Mean Field Theories And Dual Variation

Download Mean Field Theories And Dual Variation full books in PDF, epub, and Kindle. Read online Mean Field Theories And Dual Variation ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

MEAN FIELD THEORIES AND DUAL VARIATION

Author : Takashi Suzuki
Publisher : Springer Science & Business Media
ISBN 13 : 9491216228
Total Pages : 299 pages
Book Rating : 4.4/5 (912 download)

DOWNLOAD NOW!

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 and published by Springer Science & Business Media. This book was released on 2009-01-01 with total page 299 pages. 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 - Mathematical Structures of the Mesoscopic Model

Author : Takashi Suzuki
Publisher : Springer
ISBN 13 : 9462391548
Total Pages : 450 pages
Book Rating : 4.4/5 (623 download)

DOWNLOAD NOW!

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 and published by Springer. This book was released on 2015-11-19 with total page 450 pages. 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.

Free Energy and Self-Interacting Particles

Author : Takashi Suzuki
Publisher : Springer Science & Business Media
ISBN 13 : 0817644369
Total Pages : 367 pages
Book Rating : 4.8/5 (176 download)

DOWNLOAD NOW!

Book Synopsis Free Energy and Self-Interacting Particles by : Takashi Suzuki

Download or read book Free Energy and Self-Interacting Particles written by Takashi Suzuki and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Examines a nonlinear system of parabolic PDEs arising in mathematical biology and statistical mechanics * Describes the whole picture, i.e., the mathematical and physical principles * Suitable for researchers and grad students in mathematics and applied mathematics who are interested in nonlinear PDEs in stochastic processes, cellular automatons, variational methods, and their applications to physics, chemistry, biology, and engineering

Vortex Dynamics

Author : İlkay Bakırtaş
Publisher : BoD – Books on Demand
ISBN 13 : 1803550244
Total Pages : 184 pages
Book Rating : 4.8/5 (35 download)

DOWNLOAD NOW!

Book Synopsis Vortex Dynamics by : İlkay Bakırtaş

Download or read book Vortex Dynamics written by İlkay Bakırtaş and published by BoD – Books on Demand. This book was released on 2022-09-28 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses vortex dynamics theory from physics, mathematics, and engineering perspectives. It includes nine chapters that cover a variety of research results related to vortex dynamics including nonlinear optics, fluid dynamics, and plasma physics.

Probabilistic Theory of Mean Field Games with Applications II

Author : René Carmona
Publisher : Springer
ISBN 13 : 3319564366
Total Pages : 712 pages
Book Rating : 4.3/5 (195 download)

DOWNLOAD NOW!

Book Synopsis Probabilistic Theory of Mean Field Games with Applications II by : René Carmona

Download or read book Probabilistic Theory of Mean Field Games with Applications II written by René Carmona and published by Springer. This book was released on 2018-03-08 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Non-Local Partial Differential Equations for Engineering and Biology

Author : Nikos I. Kavallaris
Publisher : Springer
ISBN 13 : 3319679449
Total Pages : 310 pages
Book Rating : 4.3/5 (196 download)

DOWNLOAD NOW!

Book Synopsis Non-Local Partial Differential Equations for Engineering and Biology by : Nikos I. Kavallaris

Download or read book Non-Local Partial Differential Equations for Engineering and Biology written by Nikos I. Kavallaris and published by Springer. This book was released on 2017-11-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.

Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities

Author : Takashi Suzuki
Publisher : World Scientific
ISBN 13 : 9811287910
Total Pages : 414 pages
Book Rating : 4.8/5 (112 download)

DOWNLOAD NOW!

Book Synopsis Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities by : Takashi Suzuki

Download or read book Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities written by Takashi Suzuki and published by World Scientific. This book was released on 2024-01-22 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena.In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years, several principles that ensure these successes are discovered very recently.This monograph focuses on one of them: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis.Five objects of inquiry, scattered across different disciplines, are selected in this monograph: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - δ systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.The relaxation of internal tensions in these systems, however, is described commonly by differential forms, and the reader will be convinced of further applications of this principle to other areas.

THEORY OF CAUSAL DIFFERENTIAL EQUATIONS

Author : S. Leela
Publisher : Springer Science & Business Media
ISBN 13 : 9491216252
Total Pages : 218 pages
Book Rating : 4.4/5 (912 download)

DOWNLOAD NOW!

Book Synopsis THEORY OF CAUSAL DIFFERENTIAL EQUATIONS by : S. Leela

Download or read book THEORY OF CAUSAL DIFFERENTIAL EQUATIONS written by S. Leela and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.

Probabilistic Theory of Mean Field Games with Applications I

Author : René Carmona
Publisher : Springer
ISBN 13 : 3319589202
Total Pages : 728 pages
Book Rating : 4.3/5 (195 download)

DOWNLOAD NOW!

Book Synopsis Probabilistic Theory of Mean Field Games with Applications I by : René Carmona

Download or read book Probabilistic Theory of Mean Field Games with Applications I written by René Carmona and published by Springer. This book was released on 2018-03-01 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition)

Author : Takashi Suzuki
Publisher : World Scientific
ISBN 13 : 981125737X
Total Pages : 688 pages
Book Rating : 4.8/5 (112 download)

DOWNLOAD NOW!

Book Synopsis Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition) by : Takashi Suzuki

Download or read book Applied Analysis: Mathematics For Science, Technology, Engineering (Third Edition) written by Takashi Suzuki and published by World Scientific. This book was released on 2022-04-28 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.

Semilinear Elliptic Equations

Author : Takashi Suzuki
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110556286
Total Pages : 490 pages
Book Rating : 4.1/5 (15 download)

DOWNLOAD NOW!

Book Synopsis Semilinear Elliptic Equations by : Takashi Suzuki

Download or read book Semilinear Elliptic Equations written by Takashi Suzuki and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-12 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.

Mathematical Methods for Cancer Evolution

Author : Takashi Suzuki
Publisher : Springer
ISBN 13 : 9811036713
Total Pages : 148 pages
Book Rating : 4.8/5 (11 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Methods for Cancer Evolution by : Takashi Suzuki

Download or read book Mathematical Methods for Cancer Evolution written by Takashi Suzuki and published by Springer. This book was released on 2017-06-13 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools.The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.

Nonlinear Hybrid Continuous/Discrete-Time Models

Author : Marat Akhmet
Publisher : Springer Science & Business Media
ISBN 13 : 9491216031
Total Pages : 225 pages
Book Rating : 4.4/5 (912 download)

DOWNLOAD NOW!

Book Synopsis Nonlinear Hybrid Continuous/Discrete-Time Models by : Marat Akhmet

Download or read book Nonlinear Hybrid Continuous/Discrete-Time Models written by Marat Akhmet and published by Springer Science & Business Media. This book was released on 2011-05-03 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type.

Vortex Structures in Fluid Dynamic Problems

Author : Hector Perez-De-Tejada
Publisher : BoD – Books on Demand
ISBN 13 : 9535129430
Total Pages : 282 pages
Book Rating : 4.5/5 (351 download)

DOWNLOAD NOW!

Book Synopsis Vortex Structures in Fluid Dynamic Problems by : Hector Perez-De-Tejada

Download or read book Vortex Structures in Fluid Dynamic Problems written by Hector Perez-De-Tejada and published by BoD – Books on Demand. This book was released on 2017-03-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents of the book cover topics on vortex dynamics in a variety of flow problems and describe observational measurements and their interpretation. The book contains 13 chapters that first include vortices in the earth and planetary sciences related to vortices in the Venus plasma wake and also on tropical cyclones and on rotating shallow water in the earth's atmosphere. Vortices in fluid problems include airplane wake vortices, vorticity evolution in free-shear flows, together with axisymmetric flows with swirl, as well as thermal conductivities in fluid layers. Vortices in relativistic fluids, in magnetic disks, solitons and vortices, and relaxation for point vortices were also examined. Other chapters describe conditions in a vortex bioreactor and in vortex yarn structures.

Multidimensional Integral Equations and Inequalities

Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
ISBN 13 : 9491216171
Total Pages : 248 pages
Book Rating : 4.4/5 (912 download)

DOWNLOAD NOW!

Book Synopsis Multidimensional Integral Equations and Inequalities by : B.G. Pachpatte

Download or read book Multidimensional Integral Equations and Inequalities written by B.G. Pachpatte and published by Springer Science & Business Media. This book was released on 2011-07-26 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

THE OMEGA PROBLEM OF ALL MEMBERS OF THE UNITED NATIONS

Author : Ethelbert Nwakuche Chukwu
Publisher : Springer Science & Business Media
ISBN 13 : 9491216260
Total Pages : 214 pages
Book Rating : 4.4/5 (912 download)

DOWNLOAD NOW!

Book Synopsis THE OMEGA PROBLEM OF ALL MEMBERS OF THE UNITED NATIONS by : Ethelbert Nwakuche Chukwu

Download or read book THE OMEGA PROBLEM OF ALL MEMBERS OF THE UNITED NATIONS written by Ethelbert Nwakuche Chukwu and published by Springer Science & Business Media. This book was released on 2010-09-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, a sequel to the author's highly successfull A Mathematical Treatment of Economic Cooperation and Competition Among Nations: With Nigeria, USA, UK, China and Middle East Examples (Academic Press, 2005), extends the study to all member states of the United Nations. It derives the equations of the key economic variables of gross domestic product, interest rate, employment value of capital stock prices (inflation) and cumulative balance of payment. The derivation is based on the differential market principle of supply and demand and on the rational expectation principle. The models are validated using economic time series of each country and MATLAB programs. The emerging dynamics is a differential game of pursuit which is converted to a hereditary control system for a single nation. Following the same method we derive the full hereditary economic model of all members of the United Nations joined together by external trade, investment capital flow consumption employment and governments' economic intervention all mirrored by interacting gross domestic products. The system is validated with IMF and World Bank data.Studies are made on how to arrest economic recession and depression and promote economic growth and prosperity. Diffusion of wealth is also touched upon. Policies regarding economic stimulus, how to dam the decay of capital flow, as well as conditions to promote full employment are discussed. Examination is made to test for the global systems controllability the possibility of steering any current bad economic state to a state of growth of its GDP, low interest rate, full employment, good value of capital stock, low inflation and a positive value of the cumulative balance of payments. The book prescribes verifiable broad policies for all nations together to promote prosperity, diffusion of wealth and longevity. The book comes with full programs, output and identified equations which can be downloaded from the publishers' website. Detailed information is available inside the book.The book is a most valuable source of reference for world leaders, central bank directors, graduates and academic researchers in applied mathematics and applied economics concerned with the current problems and growth of the global economy.

BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS

Author : Goong Chen
Publisher : Springer Science & Business Media
ISBN 13 : 9491216279
Total Pages : 733 pages
Book Rating : 4.4/5 (912 download)

DOWNLOAD NOW!

Book Synopsis BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS by : Goong Chen

Download or read book BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS written by Goong Chen and published by Springer Science & Business Media. This book was released on 2010-09-01 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Element Methods have become a major numerical tool in scientific and engineering problem-solving, with particular applications to numerical computations and simulations of partial differential equations in engineering. Boundary Element Methods provides a rigorous and systematic account of the modern mathematical theory of Boundary Element Methods, including the requisite background on general partial, differential equation methods, Sobolev spaces, pseudo-differential and Fredholm operators and finite elements. It aims at the computation of many types of elliptic boundary value problems in potential theory, elasticity, wave propagation, and structural mechanics. Also presented are various methods and algorithms for nonlinear partial differential equations. This second edition has been fully revised and combines the mathematical rigour necessary for a full understanding of the subject, with extensive examples of applications illustrated with computer graphics. This book is intended as a textbook and reference for applied mathematicians, physical scientists and engineers at graduate and research level. It will be an invaluable sourcebook for all concerned with numerical modeling and the solution of partial differential equations.