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Mean field theories and dual variati...

Suzuki, Takashi.

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Mean field theories and dual variation - mathematical structures of the Mesoscopic model

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mean field theories and dual variation - mathematical structures of the Mesoscopic model/ by Takashi Suzuki.
Author:	Suzuki, Takashi.
Published:	Paris :Atlantis Press : : 2015.,
Description:	xiii, 444 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Mathematics. -
Online resource:	http://dx.doi.org/10.2991/978-94-6239-154-3
ISBN:	9789462391543

Mean field theories and dual variation - mathematical structures of the Mesoscopic model
Suzuki, Takashi.

Mean field theories and dual variation - mathematical structures of the Mesoscopic model[electronic resource] /by Takashi Suzuki. - 2nd ed. - Paris :Atlantis Press :2015. - xiii, 444 p. :ill., digital ;24 cm. - Atlantis studies in mathematics for engineering and science,v.111875-7642 ;. - Atlantis studies in mathematics for engineering and science ;v. 6..

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.

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.

ISBN: 9789462391543

Standard No.: 10.2991/978-94-6239-154-3doiSubjects--Topical Terms:

515831
Mathematics.

LC Class. No.: QA300

Dewey Class. No.: 515

Mean field theories and dual variation - mathematical structures of the Mesoscopic model
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520 $a 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.
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