An Introduction To Fronts In Random Media

Author : Jack Xin
Publisher : Springer Science & Business Media
Page : 165 pages
File Size : 44,9 Mb
Release : 2009-06-17
Category : Mathematics
ISBN : 9780387876832

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An Introduction to Fronts in Random Media by Jack Xin Pdf

This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or interfaces in random media) to senior undergraduates and beginning grad uate students with basic knowledge of partial differential equations (PDE) and prob ability. The approach taken is semiformal, using elementary methods to introduce ideas and motivate results as much as possible, then outlining how to pursue rigor ous theorems, with details to be found in the references section. Since the topic concerns both differential equations and probability, and proba bility is traditionally a quite technical subject with a heavy measure theoretic com ponent, the book strives to develop a simplistic approach so that students can grasp the essentials of fronts and random media and their applications in a self contained tutorial. The book introduces three fundamental PDEs (the Burgers equation, Hamilton– Jacobi equations, and reaction–diffusion equations), analysis of their formulas and front solutions, and related stochastic processes. It builds up tools gradually, so that students are brought to the frontiers of research at a steady pace. A moderate number of exercises are provided to consolidate the concepts and ideas. The main methods are representation formulas of solutions, Laplace meth ods, homogenization, ergodic theory, central limit theorems, large deviation princi ples, variational principles, maximum principles, and Harnack inequalities, among others. These methods are normally covered in separate books on either differential equations or probability. It is my hope that this tutorial will help to illustrate how to combine these tools in solving concrete problems.

Author : Peter Poláčik
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 47,6 Mb
Release : 2020-05-13
Category : Education
ISBN : 9781470441128

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Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R by Peter Poláčik Pdf

The author considers semilinear parabolic equations of the form ut=uxx+f(u),x∈R,t>0, where f a C1 function. Assuming that 0 and γ>0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose initial values u(x,0) are near γ for x≈−∞ and near 0 for x≈∞. If the steady states 0 and γ are both stable, the main theorem shows that at large times, the graph of u(⋅,t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). The author proves this result without requiring monotonicity of u(⋅,0) or the nondegeneracy of zeros of f. The case when one or both of the steady states 0, γ is unstable is considered as well. As a corollary to the author's theorems, he shows that all front-like solutions are quasiconvergent: their ω-limit sets with respect to the locally uniform convergence consist of steady states. In the author's proofs he employs phase plane analysis, intersection comparison (or, zero number) arguments, and a geometric method involving the spatial trajectories {(u(x,t),ux(x,t)):x∈R}, t>0, of the solutions in question.

Author : Roland Herzog,Matthias Heinkenschloss,Dante Kalise,Georg Stadler,Emmanuel Trélat
Publisher : Walter de Gruyter GmbH & Co KG
Page : 386 pages
File Size : 48,9 Mb
Release : 2022-03-07
Category : Mathematics
ISBN : 9783110696004

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Optimization and Control for Partial Differential Equations by Roland Herzog,Matthias Heinkenschloss,Dante Kalise,Georg Stadler,Emmanuel Trélat Pdf

This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Author : Tadahisa Funaki,Wojbor Woyczynski
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384687

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Nonlinear Stochastic PDEs by Tadahisa Funaki,Wojbor Woyczynski Pdf

This IMA Volume in Mathematics and its Applications NONLINEAR STOCHASTIC PDEs: HYDRODYNAMIC LIMIT AND BURGERS' TURBULENCE is based on the proceedings of the period of concentration on Stochas tic Methods for Nonlinear PDEs which was an integral part of the 1993- 94 IMA program on "Emerging Applications of Probability." We thank Tadahisa Funaki and Wojbor A. Woyczynski for organizing this meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. xiii PREFACE A workshop on Nonlinear Stochastic Partial Differential Equations was held during the week of March 21 at the Institute for Mathematics and Its Applications at the University of Minnesota. It was part of the Special Year on Emerging Applications of Probability program put together by an organizing committee chaired by J. Michael Steele. The selection of topics reflected personal interests of the organizers with two areas of emphasis: the hydrodynamic limit problems and Burgers' turbulence and related models. The talks and the papers appearing in this volume reflect a number of research directions that are currently pursued in these areas.

Author : Jean-Pierre Fouque,Josselin Garnier,G. Papanicolaou,Knut Solna
Publisher : Springer Science & Business Media
Page : 623 pages
File Size : 54,8 Mb
Release : 2007-06-30
Category : Science
ISBN : 9780387498089

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Wave Propagation and Time Reversal in Randomly Layered Media by Jean-Pierre Fouque,Josselin Garnier,G. Papanicolaou,Knut Solna Pdf

The content of this book is multidisciplinary by nature. It uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics of wave propagation and modeling of time reversal experiments. It is addressed to a wide audience of graduate students and researchers interested in the intriguing phenomena related to waves propagating in random media. At the end of each chapter there is a section of notes where the authors give references and additional comments on the various results presented in the chapter.

Author : I?Akov Borisovich Zel?dovich,Aleksandr Andreevich Ruzma?kin,Dmitri? Dmitrievich Sokolov
Publisher : World Scientific
Page : 334 pages
File Size : 45,9 Mb
Release : 1990
Category : Science
ISBN : 9971509172

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The Almighty Chance by I?Akov Borisovich Zel?dovich,Aleksandr Andreevich Ruzma?kin,Dmitri? Dmitrievich Sokolov Pdf

This book is about the importance of random phenomena occurring in nature. Cases are selected in which randomness is most important or crucial, such as Brownian motion, certain reactions in Physical Chemistry and Biology, and intermittency in magnetic field generation by turbulent fluid motion, etc. Due to ?almighty chance? the structures can originate from chaos even in linear problems. This idea is complementary as well as competes with a basic concept of synergetics where structures appear mainly due to the pan-linear nature of phenomena. This book takes a new look at the problem of structure formation in random media, qualitative physical representation of modern conceptions, intermittency, fractals, percolation and many examples from different fields of science.

Author : Leonid Piterbarg,A. Ostrovskii
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 42,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475744583

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Advection and Diffusion in Random Media by Leonid Piterbarg,A. Ostrovskii Pdf

This book originated from our interest in sea surface temperature variability. Our initial, though entirely pragmatic, goal was to derive adequate mathemat ical tools for handling certain oceanographic problems. Eventually, however, these considerations went far beyond oceanographic applications partly because one of the authors is a mathematician. We found that many theoretical issues of turbulent transport problems had been repeatedly discussed in fields of hy drodynamics, plasma and solid matter physics, and mathematics itself. There are few monographs concerned with turbulent diffusion in the ocean (Csanady 1973, Okubo 1980, Monin and Ozmidov 1988). While selecting material for this book we focused, first, on theoretical issues that could be helpful for understanding mixture processes in the ocean, and, sec ond, on our own contribution to the problem. Mathematically all of the issues addressed in this book are concentrated around a single linear equation: the stochastic advection-diffusion equation. There is no attempt to derive universal statistics for turbulent flow. Instead, the focus is on a statistical description of a passive scalar (tracer) under given velocity statistics. As for applications, this book addresses only one phenomenon: transport of sea surface temperature anomalies. Hopefully, however, our two main approaches are applicable to other subjects.

Author : J.C. Charmet,E. Guyon,Stéphane Roux
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 55,5 Mb
Release : 2013-03-08
Category : Technology & Engineering
ISBN : 9781461568643

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Disorder and Fracture by J.C. Charmet,E. Guyon,Stéphane Roux Pdf

Fracture, and particularly brittle fracture, is a good example of an instability. For a homogeneous solid, subjected to a uniform stress field, a crack may appear anywhere in the structure once the threshold stress is reached. However, once a crack has been nucleated in some place, further damage in the solid will in most cases propagate from the initial crack, and not somewhere else in the solid. In this sense fracture is an unstable process. This property makes the process extremely sensitive to any heterogeneity present in the medium, which selects the location of the first crack nucleated. In particular, fracture appears to be very sensitive to disorder, which can favor or impede local cracks. Therefore, in most realistic cases, a good description of fracture mechanics should include the effect of disorder. Recently this need has motivated work in this direction starting from the usual description of fracture mechanics. Parallel with this first trend, statistical physics underwent a very important development in the description of disordered systems. In particular, let us mention the emergence of some "new" concepts (such as fractals, scaling laws, finite size effects, and so on) in this field. However, many models considered were rather simple and well adapted to theoretical or numerical introduction into a complex body of problems. An example of this can be found in percolation theory. This area is now rather well understood and accurately described.

Author : Arthur James Wells
Publisher : Unknown
Page : 2744 pages
File Size : 47,7 Mb
Release : 2009
Category : Bibliography, National
ISBN : STANFORD:36105211722686

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The British National Bibliography by Arthur James Wells Pdf

Author : Ming-Hui Chen,Peter Müller,Dongchu Sun,Keying Ye,Dipak K. Dey
Publisher : Springer Science & Business Media
Page : 631 pages
File Size : 45,8 Mb
Release : 2010-07-24
Category : Mathematics
ISBN : 9781441969446

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Frontiers of Statistical Decision Making and Bayesian Analysis by Ming-Hui Chen,Peter Müller,Dongchu Sun,Keying Ye,Dipak K. Dey Pdf

Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

Author : Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 48,6 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401728232

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Quantum and Non-Commutative Analysis by Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima Pdf

In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Author : C.C. Barton,P.R. La Pointe
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461518150

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Fractals in Petroleum Geology and Earth Processes by C.C. Barton,P.R. La Pointe Pdf

In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results.

Author : Mark Iosifovich Freidlin
Publisher : Princeton University Press
Page : 560 pages
File Size : 53,9 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881598

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Functional Integration and Partial Differential Equations. (AM-109), Volume 109 by Mark Iosifovich Freidlin Pdf

This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.

Author : Robert Curtis Sparrock
Publisher : Unknown
Page : 264 pages
File Size : 45,9 Mb
Release : 1990
Category : Sound
ISBN : UCSD:31822005665682

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Stability of Time Fronts on a Large Vertical Array at Long Range in the Ocean by Robert Curtis Sparrock Pdf

Author : King-Yeung Lam,Yuan Lou
Publisher : Springer Nature
Page : 316 pages
File Size : 52,7 Mb
Release : 2022-12-01
Category : Mathematics
ISBN : 9783031204227

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Introduction to Reaction-Diffusion Equations by King-Yeung Lam,Yuan Lou Pdf

This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.