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Mean Field Theories and Dual Variation (Atlantis Studies in Mathematics for Engineering and Science, Band 2) - Hardcover

Buch 2 von 14: Atlantis Studies in Mathematics for Engineering and Science

Suzuki, Takashi

 
9789078677147: Mean Field Theories and Dual Variation (Atlantis Studies in Mathematics for Engineering and Science, Band 2)
Hardcover
ISBN 10: 9078677147 ISBN 13: 9789078677147
Verlag: Atlantis Press, 2009

Inhaltsangabe

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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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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Atlantis Press
Erscheinungsdatum
2009
Sprache
Englisch
ISBN 10 
9078677147
ISBN 13 
9789078677147
Einband
Gebundene Ausgabe
Anzahl der Seiten
288
Kontakt zum Hersteller
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Verantwortliche Person
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