Random Media

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Random Media

Author : George Papanicolaou
Publisher : Springer Science & Business Media
ISBN 13 : 1461387256
Total Pages : 322 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Random Media by : George Papanicolaou

Download or read book Random Media written by George Papanicolaou and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications RANDOM MEDIA represents the proceedings of a workshop which was an integral part of the 1984-85 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS We are grateful to the Scientific Committee: Daniel Stroock (Chairman) \~ende 11 Fl emi ng Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We especi ally thank George Papani col aOIJ for organi zi ng a workshop which produced fruitful interactions between mathematicians and scientists from both academia and industry. George R. Sell Hans I~ei nherger PREFACE During September 1985 a workshop on random media was held at the Institute for Mathematics and its Applications at the University of Minnesota. This was part of the program for the year on Probability and Stochastic Processes at IMA. The main objective of the workshop was to bring together researchers who work in a broad area including applications and mathematical methodology. The papers in this volume give an idea of what went on and they also represent a cross section of problems and methods that are currently of interest.

Ten Lectures on Random Media

Author : Erwin Bolthausen
Publisher : Birkhäuser
ISBN 13 : 3034881592
Total Pages : 120 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Ten Lectures on Random Media by : Erwin Bolthausen

Download or read book Ten Lectures on Random Media written by Erwin Bolthausen and published by Birkhäuser. This book was released on 2012-12-06 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The following notes grew out oflectures held during the DMV-Seminar on Random Media in November 1999 at the Mathematics Research Institute of Oberwolfach, and in February-March 2000 at the Ecole Normale Superieure in Paris. In both places the atmosphere was very friendly and stimulating. The positive response of the audience was encouragement enough to write up these notes. I hope they will carryover the enjoyment of the live lectures. I whole heartedly wish to thank Profs. Matthias Kreck and Jean-Franc;ois Le Gall who were respon sible for these two very enjoyable visits, Laurent Miclo for his comments on an earlier version of these notes, and last but not least Erwin Bolthausen who was my accomplice during the DMV-Seminar. A Brief Introduction The main theme of this series of lectures are "Random motions in random me dia". The subject gathers a variety of probabilistic models often originated from physical sciences such as solid state physics, physical chemistry, oceanography, biophysics . . . , in which typically some diffusion mechanism takes place in an inho mogeneous medium. Randomness appears at two levels. It comes in the description of the motion of the particle diffusing in the medium, this is a rather traditional point of view for probability theory; but it also comes in the very description of the medium in which the diffusion takes place.

Random Media and Composites

Author : Robert V. Kohn
Publisher : SIAM
ISBN 13 : 9780898712469
Total Pages : 236 pages
Book Rating : 4.7/5 (124 download)

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Book Synopsis Random Media and Composites by : Robert V. Kohn

Download or read book Random Media and Composites written by Robert V. Kohn and published by SIAM. This book was released on 1989-01-01 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Random Media and Boundaries

Author : Koichi Furutsu
Publisher : Springer Science & Business Media
ISBN 13 : 3642848079
Total Pages : 278 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Random Media and Boundaries by : Koichi Furutsu

Download or read book Random Media and Boundaries written by Koichi Furutsu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a system consisting of a random medium with rough boundaries, the governing (Bethe-Salpeter) equation for boundary-value transport problems can be written in a form such that the medium and the boundaries are treatedon an equal footing. This enables several expressions for the solution to be obtained by interchanging the roles of the medium and the boundaries, thus allowing the most convenient one to be selected according to the specific situation and the information required. This book presents a unified theory based on the Bethe-Salpeter equation with particular attention being paid to: boundary-value problems of transport, layer problems, a fixed scatterer imbedded in a bounded random medium, construction of an optical scattering matrix for a complete system, and optical wave propagation in a turbulent medium. The last topic is treated in terms of first moment equations combined with the cluster expansion and, second, the two-scale method based on the Lagrange variational principle.

Wave Propagation and Scattering in Random Media

Author : Akira Ishimaru
Publisher : Academic Press
ISBN 13 : 1483273156
Total Pages : 343 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Wave Propagation and Scattering in Random Media by : Akira Ishimaru

Download or read book Wave Propagation and Scattering in Random Media written by Akira Ishimaru and published by Academic Press. This book was released on 2013-10-22 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave Propagation and Scattering in Random Media, Volume 2, presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner. The topics covered in this book may be grouped into three categories: waves in random scatterers, waves in random continua, and rough surface scattering. Random scatterers are random distributions of many particles. Examples are rain, fog, smog, hail, ocean particles, red blood cells, polymers, and other particles in a state of Brownian motion. Random continua are the media whose characteristics vary randomly and continuously in time and space. Examples are clear air turbulence, jet engine exhaust, tropospheric and ionospheric turbulence, ocean turbulence, and biological media such as tissue and muscle. Rough surface examples are the ocean surface, planetary surfaces, interfaces between different biological media, and the surface roughness of an optical fiber. This book is intended for engineers and scientists interested in optical, acoustic, and microwave propagation and scattering in atmospheres, oceans, and biological media, and particularly for those involved in communication through such media and remote sensing of the characteristics of these media.

Electromagnetic Scattering from Random Media

Author : Timothy R. Field
Publisher : International Monographs on Ph
ISBN 13 : 0198570775
Total Pages : 199 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis Electromagnetic Scattering from Random Media by : Timothy R. Field

Download or read book Electromagnetic Scattering from Random Media written by Timothy R. Field and published by International Monographs on Ph. This book was released on 2009 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book develops the dynamical theory of scattering from random media from first principles. Its key findings are to characterize the time evolution of the scattered field in terms of stochastic differential equations, and to illustrate this framework in simulation and experimental data analysis. The physical models contain all correlation information and higher order statistics, which enables radar and laser scattering experiments to be interpreted. An emphasis is placed on the statistical character of the instantaneous fluctuations, as opposed to ensemble average properties. This leads to various means for detection, which have important consequences in radar signal processing and statistical optics. The book is also significant also because it illustrates how ideas in mathematical finance can be applied to physics problems in which non-Gaussian noise processes play an essential role. This pioneering book represents a significant advance in this field, and should prove valuable to leading edge researchers and practitioners at the postgraduate level and above.

Polarization Optics of Random Media

Author : Alexander Kokhanovsky
Publisher : Springer Science & Business Media
ISBN 13 : 9783540426356
Total Pages : 248 pages
Book Rating : 4.4/5 (263 download)

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Book Synopsis Polarization Optics of Random Media by : Alexander Kokhanovsky

Download or read book Polarization Optics of Random Media written by Alexander Kokhanovsky and published by Springer Science & Business Media. This book was released on 2003-07-15 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author presents for the first time the main results obtained in the field of polarization optics in a wide range of application areas. These will be used widely in different branches of modern science and technology over the next century.

Nonlinear Optics of Random Media

Author : Vladimir M. Shalaev
Publisher : Springer
ISBN 13 : 3540491848
Total Pages : 159 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Nonlinear Optics of Random Media by : Vladimir M. Shalaev

Download or read book Nonlinear Optics of Random Media written by Vladimir M. Shalaev and published by Springer. This book was released on 2007-09-28 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Optics of Random Media reviews recent advances in in one of the most prominent fields of physics. It provides an outline of the basic models of irregular structures of random inhomogeneous media and the approaches used to describe their linear electromagnetic properties. Nonlinearities in random media are also discussed. The chapters can be read independently, so scientists and students interested in a specific problem can go directly to the relevant text.

Evolution of Systems in Random Media

Author : Vladimir S. Korolyuk
Publisher : CRC Press
ISBN 13 : 9780849394058
Total Pages : 358 pages
Book Rating : 4.3/5 (94 download)

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Book Synopsis Evolution of Systems in Random Media by : Vladimir S. Korolyuk

Download or read book Evolution of Systems in Random Media written by Vladimir S. Korolyuk and published by CRC Press. This book was released on 1995-09-11 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolution of Systems in Random Media is an innovative, application-oriented text that explores stochastic models of evolutionary stochastic systems in random media. Specially designed for researchers and practitioners who do not have a background in random evolutions, the book allows non-experts to explore the potential information and applications that random evolutions can provide.

Waves in Periodic and Random Media

Author : Peter Kuchment
Publisher : American Mathematical Soc.
ISBN 13 : 0821832867
Total Pages : 232 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Waves in Periodic and Random Media by : Peter Kuchment

Download or read book Waves in Periodic and Random Media written by Peter Kuchment and published by American Mathematical Soc.. This book was released on 2003 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science and engineering have been great sources of problems and inspiration for generations of mathematicians. This is probably true now more than ever as numerous challenges in science and technology are met by mathematicians. One of these challenges is understanding propagation of waves of different nature in systems of complex structure. This book contains the proceedings of the research conference, ``Waves in Periodic and Random Media''. Papers are devoted to a number of related themes, including spectral theory of periodic differential operators, Anderson localization and spectral theory of random operators, photonic crystals, waveguide theory, mesoscopic systems, and designer random surfaces. Contributions are written by prominent experts and are of interest to researchers and graduate students in mathematical physics.

Evolution of Biological Systems in Random Media: Limit Theorems and Stability

Author : Anatoly Swishchuk
Publisher : Springer Science & Business Media
ISBN 13 : 9401715068
Total Pages : 230 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Evolution of Biological Systems in Random Media: Limit Theorems and Stability by : Anatoly Swishchuk

Download or read book Evolution of Biological Systems in Random Media: Limit Theorems and Stability written by Anatoly Swishchuk and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a new book in biomathematics, which includes new models of stochastic non-linear biological systems and new results for these systems. These results are based on the new results for non-linear difference and differential equations in random media. This book contains: -New stochastic non-linear models of biological systems, such as biological systems in random media: epidemic, genetic selection, demography, branching, logistic growth and predator-prey models; -New results for scalar and vector difference equations in random media with applications to the stochastic biological systems in 1); -New results for stochastic non-linear biological systems, such as averaging, merging, diffusion approximation, normal deviations and stability; -New approach to the study of stochastic biological systems in random media such as random evolution approach.

Wave Propagation in Random Media

Author : Joseph Bishop Keller
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Wave Propagation in Random Media by : Joseph Bishop Keller

Download or read book Wave Propagation in Random Media written by Joseph Bishop Keller and published by . This book was released on 1960 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multiscale Theory of Composites and Random Media

Author : Xi Frank Xu
Publisher : CRC Press
ISBN 13 : 0429894384
Total Pages : 306 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Multiscale Theory of Composites and Random Media by : Xi Frank Xu

Download or read book Multiscale Theory of Composites and Random Media written by Xi Frank Xu and published by CRC Press. This book was released on 2018-09-21 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to introduce Green-function-based multiscale theory and the corresponding finite element method, which are readily applicable to composites and random media. The methodology is considered to be the one that most effectively tackles the uncertainty of stress propagation in complex heterogeneities of random media, and which presents multiscale theory from distinctive scale separation and scale-coupling viewpoints. Deliberately taking a multiscale perspective, it covers scale separation and then scale coupling. Both micromechanics and novel scale-coupling mechanics are described in relation to variational principles and bounds, as well as in the emerging topics on percolation and scale-coupling computation. It gives detail on the different bounds encountered, covering classical second and third order, new fourth order, and innovative ellipsoidal variations. Green-function-based multiscale theory is addressed to applications in solid mechanics and transport of complex media ranging from micro- and nano-composites, polycrystals, soils, rocks, cementitious materials, to biological materials. It is useful as a graduate textbook in civil and mechanical engineering and as a reference.

An Introduction to Fronts in Random Media

Author : Jack Xin
Publisher : Springer Science & Business Media
ISBN 13 : 0387876839
Total Pages : 165 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis An Introduction to Fronts in Random Media by : Jack Xin

Download or read book An Introduction to Fronts in Random Media written by Jack Xin and published by Springer Science & Business Media. This book was released on 2009-06-17 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Optical Properties of Nanostructured Random Media

Author : Vladimir M. Shalaev
Publisher : Springer Science & Business Media
ISBN 13 : 3540449485
Total Pages : 480 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Optical Properties of Nanostructured Random Media by : Vladimir M. Shalaev

Download or read book Optical Properties of Nanostructured Random Media written by Vladimir M. Shalaev and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributors to the book are world best experts in the optics of random media; they provide a state-of-the-art review of recent developments in the field including nonlinear optical and magneto-optical properties, Raman and hyper-Raman scattering, laser action, plasmon excitation and localized giant fields, imaging and spectroscopy of random media

Electromagnetic Wave Propagation Through Random Media

Author :
Publisher : Johanan Codona
ISBN 13 :
Total Pages : 254 pages
Book Rating : 4./5 ( download)

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Book Synopsis Electromagnetic Wave Propagation Through Random Media by :

Download or read book Electromagnetic Wave Propagation Through Random Media written by and published by Johanan Codona. This book was released on with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advection and Diffusion in Random Media

Author : Leonid Piterbarg
Publisher : Springer Science & Business Media
ISBN 13 : 1475744587
Total Pages : 334 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Advection and Diffusion in Random Media by : Leonid Piterbarg

Download or read book Advection and Diffusion in Random Media written by Leonid Piterbarg and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.