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Free Energy And Self Interacting Particles
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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
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 444 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.
Book Synopsis Chemotaxis, Reaction, Network by : Suzuki Takashi
Download or read book Chemotaxis, Reaction, Network written by Suzuki Takashi and published by World Scientific. This book was released on 2000-03-30 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include:
Book Synopsis Research Methodologies and Practical Applications of Chemistry by : Lionello Pogliani
Download or read book Research Methodologies and Practical Applications of Chemistry written by Lionello Pogliani and published by CRC Press. This book was released on 2019-05-08 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new volume, Research Methodologies and Practical Applications of Chemistry, presents a detailed analysis of current experimental and theoretical approaches surrounding chemical science. With an emphasis on multidisciplinary as well as interdisciplinary applications, the book extensively reviews fundamental principles and presents recent research to help show logical connections between the theory and application of modern chemistry concepts. It also emphasizes the behavior of materials from the molecular point of view. The burgeoning field of chemistry and chemical science has led to many recent technological innovations and discoveries. Understanding the impact of these technologies on business, science, and industry is an important first step in developing applications for a variety of settings and contexts. The aim of this book is to present research that has transformed this discipline and aided its advancement. The book examines the strengths and future potential of chemical technologies in a variety of industries.
Book Synopsis Singularities of Solutions to Chemotaxis Systems by : Piotr Biler
Download or read book Singularities of Solutions to Chemotaxis Systems written by Piotr Biler and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-12-02 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing concentration phenomena in physics and biology. While the two-dimensional theory is by now quite complete, the questions of global-in-time solvability and blowup characterization are largely open in higher dimensions. In this book, global-in-time solutions are constructed under (nearly) optimal assumptions on initial data and rigorous blowup criteria are derived.
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.
Book Synopsis Nonlinear Elliptic and Parabolic Problems by : Michel Chipot
Download or read book Nonlinear Elliptic and Parabolic Problems written by Michel Chipot and published by Springer Science & Business Media. This book was released on 2005-10-18 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.
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.
Book Synopsis Nonlinear Oscillations of Hamiltonian PDEs by : Massimiliano Berti
Download or read book Nonlinear Oscillations of Hamiltonian PDEs written by Massimiliano Berti and published by Springer Science & Business Media. This book was released on 2007-10-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many partial differential equations (PDEs) that arise in physics can be viewed as infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. The text serves as an introduction to research in this fascinating and rapidly growing field. Graduate students and researchers interested in variational techniques and nonlinear analysis applied to Hamiltonian PDEs will find inspiration in the book.
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 300 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.
Author :Satyanad Kichenassamy Publisher :Springer Science & Business Media ISBN 13 :081764637X Total Pages :296 pages Book Rating :4.8/5 (176 download)
Book Synopsis Fuchsian Reduction by : Satyanad Kichenassamy
Download or read book Fuchsian Reduction written by Satyanad Kichenassamy and published by Springer Science & Business Media. This book was released on 2007-09-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces as well as Nash-Moser implicit function theorem are provided. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra, or as a resource for researchers working with applications to Fuchsian Reduction. The comprehensive approach features the inclusion of problems and bibliographic notes.
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.
Book Synopsis Quantum Field Theory Of Point Particles And Strings by : Brian Hatfield
Download or read book Quantum Field Theory Of Point Particles And Strings written by Brian Hatfield and published by CRC Press. This book was released on 2018-03-09 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.
Book Synopsis A Universe of Atoms, An Atom in the Universe by : Mark P. Silverman
Download or read book A Universe of Atoms, An Atom in the Universe written by Mark P. Silverman and published by Springer Science & Business Media. This book was released on 2008-04-08 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: jThis thoroughly updated and revised text contains a selection of well-written essays based on Silvermans work on a wide range of topics, including: quantum mechanics, including atomic and nuclear physics, electromagnetism and optics, gravity, thermodynamics, and the physics of fluids. Presenting a personal odyssey in physics, Silverman investigates processes for which no visualizable mechanism can be given, or that seem to violate fundamental physical laws (but do not). The discussions use little mathematics, and anyone with a little college physics will be able to read the book with pleasure. -Engagingly written -Easily understandable by both the general reader and the seasoned physicist -Covers a diversity of subjects from "hot" topics in contemporary physics to less widely known but subtle and intriguing issues in physics -Discusses real physical systems whose behavior provokes, surprises and challenges the imagination -This second edition is newly revised and updated
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 144 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.
Book Synopsis Analysis and Stochastics of Growth Processes and Interface Models by : Peter Mörters
Download or read book Analysis and Stochastics of Growth Processes and Interface Models written by Peter Mörters and published by Oxford University Press. This book was released on 2008-07-24 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of topical survey articles by researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is given to the interplay of the usually separate fields of applied analysis and probability theory.
Book Synopsis Classical Charged Particles by : Fritz Rohrlich
Download or read book Classical Charged Particles written by Fritz Rohrlich and published by CRC Press. This book was released on 2020-01-20 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Widely-discussed in the theory of classical point charges are the difficulties of divergent self-energy, self-accelerating solutions, and pre-acceleration. This book explains the theory in the context of quantum electrodynamics, the neutral particle limit, and coherence with neighboring theories.
