| Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QC174.85.SPR FCT 82974 (Browse shelf) | 1 | Available |
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| QC174.8.SPR FCT 82801 Discrete mathematics in statistical physics | QC174.8.SPR FCT 97780 Elements of nonlinear time series analysis and forecasting | QC174.85.SPR FCT 81430 Studies in phase space analysis with applications to PDEs | QC174.85.SPR FCT 82974 Mean field theories and dual variation | QC175.SPR FCT 82179 Numerical methods in multidimensional radiative transfer | QC175.SPR FCT 94830 Slow rarefied flows | QC175.16.SPR FCT 81556 Phase transition dynamics |
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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.
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