Coverart for item
The Resource Mean field theories and dual variation, Takashi Suzuki

Mean field theories and dual variation, Takashi Suzuki

Label
Mean field theories and dual variation
Title
Mean field theories and dual variation
Statement of responsibility
Takashi Suzuki
Creator
Subject
Language
eng
Summary
A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of "duality" according to the PDE weak solutions and "hierarchy" for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski-Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically
Member of
Action
digitized
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Suzuki, Takashi
Dewey number
530.15/95
Index
index present
LC call number
QC174.85.M43
LC item number
S89 2008eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Atlantis studies in mathematics for engineering and science,
Series volume
v. 2
http://library.link/vocab/subjectName
  • Mean field theory
  • Differential equations, Partial
  • SCIENCE
  • SCIENCE
  • SCIENCE
  • Differential equations, Partial
  • Mean field theory
Label
Mean field theories and dual variation, Takashi Suzuki
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 271-284) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
ch. 1. Duality -- Sealed Variation -- Chemotaxis -- Thermal Transport -- Collapse Formation -- Mean Field Hierarchy -- Stationary State -- Localization and Symmetrization -- Rescaling -- Mass Quantization -- Blowup Rate -- Blowup in Infinite Time -- Time Relaxation -- Geometric Flow -- Toland Duality -- Exponential Nonlinearity -- Full System of Chemotaxis -- Lagrangian -- Variational Equivalence -- Spectral Equivalence -- Stability -- Gradient Systems with Duality -- Entropy Functional -- Zygmund Space -- Phenomenology -- Non-Convex Evolution -- Gradient and Skew-Gradient Systems -- Skew-Gradient Systems with Duality -- Semi-Unfolding-Minimality -- Kuhn-Tucker Duality -- Thermodynamics -- Stefan Problem -- Thermal Equilibrium -- Penrose-Fife Theory -- Non-Equilibrium -- Phase Fields -- Fix-Caginalp Equation -- Penrose-Fife Equation -- Coupled Cahn-Hilliard Equation -- Shape Memory Alloys -- Time Map -- ch. 2. Scaling -- Revealing Hierarchy -- Self-Interacting Continuum -- Self-Gravitating Fluids -- Equilibrium -- Plasma Confinement -- Stable Equilibrium -- Related Problems -- Particle Kinetics -- Vortex -- Boltzmann Relation -- Ensemble -- Turbulence -- Kramers-Moyal Expansion -- Kinetic Theory -- Gauge Field -- Field Theory -- Exponential Nonlinearity Revisited -- Scaling Invariance -- Liouville-Bandle Theory -- Alexandroff-Bol's Inequality -- Pre-Scaled Analysis -- Entire Solution -- Blowup Analysis -- Higher-Dimensional Blowup -- Semilinear Parabolic Equation -- Method of Duality -- Higher-Dimensional Quantization -- Dimension Control of the Blowup Set
Control code
773812349
Dimensions
unknown
Extent
1 online resource (x, 288 pages)
File format
unknown
Form of item
online
Isbn
9789491216220
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.2991/978-94-91216-22-0
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic reproduction.
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)773812349
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Label
Mean field theories and dual variation, Takashi Suzuki
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 271-284) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
ch. 1. Duality -- Sealed Variation -- Chemotaxis -- Thermal Transport -- Collapse Formation -- Mean Field Hierarchy -- Stationary State -- Localization and Symmetrization -- Rescaling -- Mass Quantization -- Blowup Rate -- Blowup in Infinite Time -- Time Relaxation -- Geometric Flow -- Toland Duality -- Exponential Nonlinearity -- Full System of Chemotaxis -- Lagrangian -- Variational Equivalence -- Spectral Equivalence -- Stability -- Gradient Systems with Duality -- Entropy Functional -- Zygmund Space -- Phenomenology -- Non-Convex Evolution -- Gradient and Skew-Gradient Systems -- Skew-Gradient Systems with Duality -- Semi-Unfolding-Minimality -- Kuhn-Tucker Duality -- Thermodynamics -- Stefan Problem -- Thermal Equilibrium -- Penrose-Fife Theory -- Non-Equilibrium -- Phase Fields -- Fix-Caginalp Equation -- Penrose-Fife Equation -- Coupled Cahn-Hilliard Equation -- Shape Memory Alloys -- Time Map -- ch. 2. Scaling -- Revealing Hierarchy -- Self-Interacting Continuum -- Self-Gravitating Fluids -- Equilibrium -- Plasma Confinement -- Stable Equilibrium -- Related Problems -- Particle Kinetics -- Vortex -- Boltzmann Relation -- Ensemble -- Turbulence -- Kramers-Moyal Expansion -- Kinetic Theory -- Gauge Field -- Field Theory -- Exponential Nonlinearity Revisited -- Scaling Invariance -- Liouville-Bandle Theory -- Alexandroff-Bol's Inequality -- Pre-Scaled Analysis -- Entire Solution -- Blowup Analysis -- Higher-Dimensional Blowup -- Semilinear Parabolic Equation -- Method of Duality -- Higher-Dimensional Quantization -- Dimension Control of the Blowup Set
Control code
773812349
Dimensions
unknown
Extent
1 online resource (x, 288 pages)
File format
unknown
Form of item
online
Isbn
9789491216220
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.2991/978-94-91216-22-0
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic reproduction.
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)773812349
System details
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

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      38.944491 -92.326012
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