Mean Field Theories and Dual Variation
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 ma...
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| Autor Corporativo: | |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Paris :
Atlantis Press
2009.
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| Colección: | Atlantis Studies in Mathematics for Engineering and Science ;
2. Springer eBooks. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b32751072*spi |
| Sumario: | 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 zdualityy according to the PDE weak solutions and zhierarchyy 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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| Descripción Física: | X, 288 p. |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9789491216220 |
