Mean field theories and dual variation -- mathematical structures of the mesoscopic model
The book under review is the second edition of the monograph [Zbl 1247.35001], devoted to the description of macroscopic phenomena from microscopic overviews with the help of mean field approximation. In fact, the author splits the two chapters of the previous edition into several chapters, some of them being supplemented with new sections. Also, within the same conceptual framework, some new chapters were added such as those regarding the theory of perfect fluids and that of static magnetic field. In this way the new edition is assembled from 13 chapters dealing with several models in physics, chemistry and biology, treated from the perspective of two mathematical structures: the duality and scaling. Let us finally provide the titles of the thirteen chapters: Chemotaxis, Time Relaxization, Toland Duality, Phenomenology, Phase Transition, Critical Phenomena of Isolated Systems, Self-interacting Fluids, Magnetic Fields, Boltzmann-Poisson Equation, Particle Kinetics, Parabolic Equations, Gauge Fields, and Higher-Dimensional Blowup.
scientific article; zbMATH DE number 6508021