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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| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
Paris :
Atlantis Press
2009.
Cham : Springer Nature |
| Schriftenreihe: | Atlantis Studies in Mathematics for Engineering and Science
2 |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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| Autres localisations: | Voir dans le Sudoc |
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| 041 | 0 | |a eng | |
| 082 | |a 515.352 | ||
| 100 | 1 | |a Suzuki, Takashi, |d 1971- | |
| 245 | 1 | 0 | |a Mean Field Theories and Dual Variation |c by Takashi Suzuki. |
| 260 | |a Paris : |b Atlantis Press. | ||
| 260 | |a Cham : |b Springer Nature, |c 2009. | ||
| 490 | 0 | |a Atlantis Studies in Mathematics for Engineering and Science |v 2 |x 2467-9631 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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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