By Takashi Suzuki

A mathematical idea is brought during this publication to unify a wide category of nonlinear partial differential equation (PDE) types for larger knowing and research of the actual and organic phenomena they characterize. The so-called suggest box approximation process is followed to explain the macroscopic phenomena from convinced microscopic ideas for this unified mathematical formula. key parts for this process are the notions of “duality” in keeping with the PDE susceptible ideas and “hierarchy” for revealing the main points of the in a different way hidden secrets and techniques, akin to actual secret hidden among particle density and box focus, quantized blow up organic mechanism sealed in chemotaxis platforms, in addition to multi-scale mathematical reasons of the Smoluchowski–Poisson version in non-equilibrium thermodynamics, two-dimensional turbulence idea, self-dual gauge concept, and so on. This e-book indicates how and why many various nonlinear difficulties are inter-connected when it comes to the homes of duality and scaling, and how to investigate them mathematically.

Show description

Read Online or Download MEAN FIELD THEORIES AND DUAL VARIATION: A Mathematical Profile Emerged in the Nonlinear Hierarchy: 2 (Atlantis Studies in Mathematics for Engineering and Science) PDF

Similar differential equations books

Solution Techniques for Elementary Partial Differential Equations, Second Edition (Chapman Hall/CRC Mathematics Series)

Incorporating a couple of improvements, resolution concepts for ordinary Partial Differential Equations, moment version offers probably the most very important and primary tools for fixing partial differential equations (PDEs). The options coated contain separation of variables, approach to features, eigenfunction growth, Fourier and Laplace variations, Green’s capabilities, perturbation equipment, and asymptotic research.

The Universality of the Radon Transform (Oxford Mathematical Monographs)

Written by means of a number one student in arithmetic, this monograph discusses the Radon remodel, a box that has huge ranging purposes to X-ray know-how, partial differential equations, nuclear magnetic resonance scanning, and tomography. during this publication, Ehrenpreis makes a speciality of fresh examine and highlights the powerful courting among high-level natural arithmetic and purposes of the Radon rework to components akin to clinical imaging.

Abstract Parabolic Evolution Equations and their Applications (Springer Monographs in Mathematics)

This monograph is meant to offer the basics of the idea of summary parabolic evolution equations and to teach the best way to observe to varied nonlinear dif- sion equations and structures coming up in technological know-how. the idea offers us a uni? ed and s- tematic remedy for concrete nonlinear diffusion types.

Scientific Computing and Differential Equations: An Introduction to Numerical Methods

Medical Computing and Differential Equations: An advent to Numerical tools, is a superb supplement to creation to Numerical tools through Ortega and Poole. The e-book emphasizes the significance of fixing differential equations on a working laptop or computer, which includes a wide a part of what has grow to be referred to as medical computing.

Extra resources for MEAN FIELD THEORIES AND DUAL VARIATION: A Mathematical Profile Emerged in the Nonlinear Hierarchy: 2 (Atlantis Studies in Mathematics for Engineering and Science)

Sample text

Download PDF sample

Rated 4.00 of 5 – based on 11 votes