Commutability Of Gamma Limits In Problems With Multiple Scales
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Commutability Of Gamma Limits In Problems With Multiple Scales
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Author : Martin Jesenko
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2017-05-15
Commutability Of Gamma Limits In Problems With Multiple Scales written by Martin Jesenko and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-15 with Mathematics categories.
In the calculus of variations, the goal is to explore extrema of a given integral functional. From origins of the problem, it might be expected that the functional can be adequately simplified by neglecting some small quantities. A way to rigorously justify such an approximation is the Γ-convergence that ensures convergence of corresponding (global) extrema. The main motivation of this work is to investigate properties of doubly indexed integral functionals that Γ-converge for one index fixed. In other words, for two possible approximations we would like to determine whether we may perform them consecutively and if they commute. Our examples are taken from material science with homogenization being one of these two processes. In the first part we are considering a setting related to the elastic regime. However, our assumptions are fairly general and allow for applications in different areas. The second part is devoted to problems in the Hencky plasticity. They are considerably different due to special growth properties of the density.
An Introduction To Quantum Field Theory
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Author : Michael E. Peskin
language : en
Publisher: CRC Press
Release Date : 2018-05-04
An Introduction To Quantum Field Theory written by Michael E. Peskin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Science categories.
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.
Geometric Flows On Planar Lattices
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Author : Andrea Braides
language : en
Publisher: Springer Nature
Release Date : 2021-03-23
Geometric Flows On Planar Lattices written by Andrea Braides and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-23 with Mathematics categories.
This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.
Introduction To Computational Mathematics
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Author : Xin-She Yang
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-11-26
Introduction To Computational Mathematics written by Xin-She Yang and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-26 with Mathematics categories.
This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.
Theory Of Translation Closedness For Time Scales
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Author : Chao Wang
language : en
Publisher: Springer
Release Date : 2021-05-20
Theory Of Translation Closedness For Time Scales written by Chao Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-20 with Mathematics categories.
This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.
Free Discontinuity Problems
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Author : Nicola Fusco
language : en
Publisher: Springer
Release Date : 2017-02-02
Free Discontinuity Problems written by Nicola Fusco and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-02 with Mathematics categories.
This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.
Topics On Concentration Phenomena And Problems With Multiple Scales
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Author : Andrea Braides
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-14
Topics On Concentration Phenomena And Problems With Multiple Scales written by Andrea Braides and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-14 with Mathematics categories.
The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena are a challenging topic of very active research. This volume includes lecture notes devoted to the asymptotic analysis of such problems when the multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes (random, in perforated domains, on fractals), and to concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
Einstein S Intuition
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Author : Thad Roberts
language : en
Publisher:
Release Date : 2015-12-11
Einstein S Intuition written by Thad Roberts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-11 with categories.
Presented in clear and accessible language with wonderfully supportive graphics, Roberts offers the reader a voyage through the development of human knowledge. He then examines the outstanding mysteries of modern physics-the phenomena that lie outside the boarders of our current understanding (dark energy, dark matter, the Big Bang, wave-particle duality, quantum tunneling, state vector reduction, etc.) and suggests that the next step in our intellectual journey is to treat the vacuum of space as a superfluid-modeling it as being composed of interactive quanta, which, in a self similar way, are composed of subquanta, and so on. With this proposition Roberts engenders the vacuum with fractal geometry, and opens the door to explaining the outstanding mysteries of physics geometrically. Roberts' model, called quantum space theory, has been praised for how it offers an intuitively accessible picture of eleven-dimensions and for powerfully extending the insight of general relativity, eloquently translating the four forces into unique kinds of geometric distortions, while offering underlying deterministic dynamics that give rise to quantum mechanics. That remarkably simple picture explains the mysteries of modern physics in a way that is fully commensurate with Einstein's intuition. It is a refreshingly unique perspective that generates several testable predictions. "This work is mathematically beautiful and scientifically priceless, and the kicker is that it comes with a vivid and satisfying picture." Chris J. Wilshaw "This book fundamentally changed my understanding of our universe." Matt Emmi
Gamma Convergence For Beginners
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Author : Andrea Braides
language : en
Publisher: Clarendon Press
Release Date : 2002-07-25
Gamma Convergence For Beginners written by Andrea Braides and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-25 with Mathematics categories.
The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing to Fracture Mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of Gamma-convergence and at the same time provide a stimulating starting point for further studies. The main part is set in a one-dimensional framework that highlights the main issues of Gamma-convergence without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals, then homogenisation, segmentation problems, phase transitions, free-discontinuity problems and their discrete and continuous approximation, making stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, where more technical tools are usually needed, but the main techniques of Gamma-convergence illustrated in the previous section may be applied unchanged. The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of Applied Analysis, and from the interaction with many specialists in Mechanics and Computer Vision, which have helped in making the text addressed also to a non-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.
The Analytical Theory Of Heat
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Author : Jean-Baptiste-Joseph Fourier
language : en
Publisher:
Release Date : 1878
The Analytical Theory Of Heat written by Jean-Baptiste-Joseph Fourier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1878 with Heat categories.