Quantitative Stochastic Homogenization And Large Scale Regularity

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Quantitative Stochastic Homogenization and Large-Scale Regularity

Author : Scott Armstrong
Publisher : Springer
ISBN 13 : 3030155455
Total Pages : 518 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Quantitative Stochastic Homogenization and Large-Scale Regularity by : Scott Armstrong

Download or read book Quantitative Stochastic Homogenization and Large-Scale Regularity written by Scott Armstrong and published by Springer. This book was released on 2019-05-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is the large-scale statistical behavior of solutions of divergence-form elliptic equations with random coefficients, which is closely related to the long-time asymptotics of reversible diffusions in random media and other basic models of statistical physics. Of particular interest is the quantification of the rate at which solutions converge to those of the limiting, homogenized equation in the regime of large scale separation, and the description of their fluctuations around this limit. This self-contained presentation gives a complete account of the essential ideas and fundamental results of this new theory of quantitative stochastic homogenization, including the latest research on the topic, and is supplemented with many new results. The book serves as an introduction to the subject for advanced graduate students and researchers working in partial differential equations, statistical physics, probability and related fields, as well as a comprehensive reference for experts in homogenization. Being the first text concerned primarily with stochastic (as opposed to periodic) homogenization and which focuses on quantitative results, its perspective and approach are entirely different from other books in the literature.

Harmonic Analysis and Applications

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
ISBN 13 : 1470461277
Total Pages : 345 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Harmonic Analysis and Applications by : Carlos E. Kenig

Download or read book Harmonic Analysis and Applications written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.

Flowing Matter

Author : Federico Toschi
Publisher : Springer Nature
ISBN 13 : 3030233707
Total Pages : 309 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Flowing Matter by : Federico Toschi

Download or read book Flowing Matter written by Federico Toschi and published by Springer Nature. This book was released on 2019-09-25 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book, published in the Soft and Biological Matter series, presents an introduction to selected research topics in the broad field of flowing matter, including the dynamics of fluids with a complex internal structure -from nematic fluids to soft glasses- as well as active matter and turbulent phenomena. Flowing matter is a subject at the crossroads between physics, mathematics, chemistry, engineering, biology and earth sciences, and relies on a multidisciplinary approach to describe the emergence of the macroscopic behaviours in a system from the coordinated dynamics of its microscopic constituents. Depending on the microscopic interactions, an assembly of molecules or of mesoscopic particles can flow like a simple Newtonian fluid, deform elastically like a solid or behave in a complex manner. When the internal constituents are active, as for biological entities, one generally observes complex large-scale collective motions. Phenomenology is further complicated by the invariable tendency of fluids to display chaos at the large scales or when stirred strongly enough. This volume presents several research topics that address these phenomena encompassing the traditional micro-, meso-, and macro-scales descriptions, and contributes to our understanding of the fundamentals of flowing matter. This book is the legacy of the COST Action MP1305 “Flowing Matter”.

Random Graphs, Phase Transitions, and the Gaussian Free Field

Author : Martin T. Barlow
Publisher : Springer Nature
ISBN 13 : 3030320111
Total Pages : 421 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Random Graphs, Phase Transitions, and the Gaussian Free Field by : Martin T. Barlow

Download or read book Random Graphs, Phase Transitions, and the Gaussian Free Field written by Martin T. Barlow and published by Springer Nature. This book was released on 2019-12-03 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2017 PIMS-CRM Summer School in Probability was held at the Pacific Institute for the Mathematical Sciences (PIMS) at the University of British Columbia in Vancouver, Canada, during June 5-30, 2017. It had 125 participants from 20 different countries, and featured two main courses, three mini-courses, and twenty-nine lectures. The lecture notes contained in this volume provide introductory accounts of three of the most active and fascinating areas of research in modern probability theory, especially designed for graduate students entering research: Scaling limits of random trees and random graphs (Christina Goldschmidt) Lectures on the Ising and Potts models on the hypercubic lattice (Hugo Duminil-Copin) Extrema of the two-dimensional discrete Gaussian free field (Marek Biskup) Each of these contributions provides a thorough introduction that will be of value to beginners and experts alike.

Research in Mathematics of Materials Science

Author : Malena I. Español
Publisher : Springer Nature
ISBN 13 : 3031044967
Total Pages : 514 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Research in Mathematics of Materials Science by : Malena I. Español

Download or read book Research in Mathematics of Materials Science written by Malena I. Español and published by Springer Nature. This book was released on 2022-09-27 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights contributions of women mathematicians in the study of complex materials and includes both original research papers and reviews. The featured topics and methods draw on the fields of Calculus of Variations, Partial Differential Equations, Functional Analysis, Differential Geometry and Topology, as well as Numerical Analysis and Mathematical Modelling. Areas of applications include foams, fluid-solid interactions, liquid crystals, shape-memory alloys, magnetic suspensions, failure in solids, plasticity, viscoelasticity, homogenization, crystallization, grain growth, and phase-field models.

Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems

Author : Omar Anza Hafsa
Publisher : World Scientific
ISBN 13 : 9811258503
Total Pages : 321 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems by : Omar Anza Hafsa

Download or read book Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems written by Omar Anza Hafsa and published by World Scientific. This book was released on 2022-06-21 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.

Periodic Homogenization of Elliptic Systems

Author : Zhongwei Shen
Publisher : Springer
ISBN 13 : 3319912143
Total Pages : 291 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Periodic Homogenization of Elliptic Systems by : Zhongwei Shen

Download or read book Periodic Homogenization of Elliptic Systems written by Zhongwei Shen and published by Springer. This book was released on 2018-09-04 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.

Mathematics and Materials

Author : Mark J. Bowick
Publisher : American Mathematical Soc.
ISBN 13 : 1470429195
Total Pages : 327 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematics and Materials by : Mark J. Bowick

Download or read book Mathematics and Materials written by Mark J. Bowick and published by American Mathematical Soc.. This book was released on 2017-08-25 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: A co-publication of the AMS, IAS/Park City Mathematics Institute, and Society for Industrial and Applied Mathematics Articles in this volume are based on lectures presented at the Park City summer school on “Mathematics and Materials” in July 2014. The central theme is a description of material behavior that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. All the lectures present unique pedagogical introductions to the rich variety of material behavior that emerges from the interplay of geometry and statistical mechanics. The topics include the order-disorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic self-assembly. Several lectures touch on discrete geometry (especially packing) and statistical mechanics. The problems discussed in this book have an immediate mathematical appeal and are of increasing importance in applications, but are not as widely known as they should be to mathematicians interested in materials science. The volume will be of interest to graduate students and researchers in analysis and partial differential equations, continuum mechanics, condensed matter physics, discrete geometry, and mathematical physics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. NOTE: This discount does not apply to volumes in this series co-published with the Society for Industrial and Applied Mathematics (SIAM).

Homogenization Theory for Multiscale Problems

Author : Xavier Blanc
Publisher : Springer Nature
ISBN 13 : 3031218337
Total Pages : 469 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Homogenization Theory for Multiscale Problems by : Xavier Blanc

Download or read book Homogenization Theory for Multiscale Problems written by Xavier Blanc and published by Springer Nature. This book was released on 2023-04-29 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.

A Course on Rough Paths

Author : Peter K. Friz
Publisher : Springer Nature
ISBN 13 : 3030415562
Total Pages : 346 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis A Course on Rough Paths by : Peter K. Friz

Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH

Stochastic Optimization for Large-scale Machine Learning

Author : Vinod Kumar Chauhan
Publisher : CRC Press
ISBN 13 : 1000505618
Total Pages : 189 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Stochastic Optimization for Large-scale Machine Learning by : Vinod Kumar Chauhan

Download or read book Stochastic Optimization for Large-scale Machine Learning written by Vinod Kumar Chauhan and published by CRC Press. This book was released on 2021-11-18 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advancements in the technology and availability of data sources have led to the `Big Data' era. Working with large data offers the potential to uncover more fine-grained patterns and take timely and accurate decisions, but it also creates a lot of challenges such as slow training and scalability of machine learning models. One of the major challenges in machine learning is to develop efficient and scalable learning algorithms, i.e., optimization techniques to solve large scale learning problems. Stochastic Optimization for Large-scale Machine Learning identifies different areas of improvement and recent research directions to tackle the challenge. Developed optimisation techniques are also explored to improve machine learning algorithms based on data access and on first and second order optimisation methods. Key Features: Bridges machine learning and Optimisation. Bridges theory and practice in machine learning. Identifies key research areas and recent research directions to solve large-scale machine learning problems. Develops optimisation techniques to improve machine learning algorithms for big data problems. The book will be a valuable reference to practitioners and researchers as well as students in the field of machine learning.

Stochastic Processes and Applications

Author : Grigorios A. Pavliotis
Publisher : Springer
ISBN 13 : 1493913239
Total Pages : 345 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Platform Scale

Author : Sangeet Paul Choudary
Publisher :
ISBN 13 : 9789810967581
Total Pages : 325 pages
Book Rating : 4.9/5 (675 download)

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Book Synopsis Platform Scale by : Sangeet Paul Choudary

Download or read book Platform Scale written by Sangeet Paul Choudary and published by . This book was released on 2015 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Platform Scale explains the design of a family of emerging digital business models that enables today's startups to achieve rapid scale: the platform business model. The many manifestations of the platform business model - social media, the peer economy, cryptocurrencies, APIs and developer ecosystems, the Internet of things, crowdsourcing models, and many others - are becoming increasingly relevant. Yet, most new platform ideas fail because the business design and growth strategies involved in building platforms are not well understood. Platform scale is a builder's manual for anyone building a platform business today. It lays out a structured approach to desinging and growing a platform business model and addressess the key factors that lead to the success and failure of these businesses."--back cover.

Homogenization of Differential Operators and Integral Functionals

Author : V.V. Jikov
Publisher : Springer Science & Business Media
ISBN 13 : 3642846599
Total Pages : 583 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Homogenization of Differential Operators and Integral Functionals by : V.V. Jikov

Download or read book Homogenization of Differential Operators and Integral Functionals written by V.V. Jikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

Turbulence

Author : Uriel Frisch
Publisher : Cambridge University Press
ISBN 13 : 1139935976
Total Pages : 318 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Turbulence by : Uriel Frisch

Download or read book Turbulence written by Uriel Frisch and published by Cambridge University Press. This book was released on 1995-11-30 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.

Conjugate Duality and Optimization

Author : R. Tyrrell Rockafellar
Publisher : SIAM
ISBN 13 : 9781611970524
Total Pages : 80 pages
Book Rating : 4.9/5 (75 download)

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Book Synopsis Conjugate Duality and Optimization by : R. Tyrrell Rockafellar

Download or read book Conjugate Duality and Optimization written by R. Tyrrell Rockafellar and published by SIAM. This book was released on 1974-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.

Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

Author : Alexander N. Gorban
Publisher : Springer Science & Business Media
ISBN 13 : 3540358889
Total Pages : 554 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena by : Alexander N. Gorban

Download or read book Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena written by Alexander N. Gorban and published by Springer Science & Business Media. This book was released on 2006-09-22 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.