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Mean Field Theories and Dual Variation: A Mathematical Profile Emerged in the Nonlinear Hierarchy: 2 (Atlantis Studies In Mathematics For Engineering And Science)

by Suzuki Takashi

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Author Suzuki Takashi

Publisher World Scientific Publishing Company

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 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.

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Binding: Hardcover

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Specifications

Language: English
Publisher: World Scientific Publishing Company
Pages: 300 pages
Binding: Hardcover

ISBN: 9789078677147
Category: Mathematics & logic
Related Category: Natural Sciences