Availability: Complex dynamics of glass-forming liquids

Complex dynamics of glass-forming liquids: a mode-coupling theory

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Bibliographic Details
Main Author:	Götze, Wolfgang 1937-2021 (Author)
Format:	Book
Language:	English
Published:	Oxford Oxford Univ. Press 2009
Series:	International series of monographs on physics 143
Subjects:	Viscosity Mode-coupling theory Equations of motion Complex fluids Molecular dynamics Komplexe Flüssigkeit Glasumwandlung Molekulardynamik Modenkopplung
Links:	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
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XI, 641 S. graph. Darst.
ISBN:	9780199235346 9780199656141

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Record in the Search Index

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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
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author	Götze, Wolfgang 1937-2021
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series	International series of monographs on physics
series2	International series of monographs on physics
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_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

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