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Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model

2015-11-19 Mathematics
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Release : 2015-11-19
Genre : Mathematics
Kind : eBook
Book Rating : 548/5 ( reviews)

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

Download or read book Mean Field Theories and Dual Variation - Mathematical Structures of the Mesoscopic Model written by Takashi Suzuki. This book was released on 2015-11-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

MEAN FIELD THEORIES AND DUAL VARIATION

2009-01-01 Mathematics
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Release : 2009-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 228/5 ( reviews)

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Book Synopsis MEAN FIELD THEORIES AND DUAL VARIATION by : Takashi Suzuki

Download or read book MEAN FIELD THEORIES AND DUAL VARIATION written by Takashi Suzuki. This book was released on 2009-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mean Field Theories and Dual Variation

2008-09-01 Mathematics
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Release : 2008-09-01
Genre : Mathematics
Kind : eBook
Book Rating : 093/5 ( reviews)

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Book Synopsis Mean Field Theories and Dual Variation by : Takashi Suzuki

Download or read book Mean Field Theories and Dual Variation written by Takashi Suzuki. This book was released on 2008-09-01. Available in PDF, EPUB and Kindle. Book excerpt: 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 SmoluchowskiPoisson 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.

Mean Field Theories and Dual Variation ; a Mathematical Profile Emerged in the Nonlinear Hierarchy. Atlantis Studies in Mathematics for Engineering and Science

2008
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Release : 2008
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Mean Field Theories and Dual Variation ; a Mathematical Profile Emerged in the Nonlinear Hierarchy. Atlantis Studies in Mathematics for Engineering and Science by : T. Suzuki

Download or read book Mean Field Theories and Dual Variation ; a Mathematical Profile Emerged in the Nonlinear Hierarchy. Atlantis Studies in Mathematics for Engineering and Science written by T. Suzuki. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: 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 Smoluchowskiâ€"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.

Mean Field Theory

2020-05-08 Science
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Release : 2020-05-08
Genre : Science
Kind : eBook
Book Rating : 795/5 ( reviews)

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Book Synopsis Mean Field Theory by : Vladimir M Kolomietz

Download or read book Mean Field Theory written by Vladimir M Kolomietz. This book was released on 2020-05-08. Available in PDF, EPUB and Kindle. Book excerpt: This book describes recent theoretical and experimental developments in the study of static and dynamic properties of atomic nuclei, many-body systems of strongly interacting neutrons and protons. The theoretical approach is based on the concept of the mean field, describing the motion of a nucleon in terms of a self-consistent single-particle potential well which approximates the interactions of a nucleon with all the other nucleons. The theoretical approaches also go beyond the mean-field approximation by including the effects of two-body collisions.The self-consistent mean-field approximation is derived using the effective nucleon-nucleon Skyrme-type interaction. The many-body problem is described next in terms of the Wigner phase space of the one-body density, which provides a basis for semi-classical approximations and leads to kinetic equations. Results of static properties of nuclei and properties associated with small amplitude dynamics are also presented. Relaxation processes, due to nucleon-nucleon collisions, are discussed next, followed by instability and large amplitude motion of excited nuclei. Lastly, the book ends with the dynamics of hot nuclei. The concepts and methods developed in this book can be used for describing properties of other many-body systems.

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