Waves in Periodic and Random Media

Waves in Periodic and Random Media
Title Waves in Periodic and Random Media PDF eBook
Author Peter Kuchment
Publisher American Mathematical Soc.
Pages 232
Release 2003
Genre Mathematics
ISBN 0821832867

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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.

The Topology of 4-Manifolds

The Topology of 4-Manifolds
Title The Topology of 4-Manifolds PDF eBook
Author Robion C. Kirby
Publisher Springer
Pages 114
Release 2006-11-14
Genre Mathematics
ISBN 354046171X

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This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin's theorem using spin structures. There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.

Random Media

Random Media
Title Random Media PDF eBook
Author George Papanicolaou
Publisher Springer Science & Business Media
Pages 322
Release 2012-12-06
Genre Mathematics
ISBN 1461387256

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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.

An Introduction to Fronts in Random Media

An Introduction to Fronts in Random Media
Title An Introduction to Fronts in Random Media PDF eBook
Author Jack Xin
Publisher Springer Science & Business Media
Pages 165
Release 2009-06-17
Genre Mathematics
ISBN 0387876839

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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.

Waves in Complex Media

Waves in Complex Media
Title Waves in Complex Media PDF eBook
Author Luca Dal Negro
Publisher Cambridge University Press
Pages 713
Release 2022-05-19
Genre Science
ISBN 1107037506

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An interdisciplinary introduction to the structural and scattering properties of complex photonic media, focusing on deterministic aperiodic structures and their conceptual roots in geometry and number theory. An essential tool for students at the graduate or advanced undergraduate level.

Wave Propagation in Random Media (scintillation)

Wave Propagation in Random Media (scintillation)
Title Wave Propagation in Random Media (scintillation) PDF eBook
Author Akira Ishimaru
Publisher
Pages 0
Release 1993
Genre Ionospheric radio wave propagation
ISBN

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Surface Acoustic Waves in Inhomogeneous Media

Surface Acoustic Waves in Inhomogeneous Media
Title Surface Acoustic Waves in Inhomogeneous Media PDF eBook
Author Sergey V. Biryukov
Publisher Springer Science & Business Media
Pages 398
Release 2012-12-06
Genre Science
ISBN 3642577679

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Surface Acoustic Waves in Inhomogeneous Media covers almost all important problems of the interaction of different types of surface acoustic waves with surface inhomogeneities. The problems of surface acoustic wave interaction with periodic topographic gratings widely used in filters and resonators are under careful consideration. The most important results of surface wave scattering by local defects such as grooves, random roughness, elastic wedges are given. Different theoretical approaches and practical rules for solving the surface wave problems are presented.