Asymptotic Analysis for Periodic Structures

Asymptotic Analysis for Periodic Structures

Author: Alain Bensoussan

Publisher: American Mathematical Soc.

Published: 2011-10-26

Total Pages: 410

ISBN-13: 0821853244

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This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence methods. Before this book, multiple scale methods were primarily used for non-linear oscillation problems in the applied mathematics community, not for analyzing spatial oscillations as in homogenization. In the current printing a number of minor corrections have been made, and the bibliography was significantly expanded to include some of the most important recent references. This book gives systematic introduction of multiple scale methods for partial differential equations, including their original use for rigorous mathematical analysis in elliptic, parabolic, and hyperbolic problems, and with the use of probabilistic methods when appropriate. The book continues to be interesting and useful to readers of different backgrounds, both from pure and applied mathematics, because of its informal style of introducing the multiple scale methodology and the detailed proofs.


Asymptotic Analysis for Periodic Structures

Asymptotic Analysis for Periodic Structures

Author: Alain Bensoussan

Publisher:

Published: 2011

Total Pages:

ISBN-13: 9781470415815

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This is a reprinting of a book originally published in 1978. At that time it was the first book on the subject of homogenization, which is the asymptotic analysis of partial differential equations with rapidly oscillating coefficients, and as such it sets the stage for what problems to consider and what methods to use, including probabilistic methods. At the time the book was written the use of asymptotic expansions with multiple scales was new, especially their use as a theoretical tool, combined with energy methods and the construction of test functions for analysis with weak convergence met.


Fundamentals and Applications of Acoustic Metamaterials

Fundamentals and Applications of Acoustic Metamaterials

Author: Vicente Romero-Garcia

Publisher: John Wiley & Sons

Published: 2019-08-08

Total Pages: 326

ISBN-13: 1119649161

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In the last few decades, metamaterials have revolutionized the ways in which waves are controlled, and applied in physics and practical situations. The extraordinary properties of metamaterials, such as their locally resonant structure with deep subwavelength band gaps and their ranges of frequency where propagation is impossible, have opened the way to a host of applications that were previously unavailable. Acoustic metamaterials have been able to replace traditional treatments in several sectors, due to their better performance in targeted and tunable frequency ranges with strongly reduced dimensions. This is a training book composed of nine chapters written by experts in the field, giving a broad overview of acoustic metamaterials and their uses. The book is divided into three parts, covering the state-of-the-art, the fundamentals and the real-life applications of acoustic metamaterials.


Research Directions in Distributed Parameter Systems

Research Directions in Distributed Parameter Systems

Author: Ralph C. Smith

Publisher: SIAM

Published: 2003-01-01

Total Pages: 283

ISBN-13: 0898715482

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Eleven chapters, written by experts in their respective fields, on topics ranging from control of the Navier-Stokes equations to nondestructive evaluation - all of which are modeled by distributed parameter systems.


Theoretical Analyses, Computations, and Experiments of Multiscale Materials

Theoretical Analyses, Computations, and Experiments of Multiscale Materials

Author: Ivan Giorgio

Publisher: Springer Nature

Published: 2022-05-03

Total Pages: 739

ISBN-13: 3031045483

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This book is devoted to the 60th birthday of the Prof. Francesco dell’Isola, who is known for his long-term contribution in the field of multiscale materials. It contains several contributions from researchers in the field, covering theoretical analyses, computational aspects and experiments.


Shell Structures: Theory and Applications (Vol. 2)

Shell Structures: Theory and Applications (Vol. 2)

Author: Wojciech Pietraszkiewicz

Publisher: CRC Press

Published: 2009-09-22

Total Pages: 361

ISBN-13: 0203859766

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Shell Structures. Theory and Applications, Volume 2 contains 77 contributions from over 17 countries, reflecting a wide spectrum of scientific and engineering problems of shell structures. The papers are divided into six broad groups: 1. General lectures; 2. Theoretical modeling; 3. Stability; 4. Dynamics; 5. Numerical analysis; 6. Engineering


Homogenization of Differential Operators and Integral Functionals

Homogenization of Differential Operators and Integral Functionals

Author: V.V. Jikov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 583

ISBN-13: 3642846599

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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.