1.

Record Nr.

UNINA9910300254203321

Autore

Suzuki Takashi

Titolo

Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model / / by Takashi Suzuki

Pubbl/distr/stampa

Paris : , : Atlantis Press : , : Imprint : Atlantis Press, , 2015

ISBN

94-6239-154-8

Edizione

[2nd ed. 2015.]

Descrizione fisica

1 online resource (450 p.)

Collana

Atlantis Studies in Mathematics for Engineering and Science, , 2467-9631 ; ; 11

Disciplina

510

Soggetti

Mathematical analysis

Mathematical optimization

Calculus of variations

Mathematical physics

Population genetics

Biomathematics

Analysis

Calculus of Variations and Optimization

Mathematical Physics

Population Genetics

Mathematical and Computational Biology

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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 -- Higher- Dimensional Blowup.

Sommario/riassunto

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics.  spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been



discussed explicitly in the open literature.  The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.