Local Minimization Variational Evolution And Convergence
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Local Minimization Variational Evolution And Convergence
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Author : Andrea Braides
language : en
Publisher: Springer
Release Date : 2014-07-08
Local Minimization Variational Evolution And Convergence written by Andrea Braides and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Mathematics categories.
This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.
Discrete Variational Problems With Interfaces
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Author : Roberto Alicandro
language : en
Publisher: Cambridge University Press
Release Date : 2024-01-31
Discrete Variational Problems With Interfaces written by Roberto Alicandro and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-31 with Mathematics categories.
A systematic presentation of discrete-to-continuum results and methods, offering new perspectives on intrinsically discrete problems.
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.
Control Of Self Organizing Nonlinear Systems
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Author : Eckehard Schöll
language : en
Publisher: Springer
Release Date : 2016-01-22
Control Of Self Organizing Nonlinear Systems written by Eckehard Schöll and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-22 with Science categories.
The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.
Macroscopic And Large Scale Phenomena Coarse Graining Mean Field Limits And Ergodicity
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Author : Adrian Muntean
language : en
Publisher: Springer
Release Date : 2016-01-28
Macroscopic And Large Scale Phenomena Coarse Graining Mean Field Limits And Ergodicity written by Adrian Muntean and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-28 with Science categories.
This book is the offspring of a summer school school “Macroscopic and large scale phenomena: coarse graining, mean field limits and ergodicity”, which was held in 2012 at the University of Twente, the Netherlands. The focus lies on mathematically rigorous methods for multiscale problems of physical origins. Each of the four book chapters is based on a set of lectures delivered at the school, yet all authors have expanded and refined their contributions. Francois Golse delivers a chapter on the dynamics of large particle systems in the mean field limit and surveys the most significant tools and methods to establish such limits with mathematical rigor. Golse discusses in depth a variety of examples, including Vlasov--Poisson and Vlasov--Maxwell systems. Lucia Scardia focuses on the rigorous derivation of macroscopic models using $\Gamma$-convergence, a more recent variational method, which has proved very powerful for problems in material science. Scardia illustrates this by various basic examples and a more advanced case study from dislocation theory. Alexander Mielke's contribution focuses on the multiscale modeling and rigorous analysis of generalized gradient systems through the new concept of evolutionary $\Gamma$-convergence. Numerous evocative examples are given, e.g., relating to periodic homogenization and the passage from viscous to dry friction. Martin Göll and Evgeny Verbitskiy conclude this volume, taking a dynamical systems and ergodic theory viewpoint. They review recent developments in the study of homoclinic points for certain discrete dynamical systems, relating to particle systems via ergodic properties of lattices configurations.
Mathematical Analysis Of Continuum Mechanics And Industrial Applications Ii
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Author : Patrick van Meurs
language : en
Publisher: Springer
Release Date : 2017-11-16
Mathematical Analysis Of Continuum Mechanics And Industrial Applications Ii written by Patrick van Meurs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Science categories.
As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, modeling of earthquakes, material structure, interface dynamics and complex systems.. The authors are leading researchers with a profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry. The book helps readers to understand how mathematical theory can be applied to various industrial problems, and conversely, how industrial problems lead to new mathematical challenges.
Analysis On Function Spaces Of Musielak Orlicz Type
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Author : Osvaldo Mendez
language : en
Publisher: CRC Press
Release Date : 2019-01-21
Analysis On Function Spaces Of Musielak Orlicz Type written by Osvaldo Mendez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-21 with Mathematics categories.
Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introduction to the theory of Musielak–Orlicz spaces, and introduces associated function spaces, extending up to the current research on the topic Musielak-Orlicz spaces came under renewed interest when applications to electrorheological hydrodynamics forced the particular case of the variable exponent Lebesgue spaces on to center stage. Since then, research efforts have typically been oriented towards carrying over the results of classical analysis into the framework of variable exponent function spaces. In recent years it has been suggested that many of the fundamental results in the realm of variable exponent Lebesgue spaces depend only on the intrinsic structure of the Musielak-Orlicz function, thus opening the door for a unified theory which encompasses that of Lebesgue function spaces with variable exponent. Features Gives a self-contained, concise account of the basic theory, in such a way that even early-stage graduate students will find it useful Contains numerous applications Facilitates the unified treatment of seemingly different theoretical and applied problems Includes a number of open problems in the area
Variational Models And Methods In Solid And Fluid Mechanics
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Author : Francesco dell'Isola
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-15
Variational Models And Methods In Solid And Fluid Mechanics written by Francesco dell'Isola 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 2012-01-15 with Technology & Engineering categories.
F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
Applications Of The Topological Derivative Method
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Author : Antonio André Novotny
language : en
Publisher: Springer
Release Date : 2018-12-28
Applications Of The Topological Derivative Method written by Antonio André Novotny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-28 with Technology & Engineering categories.
The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.
Evolutionary Multi Criterion Optimization
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Author : Kalyanmoy Deb
language : en
Publisher: Springer
Release Date : 2019-02-28
Evolutionary Multi Criterion Optimization written by Kalyanmoy Deb and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-28 with Computers categories.
This book constitutes the refereed proceedings of the 10th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2019 held in East Lansing, MI, USA, in March 2019. The 59 revised full papers were carefully reviewed and selected from 76 submissions. The papers are divided into 8 categories, each representing a key area of current interest in the EMO field today. They include theoretical developments, algorithmic developments, issues in many-objective optimization, performance metrics, knowledge extraction and surrogate-based EMO, multi-objective combinatorial problem solving, MCDM and interactive EMO methods, and applications.