Mean Field Theories And Dual Variation: A Mathematical Profile Emerged In The Nonlinear Hierarchy: 2 (Atlantis Studies In Mathematics For Engineering And Science) - Hardcover

Suzuki Takashi

 
9789078677147: Mean Field Theories And Dual Variation: A Mathematical Profile Emerged In The Nonlinear Hierarchy: 2 (Atlantis Studies In Mathematics For Engineering And Science)
Hardcover
ISBN 10: 9078677147 ISBN 13: 9789078677147
Publisher: World Scientific Publishing, 2009

Synopsis

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 SmoluchowskiPoisson 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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
World Scientific Publishing
Publication date
2009
Language
English
ISBN 10 
9078677147
ISBN 13 
9789078677147
Binding
Hardcover
Number of pages
290

Other Popular Editions of the Same Title

9789078677093: Mean Field Theories and Dual Variation: A Mathematical Profile Emerged in the Nonlinear Hierarchy: v. 2 (Atlantis Studies in Mathematics for Engineering and Science)

Featured Edition

ISBN 10:  9078677090 ISBN 13:  9789078677093
Publisher: Atlantis Press, 2009
Hardcover