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

Author: Takashi Suzuki

Publisher: Springer

Published: 2015-11-19

Total Pages: 450

ISBN-13: 9462391548

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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.

Non-Local Partial Differential Equations for Engineering and Biology
Non-Local Partial Differential Equations for Engineering and Biology

Author: Nikos I. Kavallaris

Publisher: Springer

Published: 2017-11-28

Total Pages: 310

ISBN-13: 3319679449

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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.

Shape Memory Alloys
Shape Memory Alloys

Author: Farzad Ebrahimi

Publisher: BoD – Books on Demand

Published: 2017-09-20

Total Pages: 138

ISBN-13: 9535134558

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This book is a result of contributions of experts from international scientific community working in different aspects of shape memory alloys (SMAs) and reports on the state-of-the-art research and development findings on this topic through original and innovative research studies. Through its five chapters, the reader will have access to works related to ferromagnetic SMAs, while it introduces some specific applications like development of faster SMA actuators and application of nanostructural SMAs in medical devices. The book contains up-to-date publications of leading experts, and the edition is intended to furnish valuable recent information to the professionals involved in shape memory alloys analysis and applications. The text is addressed not only to researchers but also to professional engineers, students, and other experts in a variety of disciplines, both academic and industrial, seeking to gain a better understanding of what has been done in the field recently and what kind of open problems are in this area.

Vortex Dynamics
Vortex Dynamics

Author: İlkay Bakırtaş

Publisher: BoD – Books on Demand

Published: 2022-09-28

Total Pages: 184

ISBN-13: 1803550244

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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.

Vortex Structures in Fluid Dynamic Problems
Vortex Structures in Fluid Dynamic Problems

Author: Hector Perez-De-Tejada

Publisher: BoD – Books on Demand

Published: 2017-03-01

Total Pages: 282

ISBN-13: 9535129430

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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.

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

Author: Takashi Suzuki

Publisher: World Scientific

Published: 2022-04-28

Total Pages: 688

ISBN-13: 981125737X

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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
Semilinear Elliptic Equations

Author: Takashi Suzuki

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-10-12

Total Pages: 490

ISBN-13: 3110556286

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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.

Lectures on Field Theory and Topology
Lectures on Field Theory and Topology

Author: Daniel S. Freed

Publisher: American Mathematical Soc.

Published: 2019-08-23

Total Pages: 202

ISBN-13: 1470452065

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These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

Condensed Matter Field Theory
Condensed Matter Field Theory

Author: Alexander Altland

Publisher: Cambridge University Press

Published: 2010-03-11

Total Pages: 785

ISBN-13: 0521769752

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This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences
Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences

Author: Giovanni Naldi

Publisher: Springer Science & Business Media

Published: 2010-08-12

Total Pages: 437

ISBN-13: 0817649468

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Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.