Complex dynamics of glass-forming liquids: a mode-coupling theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford Univ. Press
2009
|
| Schriftenreihe: | International series of monographs on physics
143 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XI, 641 S. graph. Darst. |
| ISBN: | 9780199235346 9780199656141 |
Internformat
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| 100 | 1 | |a Götze, Wolfgang |d 1937-2021 |e Verfasser |0 (DE-588)137682530 |4 aut | |
| 245 | 1 | 0 | |a Complex dynamics of glass-forming liquids |b a mode-coupling theory |c Wolfgang Götze |
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2009 | |
| 300 | |a XI, 641 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a International series of monographs on physics |v 143 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Viscosity | |
| 650 | 4 | |a Mode-coupling theory | |
| 650 | 4 | |a Equations of motion | |
| 650 | 4 | |a Complex fluids | |
| 650 | 4 | |a Molecular dynamics | |
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Datensatz im Suchindex
| _version_ | 1804138085131223040 |
|---|---|
| adam_text | CONTENTS
Preface
Glassy dynamics of liquids-facets of the phenomenon
1
1.1
Stretching of the dynamics
1
1.2
Power-law relaxation
g
1.3
Superposition principles
15
1.4
Two-step relaxation through a plateau
21
1.5
The cage effect
24
1.6
Crossover phenomena
30
1.7
Hard-sphere systems: the paradigms
37
1.8
Hard-sphere systems with short-range attraction
44
Correlation functions
51
2.1
The evolution of dynamical variables
54
2.2
Correlation-function description of the dynamics
61
2.3
Spectral representations
66
2.4
Memory-kernel descriptions of correlators
72
2.4.1
Zwanzig-Mori equations
72
2.4.2
Models for correlation functions
78
2.5
Linear-response theory
82
2.6
The arrested parts of correlation functions
89
Elements of liquid dynamics
96
3.1
Preliminaries
96
3.1.1
Homogeneous
isotropie
systems without chirality
96
3.1.2
Densities and density fluctuations
100
3.2
Tagged-particle dynamics
107
3.2.1
Basic concepts and general equations
107
3.2.2
Tagged-particle diffusion
112
3.2.3
The friction coefficient
120
3.2.4
The cage effect and glassy-dynamics precursors
of the velocity correlations
125
3.3
Densities and currents in simple liquids
132
3.3.1
Definitions and general equations
132
3.3.2
Transverse-current diffusion
142
3.3.3
The generalized-hydrodynamics description of
transverse-current correlations
145
3.3.4
Visco-elastic features and glassy-dynamics precursors
of the transverse-current correlators
149
Contents
3.3.5
Representations of the density correlators
in terms of relaxation kernels
154
3.3.6
Sound waves and heat diffusion
161
3.3.7
Visco-elastic features and glassy-dynamics precursors
of the density-fluctuation correlators
169
Foundations of the mode-coupling theory for the
evolution of glassy dynamics in liquids
177
4.1
Self-consistent-current-relaxation approaches
178
4.1.1
The factorization ansatz
178
4.1.2
Self-consistency equations for density correlators
185
4.2
A mode-coupling theory
191
4.2.1
Equations of motion and fixed-point equations
191
4.2.2
Mode-coupling-theory models
196
4.2.3
The basic version of microscopic mode-coupling
theories
204
4.2.4
An elementary mode-coupling-theory model
209
4.3
Glass-transition singularities
217
4.3.1
Regular and critical states
217
4.3.2
Examples for bifurcation diagrams
224
4.3.3
Classification of the critical states
235
4.3.4
Correlation arrest near A2 singularities
242
4.3.5
Density-fluctuation arrest in hard-sphere-like systems
250
4.3.6
Arrest in systems with short-ranged-attraction
256
4.4
Dynamics near glass-transition singularities
267
4.4.1
Relaxation through plateaus
267
4.4.2
Below-plateau relaxation
281
4.4.3
Structure and structure relaxation
289
4.4.4
Descriptions of some glassy-dynamics data
292
Extensions of the mode-coupling theory for the
evolution of glassy dynamics of liquids
304
5.1
Extensions of the MCT for simple systems
305
5.1.1
MCT equations for the glassy shear dynamics
305
5.1.2
Glassy-relaxation features of shear correlations
308
5.1.3
MCT equations for the tagged-particle dynamics
320
5.1.4
Idealized transitions from diffusion to localization
331
5.1.5
Glassy-dynamics features of tagged-particle motions
345
5.2
A mode-coupling theory for mixtures of spherical particles
356
5.2.1
The equations of motion
357
5.2.2
Density-fluctuation arrest
366
5.2.3
Hard-sphere mixtures
375
5.2.4
Sodium-disilicate melts
383
Contents xi
5.3
A mode-coupling theory for molecular liquids
386
5.3.1
A theory for interaction-site-density correlators
387
5.3.2
Systems of symmetric dumbbells
395
5.3.3
Glassy Rouse dynamics
427
5.4
Some addenda
432
6
Asymptotic relaxation laws
437
6.1
Dynamics of the first-scaling-law regime
438
6.1.1
Reformulation of the MCT equations of motion
438
6.1.2
The critical dynamics
443
6.1.3
Asymptotic description of the ^-bifurcation dynamics
470
6.1.4
The scaling-limit description of the generic
liquid-glass-transition dynamics
492
6.1.5
Extended scaling-limit description of the
generic ^-bifurcation dynamics
502
6.2
Dynamics of the second-scaling-law regime
513
6.2.1
Equations of motion for the second-scaling-law regime
514
6.2.2
The second-scaling-law description of the liquid
dynamics
519
6.2.3
Asymptotic corrections for the second scaling limit
533
6.3
Relaxation near higher-order singularities
538
6.3.1
Correlation arrest near higher-order singularities
539
6.3.2
Logarithmic relaxation
553
A Mathematical miscellanies
577
A.I Laplace transforms
577
A.2 Fourier transforms
580
A.3 Positive-definite and positive-analytic functions
583
A.4 Harmonic-oscillator correlators
588
A.
5
Matrix correlators
591
A.6 Product correlators
594
A.
7
Power-law variations
596
A.
8
Logarithmic variations
601
В
Symmetries of fluctuation correlators
603
С
Smoothened correlators
608
D
Theorems on MCT equations
611
D.I Convergence of the approximant sequences
611
D.2 Completely
monotonie
approximants
613
D.3 The maximum-eigenvalue inequality
616
D.4 Further properties of stability matrices
618
Bibliography
621
Index
635
|
| adam_txt |
CONTENTS
Preface
Glassy dynamics of liquids-facets of the phenomenon
1
1.1
Stretching of the dynamics
1
1.2
Power-law relaxation
g
1.3
Superposition principles
15
1.4
Two-step relaxation through a plateau
21
1.5
The cage effect
24
1.6
Crossover phenomena
30
1.7
Hard-sphere systems: the paradigms
37
1.8
Hard-sphere systems with short-range attraction
44
Correlation functions
51
2.1
The evolution of dynamical variables
54
2.2
Correlation-function description of the dynamics
61
2.3
Spectral representations
66
2.4
Memory-kernel descriptions of correlators
72
2.4.1
Zwanzig-Mori equations
72
2.4.2
Models for correlation functions
78
2.5
Linear-response theory
82
2.6
The arrested parts of correlation functions
89
Elements of liquid dynamics
96
3.1
Preliminaries
96
3.1.1
Homogeneous
isotropie
systems without chirality
96
3.1.2
Densities and density fluctuations
100
3.2
Tagged-particle dynamics
107
3.2.1
Basic concepts and general equations
107
3.2.2
Tagged-particle diffusion
112
3.2.3
The friction coefficient
120
3.2.4
The cage effect and glassy-dynamics precursors
of the velocity correlations
125
3.3
Densities and currents in simple liquids
132
3.3.1
Definitions and general equations
132
3.3.2
Transverse-current diffusion
142
3.3.3
The generalized-hydrodynamics description of
transverse-current correlations
145
3.3.4
Visco-elastic features and glassy-dynamics precursors
of the transverse-current correlators
149
Contents
3.3.5
Representations of the density correlators
in terms of relaxation kernels
154
3.3.6
Sound waves and heat diffusion
161
3.3.7
Visco-elastic features and glassy-dynamics precursors
of the density-fluctuation correlators
169
Foundations of the mode-coupling theory for the
evolution of glassy dynamics in liquids
177
4.1
Self-consistent-current-relaxation approaches
178
4.1.1
The factorization ansatz
178
4.1.2
Self-consistency equations for density correlators
185
4.2
A mode-coupling theory
191
4.2.1
Equations of motion and fixed-point equations
191
4.2.2
Mode-coupling-theory models
196
4.2.3
The basic version of microscopic mode-coupling
theories
204
4.2.4
An elementary mode-coupling-theory model
209
4.3
Glass-transition singularities
217
4.3.1
Regular and critical states
217
4.3.2
Examples for bifurcation diagrams
224
4.3.3
Classification of the critical states
235
4.3.4
Correlation arrest near A2 singularities
242
4.3.5
Density-fluctuation arrest in hard-sphere-like systems
250
4.3.6
Arrest in systems with short-ranged-attraction
256
4.4
Dynamics near glass-transition singularities
267
4.4.1
Relaxation through plateaus
267
4.4.2
Below-plateau relaxation
281
4.4.3
Structure and structure relaxation
289
4.4.4
Descriptions of some glassy-dynamics data
292
Extensions of the mode-coupling theory for the
evolution of glassy dynamics of liquids
304
5.1
Extensions of the MCT for simple systems
305
5.1.1
MCT equations for the glassy shear dynamics
305
5.1.2
Glassy-relaxation features of shear correlations
308
5.1.3
MCT equations for the tagged-particle dynamics
320
5.1.4
Idealized transitions from diffusion to localization
331
5.1.5
Glassy-dynamics features of tagged-particle motions
345
5.2
A mode-coupling theory for mixtures of spherical particles
356
5.2.1
The equations of motion
357
5.2.2
Density-fluctuation arrest
366
5.2.3
Hard-sphere mixtures
375
5.2.4
Sodium-disilicate melts
383
Contents xi
5.3
A mode-coupling theory for molecular liquids
386
5.3.1
A theory for interaction-site-density correlators
387
5.3.2
Systems of symmetric dumbbells
395
5.3.3
Glassy Rouse dynamics
427
5.4
Some addenda
432
6
Asymptotic relaxation laws
437
6.1
Dynamics of the first-scaling-law regime
438
6.1.1
Reformulation of the MCT equations of motion
438
6.1.2
The critical dynamics
443
6.1.3
Asymptotic description of the ^-bifurcation dynamics
470
6.1.4
The scaling-limit description of the generic
liquid-glass-transition dynamics
492
6.1.5
Extended scaling-limit description of the
generic ^-bifurcation dynamics
502
6.2
Dynamics of the second-scaling-law regime
513
6.2.1
Equations of motion for the second-scaling-law regime
514
6.2.2
The second-scaling-law description of the liquid
dynamics
519
6.2.3
Asymptotic corrections for the second scaling limit
533
6.3
Relaxation near higher-order singularities
538
6.3.1
Correlation arrest near higher-order singularities
539
6.3.2
Logarithmic relaxation
553
A Mathematical miscellanies
577
A.I Laplace transforms
577
A.2 Fourier transforms
580
A.3 Positive-definite and positive-analytic functions
583
A.4 Harmonic-oscillator correlators
588
A.
5
Matrix correlators
591
A.6 Product correlators
594
A.
7
Power-law variations
596
A.
8
Logarithmic variations
601
В
Symmetries of fluctuation correlators
603
С
Smoothened correlators
608
D
Theorems on MCT equations
611
D.I Convergence of the approximant sequences
611
D.2 Completely
monotonie
approximants
613
D.3 The maximum-eigenvalue inequality
616
D.4 Further properties of stability matrices
618
Bibliography
621
Index
635 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Götze, Wolfgang 1937-2021 |
| author_GND | (DE-588)137682530 |
| author_facet | Götze, Wolfgang 1937-2021 |
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| author_sort | Götze, Wolfgang 1937-2021 |
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| classification_tum | PHY 641f PHY 604f |
| ctrlnum | (OCoLC)236142612 (DE-599)BVBBV035112030 |
| dewey-full | 532/.0533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
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| dewey-search | 532/.0533 |
| dewey-sort | 3532 3533 |
| dewey-tens | 530 - Physics |
| discipline | Physik Werkstoffwissenschaften / Fertigungstechnik |
| discipline_str_mv | Physik Werkstoffwissenschaften / Fertigungstechnik |
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| id | DE-604.BV035112030 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:17:54Z |
| indexdate | 2024-07-09T21:22:34Z |
| institution | BVB |
| isbn | 9780199235346 9780199656141 |
| language | English |
| lccn | 2008031894 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016779841 |
| oclc_num | 236142612 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-91G DE-BY-TUM DE-12 DE-83 DE-11 DE-29T DE-19 DE-BY-UBM |
| owner_facet | DE-703 DE-384 DE-91G DE-BY-TUM DE-12 DE-83 DE-11 DE-29T DE-19 DE-BY-UBM |
| physical | XI, 641 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | International series of monographs on physics |
| series2 | International series of monographs on physics |
| spelling | Götze, Wolfgang 1937-2021 Verfasser (DE-588)137682530 aut Complex dynamics of glass-forming liquids a mode-coupling theory Wolfgang Götze Oxford Oxford Univ. Press 2009 XI, 641 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on physics 143 Hier auch später erschienene, unveränderte Nachdrucke Viscosity Mode-coupling theory Equations of motion Complex fluids Molecular dynamics Komplexe Flüssigkeit (DE-588)4311495-7 gnd rswk-swf Glasumwandlung (DE-588)4215431-5 gnd rswk-swf Molekulardynamik (DE-588)4170370-4 gnd rswk-swf Modenkopplung (DE-588)4191469-7 gnd rswk-swf Komplexe Flüssigkeit (DE-588)4311495-7 s Molekulardynamik (DE-588)4170370-4 s DE-604 Glasumwandlung (DE-588)4215431-5 s Modenkopplung (DE-588)4191469-7 s International series of monographs on physics 143 (DE-604)BV000106406 143 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016779841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Götze, Wolfgang 1937-2021 Complex dynamics of glass-forming liquids a mode-coupling theory International series of monographs on physics Viscosity Mode-coupling theory Equations of motion Complex fluids Molecular dynamics Komplexe Flüssigkeit (DE-588)4311495-7 gnd Glasumwandlung (DE-588)4215431-5 gnd Molekulardynamik (DE-588)4170370-4 gnd Modenkopplung (DE-588)4191469-7 gnd |
| subject_GND | (DE-588)4311495-7 (DE-588)4215431-5 (DE-588)4170370-4 (DE-588)4191469-7 |
| title | Complex dynamics of glass-forming liquids a mode-coupling theory |
| title_auth | Complex dynamics of glass-forming liquids a mode-coupling theory |
| title_exact_search | Complex dynamics of glass-forming liquids a mode-coupling theory |
| title_exact_search_txtP | Complex dynamics of glass-forming liquids a mode-coupling theory |
| title_full | Complex dynamics of glass-forming liquids a mode-coupling theory Wolfgang Götze |
| title_fullStr | Complex dynamics of glass-forming liquids a mode-coupling theory Wolfgang Götze |
| title_full_unstemmed | Complex dynamics of glass-forming liquids a mode-coupling theory Wolfgang Götze |
| title_short | Complex dynamics of glass-forming liquids |
| title_sort | complex dynamics of glass forming liquids a mode coupling theory |
| title_sub | a mode-coupling theory |
| topic | Viscosity Mode-coupling theory Equations of motion Complex fluids Molecular dynamics Komplexe Flüssigkeit (DE-588)4311495-7 gnd Glasumwandlung (DE-588)4215431-5 gnd Molekulardynamik (DE-588)4170370-4 gnd Modenkopplung (DE-588)4191469-7 gnd |
| topic_facet | Viscosity Mode-coupling theory Equations of motion Complex fluids Molecular dynamics Komplexe Flüssigkeit Glasumwandlung Molekulardynamik Modenkopplung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016779841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000106406 |
| work_keys_str_mv | AT gotzewolfgang complexdynamicsofglassformingliquidsamodecouplingtheory |