Topics On Concentration Phenomena And Problems With Multiple Scales

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Topics On Concentration Phenomena And Problems With Multiple Scales

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Author : Andrea Braides
language : en
Publisher: Springer
Release Date : 2009-09-02

Topics On Concentration Phenomena And Problems With Multiple Scales 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 2009-09-02 with Mathematics categories.

The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when 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, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.

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 : 2006-11-22

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 2006-11-22 with Mathematics categories.

The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when 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, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.

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.

Handbook Of Differential Equations Stationary Partial Differential Equations

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Author : Michel Chipot
language : en
Publisher: Elsevier
Release Date : 2006-08-08

Handbook Of Differential Equations Stationary Partial Differential Equations written by Michel Chipot and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-08 with Mathematics categories.

This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics.Key features: - Written by well-known experts in the field- Self-contained volume in series covering one of the most rapid developing topics in mathematics- Written by well-known experts in the field- Self-contained volume in series covering one of the most rapid developing topics in mathematics

Analysis On Graphs And Its Applications

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Author : Pavel Exner
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Analysis On Graphs And Its Applications written by Pavel Exner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.

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.

Ludwig Faddeev Memorial Volume A Life In Mathematical Physics

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Author : Mo-lin Ge
language : en
Publisher: World Scientific
Release Date : 2018-05-21

Ludwig Faddeev Memorial Volume A Life In Mathematical Physics written by Mo-lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-21 with Science categories.

Ludwig Faddeev is widely recognized as one of the titans of 20th century mathematical physics. His fundamental contributions to scattering theory, quantum gauge theories, and the theory of classical and quantum completely integrable systems played a key role in shaping modern mathematical physics.Ludwig Faddeev's major achievements include the solution of the three-body problem in quantum mechanics, the mathematical formulation of quantum gauge theories and corresponding Feynman rules, Hamiltonian and algebraic methods in mathematical physics, with applications to gauge theories with anomalies, quantum systems with constraints and solitons, the discovery of the algebraic structure of classical and quantum integrable systems and quantum groups, and solitons with the topology of knots.Faddeev's name is imprinted in many areas of mathematics and theoretical physics, including 'Faddeev's equations' and 'Faddeev's Green function' in scattering theory, 'Faddeev-Popov ghosts' and 'Faddeev-Popov determinant' in gauge theories, 'Gardner-Faddeev-Zakharov bracket' for the KdV equation, 'Faddeev-Zamolodchikov algebra' in quantum integrable systems, 'Faddeev-Reshetikhin-Takhtajan construction' in the theory of quantum groups, knotted solitons in the 'Skyrme-Faddeev model' and many others.Ludwig Faddeev founded the St. Petersburg school of modern mathematical physics and distinguished himself by serving the mathematics community for over three decades including his leadership of the International Mathematical Union in the period of 1986-1990. He was conferred numerous prizes and memberships of prestigious institutions in recognition of the importance of his work. These include the Dannie Heineman Prize for Mathematical Physics, the Dirac Medal, the Max Planck Medal, the Shaw Prize and the Lomonosov Gold Medal among others.A gathering of contributions from some of the biggest names in mathematics and physics, this volume serves as a tribute to this legendary figure. Volume contributors include: Fields medalist Sir Michael Atiyah, Jürg Fröhlich, Roman Jackiw, Vladimir Korepin, Nikita Nekrasov, André Neveu, Alexander M Polyakov, Samson Shatashvili, Fedor Smirnov as well as Nobel laureates Frank Wilczek and C N Yang.

Dynamical System Models In The Life Sciences And Their Underlying Scientific Issues

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Author : Frederic Y M Wan
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-08-16

Dynamical System Models In The Life Sciences And Their Underlying Scientific Issues written by Frederic Y M Wan 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 2017-08-16 with Mathematics categories.

Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) the case study approach, and 2) the method based approach (that teaches mathematical techniques with applications to relevant mathematical models). This text emphasizes instead the scientific issues for modeling different phenomena. For the natural or harvested growth of a fish population, we may be interested in the evolution of the population, whether it reaches a steady state (equilibrium or cycle), stable or unstable with respect to a small perturbation from equilibrium, or whether a small change in the environment would cause a catastrophic change, etc. Each scientific issue requires an appropriate model and a different set of mathematical tools to extract information from the model. Models examined are chosen to help explain or justify empirical observations such as cocktail drug treatments are more effective and regenerations after injuries or illness are fast-tracked (compared to original developments).Volume I of this three-volume set limits its scope to phenomena and scientific issues that are modeled by ordinary differential equations (ODE). Scientific issues such as signal and wave propagation, diffusion, and shock formation involving spatial dynamics to be modeled by partial differential equations (PDE) will be treated in Vol. II. Scientific issues involving randomness and uncertainty are examined in Vol. III.

Issues In Specialized Chemical And Chemistry Topics 2011 Edition

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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2012-01-09

Issues In Specialized Chemical And Chemistry Topics 2011 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-09 with Science categories.

Issues in Specialized Chemical and Chemistry Topics: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Specialized Chemical and Chemistry Topics. The editors have built Issues in Specialized Chemical and Chemistry Topics: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Specialized Chemical and Chemistry Topics in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Specialized Chemical and Chemistry Topics: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Soil And Water Quality At Different Scales

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Author : Peter A. Finke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Soil And Water Quality At Different Scales written by Peter A. Finke 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 2013-03-14 with Science categories.

Integrated studies on the assessment and improvement of soil and water quality have to deal almost inevitably with issues of scale, since the spatial support of measurements, the model calculations and the presentation of results usually vary. This book contains the selected and edited proceedings of a workshop devoted to issues of scale entitled: `Soil and Water Quality at Different Scales', which was held in 1996 in Wageningen. It is intended for environmental researchers, scientists and MSc and PhD students. Part 1 covers current issues and methodologies with scale related soil and water quality research. Part 2 covers agroecological and hydrological case studies in which scale transforms form an important part of the research chain. Part 3 consists of papers focusing on methodologies and up and downscaling. Part 4 contains review papers based on modellers' and statisticians' considerations as well as the papers and posters presented during the workshop. Part 5 consists of short research notes.