problems
.......... 5
1.2
Introduction to Dynamic Transition Theory
..................... 7
1.2.1
Motivation and Key Philosophy
........................ 7
1.2.2
Principle of Exchange of Stability
...................... 7
1.2.3
Equation of Critical Parameters
........................ 8
1.2.4
Classifications of Dynamic Transitions
.................. 9
1.2.5
Structure and Characterization of Dynamic Transitions
..... 11
1.2.6
General Features of Dynamic Transitions
................ 12
1.3
Examples of Typical Phase Transition Problems
................. 14
1.3.1
Rayleigh-Bénard
Convection
.......................... 14
1.3.2
El Niño
Southern Oscillation
.......................... 15
1.3.3
Dynamic Transition Versus Transition in Physical Space
... 17
1.3.4
Andrews Critical Point and Third-Order Gas-Liquid
Transition
.......................................... 20
1.3.5
Binary Systems
...................................... 21
2
Dynamic Transition Theory
..................................... 25
2.1
General Dynamic Transition Theory
........................... 25
2.1.1
Classification of Dynamic Transitions
................... 25
2.1.2
Characterization of Transition Types
.................... 28
2.1.3
Local Topological Structure of Transitions
............... 30
2.2
Continuous Transition
....................................... 34
2.2.1
Finite-Dimensional Systems
........................... 34
2.2.2
Sl -Attractor Bifurcation
............................... 35
2.2.3
y-Attractor Bifurcation
.............................. 42
Xl
Contents
2.2.4
Structural Stability of Dynamic Transitions
.............. 42
2.2.5
Infinite-Dimensional Systems
.......................... 44
2.3
Transition from Simple Eigenvalues
........................... 46
2.3.1
Real Simple Eigenvalues
.............................. 46
2.3.2
Transitions from Complex Simple Eigenvalues
........... 49
2.3.3
Computation of
b
.................................... 55
2.4
Transition from Eigenvalues with Multiplicity Two
.............. 57
2.4.1
Index Formula for Second-Order
Nondegenerate
Singularities
........................................ 57
2.4.2
Bifurcation at Second-Order Singular Points
............. 60
2.4.3
The Case
ind (F,0) =
-2............................. 65
2.4.4
The Case
ind
(F,0)
= 2............................... 70
2.4.5
The Case
ind
(F,
0) = 0............................... 78
2.4.6
Indices of
Äth-order
Nondegenerate
Singularities
.......... 80
2.4.7
Structure of fcth-Order
Nondegenerate
Singularities
........ 91
2.4.8
Transition from
fcth-Order Nondegenerate
Singularities
.... 93
2.4.9
Bifurcation to Periodic Orbits
.......................... 97
2.4.10
Application to Parabolic Systems
....................... 99
2.5
Singular Separation
......................................... 101
2.5.1
General Principle
....................................101
2.5.2
Saddle-Node Bifurcation
..............................103
2.5.3
Singular Separation of Periodic Orbits
...................106
2.6
Perturbed Systems
..........................................107
2.6.1
General Eigenvalues
..................................107
2.6.2
Simple Eigenvalues
..................................109
2.6.3
Complex Eigenvalues
.................................113
2.7
Notes
.....................................................121
Equilibrium Phase Transition in Statistical Physics
................123
3.1
Dynamic Models for Equilibrium Phase Transitions
..............124
3.1.1
Thermodynamic Potentials
............................125
3.1.2
Time-Dependent Equations
............................127
3.2
Classification of Equilibrium Phase Transitions
.................131
3.3
Third-Order Gas-Liquid Phase Transition
......................133
3.3.1
Introduction
.........................................133
3.3.2
Time-Dependent Models for PVT Systems
...............134
3.3.3
Phase Transition Dynamics for PVT Systems
.............136
3.3.4
Physical Conclusions
.................................139
3.4
Ferromagnetism
............................................142
3.4.1
Classical Theory of Ferromagnetism
....................142
3.4.2
Dynamic Transitions in Ferromagnetism
.................146
3.4.3
Physical Implications
.................................150
3.4.4
Asymmetry of Fluctuations
............................152
3.5
Phase Separation in Binary Systems
...........................153
3.5.1
Modeling
...........................................154
Contents
Xlii
3.5.2 Phase Transition in General Domains...................155
3.5.3 Phase Transition in
Rectangular
Domains................160
3.5.4
Spatial
Geometry,
Transitions,
and Pattern Formation
......171
3.5.5
Phase Diagrams and Physical Conclusions
...............174
3.6
Superconductivity
..........................................181
3.6.1
Ginzburg-Landau Model
..............................182
3.6.2
TGDL as a Gradient-Type System
......................186
3.6.3
Phase Transition Theorems
............................189
3.6.4
Model Coupled with Entropy
..........................197
3.6.5
Physical Conclusions
.................................198
3.7
Liquid Helium^
...........................................208
3.7.1
Dynamic Model for Liquid Helium-4
...................209
3.7.2
Dynamic Phase Transition for Liquid 4He
...............212
3.8
Superfluidity of Helium-3
...................................218
3.8.1
Dynamic Model for Liquid 3He with Zero Applied Field
... 221
3.8.2
Critical Parameter Curves and
РГ
-Phase
Diagram
.........223
3.8.3
Classification of Superfluid Transitions
..................229
3.8.4
Liquid 3He with Nonzero Applied Field
.................235
3.8.5
Physical Remarks
....................................239
3.9
Mixture of He-3 and He-4
...................................239
3.9.1
Model for Liquid Mixture of 3He and 4He
...............240
3.9.2
Critical Parameter Curves
.............................242
3.9.3
Transition Theorems
.................................243
3.9.4
Physical Conclusions
.................................248
4
Fluid Dynamics
................................................249
4.1
Rayleigh-Bénard
Convection
.................................250
4.1.1
Benard
Problem
.....................................250
4.1.2
Boussinesq Equations
................................251
4.1.3
Dynamic Transition Theorems
.........................253
4.1.4
Topological Structure and Pattern Formation
.............258
4.1.5
Asymptotic Structure of Solutions for the
Benard
Problem
............................................267
4.1.6
Structure of Bifurcated Attractors
.......................269
4.1.7
Physical Remarks
....................................277
4.2
Taylor-Couette Flow
........................................277
4.2.1
Taylor Problem
......................................278
4.2.2
Governing Equations
.................................279
4.2.3
Narrow-Gap Case with Axisymmetric Perturbations
.......282
4.2.4
Asymptotic Structure of Solutions and Taylor Vortices
.....286
4.2.5
Taylor Problem with z-Periodic Boundary Condition
.......293
4.2.6
Other Boundary Conditions
............................309
4.2.7
Three-Dimensional Perturbation for the Narrow-Gap
Case
...............................................313
4.2.8
Physical Remarks
....................................315
xiv Contents
4.3
Boundary-Layer and Interior Separations in the Taylor-Couette—
Poiseuille Flow
............................................317
4.3.1
Model for the Taylor-Couette-Poiseuille Problem
.........318
4.3.2
Phase Transition of the TCP Problem
...................321
4.3.3
Boundary-Layer Separation from the
Couette—
Poiseuille
Row
...............................................325
4.3.4
Interior Separation from the
Couette—
Poiseuille Flow
......332
4.3.5
Nature of Boundary-Layer and Interior Separations
........336
4.4
Rotating Convection Problem
................................340
4.4.1
Rotating Boussinesq Equations
.........................341
4.4.2
Eigenvalue Problem
..................................342
4.4.3
Principle of Exchange of Stabilities
.....................347
4.4.4
Transition from First Real Eigenvalues
..................354
4.4.5
Transition from First Complex Eigenvalues
..............360
4.4.6
Physical Remarks
....................................365
4.5
Convection Scale Theory
....................................368
5
Geophysical Fluid Dynamics and Climate Dynamics
...............373
5.1
Modeling and General Characteristics of Geophysical Flows
......374
5.2
El Niño—
Southern Oscillation
................................376
5.2.1
Walker Circulation and ENSO
.........................377
5.2.2
Equatorial Circulation Equations
.......................378
5.2.3
Walker Circulation Under Idealized Conditions
...........380
5.2.4
Walker Circulation Under Natural Conditions
............387
5.2.5
ENSO: Metastable Oscillation Theory
...................393
5.3
Thermohaline Ocean Circulation
..............................396
5.3.1
Boussinesq Equations
................................398
5.3.2
Linear Analysis
......................................400
5.3.3
Nonlinear Dynamic Transitions
........................409
5.3.4
Convection Scales and Dynamic Transition
..............416
5.4
Arctic Ocean Circulations
...................................425
5.4.1
Model
..............................................426
5.4.2
Linear Theory
.......................................427
5.4.3
Transition Theorems
.................................432
5.4.4
Revised Transition Theory
............................435
5.4.5
Physical Conclusions
.................................437
5.5
Large-Scale Meridional Atmospheric Circulation
................438
5.5.1
Polar,
Ferrei,
and Hadley Cells
.........................438
5.5.2
0-Plane Assumption
.................................439
5.5.3
Meridional Circulation Under Idealized Conditions
........441
5.5.4
Physical Implications
.................................445
Contents xv
6
Dynamical Transitions in Chemistry and Biology
..................447
6.1
Modeling
.................................................448
6.1.1
Dynamical Equations of Chemical Reactions
.............448
6.1.2
Population Models of Biological Species
................450
6.2
Belousov-Zhabotinsky Chemical Reactions:
Oregonator
..........452
6.2.1
The
Field-Kőrös-Noyes
Equations
.....................452
6.2.2
Transition Under the Dirichlet Boundary Condition
........455
6.2.3
Transitions Under the Neumann Boundary Condition
......459
6.2.4
Phase Transition in the Realistic
Oregonator
..............470
6.3
Belousov-Zhabotinsky Reactions: Brusselator
..................475
6.3.1
Prigogine-Lefever Model
.............................476
6.3.2
Linearized Problem
..................................477
6.3.3
Transition from Real Eigenvalues
.......................479
6.3.4
Transition from Complex Eigenvalues
...................480
6.4
Bacterial Chemotaxis
.......................................482
6.4.1 Keller-Segel
Models
.................................483
6.4.2
Dynamic Transitions for a Rich Stimulant System
.........489
6.4.3
Transition of Three-Component Systems
................499
6.4.4
Biological Conclusions
...............................506
6.5
Biological Species
..........................................508
6.5.1
Modeling
...........................................508
6.5.2
Predator-Prey Systems
...............................510
6.5.3
Three-Species Systems
...............................517
Appendix A
........................................................527
A.
1
Formulas for Center Manifold Functions
.......................527
A.2 Dynamics of Gradient-Type Systems
..........................533
References
.........................................................541
Index
.............................................................553
Tian
Ma
·
Shouhong
Wang
Phase Transition Dynamics
This book is
an introduction
to a comprehensive and unified dynamic transition theory
for dissipative systems and to applications of the theory to a range of problems in
the nonlinear sciences. The main objectives of this book are to introduce a general
principle of dynamic transitions for dissipative systems, to establish a systematic
dynamic transition theory, and to explore the physical implications of applications of
the theory to a range of problems in the nonlinear sciences. The basic philosophy of
the theory is to search for a complete set of transition states, and the general principle
states that dynamic transitions of all dissipative systems can be classified into three
categories: continuous, catastrophic and random. The audience for this book includes
advanced graduate students and researchers in mathematics and physics as well as in
other related fields.
|
| any_adam_object | 1 |
| author | Ma, Tian 1956- Wang, Shouhong 1962- |
| author_GND | (DE-588)136728367 (DE-588)1065187831 |
| author_facet | Ma, Tian 1956- Wang, Shouhong 1962- |
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| author_sort | Ma, Tian 1956- |
| author_variant | t m tm s w sw |
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| bvnumber | BV041256048 |
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| discipline | Physik Mathematik |
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| id | DE-604.BV041256048 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:43:18Z |
| institution | BVB |
| isbn | 9781461489627 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026229985 |
| oclc_num | 869849787 |
| open_access_boolean | |
| owner | DE-703 DE-11 DE-83 DE-188 |
| owner_facet | DE-703 DE-11 DE-83 DE-188 |
| physical | XXII, 555 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| spelling | Ma, Tian 1956- Verfasser (DE-588)136728367 aut Phase transition dynamics Tian Ma ; Shouhong Wang New York [u.a.] Springer 2014 XXII, 555 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Topologische Phase (DE-588)113303408X gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Dissipatives System (DE-588)4209641-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Phasenumwandlung (DE-588)4132140-6 s Dissipatives System (DE-588)4209641-8 s Dynamik (DE-588)4013384-9 s Topologische Phase (DE-588)113303408X s 1\p DE-604 Wang, Shouhong 1962- Verfasser (DE-588)1065187831 aut Erscheint auch als Online-Ausgabe 978-1-4614-8963-4 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026229985&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026229985&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ma, Tian 1956- Wang, Shouhong 1962- Phase transition dynamics Phasenumwandlung (DE-588)4132140-6 gnd Topologische Phase (DE-588)113303408X gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Dynamik (DE-588)4013384-9 gnd Dissipatives System (DE-588)4209641-8 gnd |
| subject_GND | (DE-588)4132140-6 (DE-588)113303408X (DE-588)4044779-0 (DE-588)4013384-9 (DE-588)4209641-8 |
| title | Phase transition dynamics |
| title_auth | Phase transition dynamics |
| title_exact_search | Phase transition dynamics |
| title_full | Phase transition dynamics Tian Ma ; Shouhong Wang |
| title_fullStr | Phase transition dynamics Tian Ma ; Shouhong Wang |
| title_full_unstemmed | Phase transition dynamics Tian Ma ; Shouhong Wang |
| title_short | Phase transition dynamics |
| title_sort | phase transition dynamics |
| topic | Phasenumwandlung (DE-588)4132140-6 gnd Topologische Phase (DE-588)113303408X gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Dynamik (DE-588)4013384-9 gnd Dissipatives System (DE-588)4209641-8 gnd |
| topic_facet | Phasenumwandlung Topologische Phase Partielle Differentialgleichung Dynamik Dissipatives System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026229985&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026229985&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT matian phasetransitiondynamics AT wangshouhong phasetransitiondynamics |