* 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

Free Energy and Self-Interacting Particles (Progress in Nonlinear Differential Equations and Their Applications, 62)

Science & Math

Suzuki, Takashi

Biological Sciences

Birkhauser

A historical account of the development of engines, from Newcomen's and Watt's steam engines through the Daimler-Benz DB601. Discusses such aspects as piston and cylinder problems, engine life, cooling, compartments, and energy conservation. Well illustrated with photographs, drawings, graphs, and cartoons. Originally published as Enjin no roman in 1983 and translated from the second edition. Annotation c. by Book News, Inc., Portland, Or.

The Romance of Engines

Business & Money

Industries

SAE, International

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-Chief Jürgen Appell, Würzburg, Germany Honorary and Advisory Editors Catherine Bandle, Basel, Switzerland Alain Bensoussan, Richardson, Texas, USA Avner Friedman, Columbus, Ohio, USA Umberto Mosco, Worcester, Massachusetts, USA Editorial Board Manuel del Pino, Bath, UK, and Santiago, Chile Mikio Kato, Nagano, Japan Wojciech Kryszewski, Toru&#324;, Poland Vicen&#355;iu D. R&#259;dulescu, Kraków, Poland Simeon Reich, Haifa, Israel Please submit book proposals to <a>Jürgen Appell</a>. Titles in planning include Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020) Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020) Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Semilinear Elliptic Equations: Classical and Modern Theories (De Gruyter Series in Nonlinear Analysis and Applications, 35)

Mathematics

de Gruyter

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.

Non-Local Partial Differential Equations for Engineering and Biology: Mathematical Modeling and Analysis (Mathematics for Industry, 31)

Kavallaris, Nikos I.

Springer

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: A Mathematical Profile Emerged in the Nonlinear Hierarchy (Atlantis Studies in Mathematics for Engineering and Science)

Atlantis Pr

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: A MATHEMATICAL PROFILE EMERGED IN THE NONLINEAR HIERARCHY (Atlantis Studies in Mathematics for Engineering and Science)

Atlantis Press / World Scientific

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 - Mathematical Structures of the Mesoscopic Model (Atlantis Studies in Mathematics for Engineering and Science, 11)

Atlantis Press

"The aim of this book is to incorporate Marshallian ideas such as external increasing returns and monopolistic competitions into the general equilibrium framework of Walrasian tradition. New chapters and sections have been added to this revised and expanded edition of General Equilibrium Analysis of Production and Increasing Returns (World Scientific, 2009). The new material includes a presentation of equilibrium existence and core equivalence theorems for an infinite horizon economy with a measure space of consumers. These results are currently the focus of extensive studies by mathematical theorists, and are obtained by an application of an advanced mathematical concept called saturated (super-atomless) measure space. The second major change is the inclusion of a simple toy model of a liberal society which implements the difference principle proposed by J Rawls as a principle of distributive justice. This new section opens up a possibility to connect theoretical economics and political philosophy. Thirdly, the author presents the marginal cost pricing equilibrium and discusses welfare properties of the external increasing returns, which also belong to Marshall/ Pigou tradition of the Cambridge school. Finally, a new mathematical appendix treats basics of singular homology theory. Although the fixed point theorem is originally a theorem of algebraic topology, most economic students know its proof only in the context of the differentiable manifold theory presented by J Milnor. Considering the significance of the fixed point theorem and its playing a key role in general equilibrium theory, the purpose of this new appendix is to provide readers with the idea of a proof of Brower's fixed point theorem from the "right place". This volume will be helpful for graduate students and researchers of mathematical economics, game theory, and microeconomics"--

Fundamentals of General Equilibrium Analysis (Mathematical Economics and Game Theory)

Economics

World Scientific Publishing Company

"Provides a general introduction to applied analysis. Discusses developments in nonlinear science using fundamental ideas of applied mathematics, and describes tools in linear PDE theory"--

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

World Scientific Pub Co Inc

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

WSPC

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