Maxwells Equations In A Periodic Structure
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| Author | : Gang Bao |
| Publisher | : Springer Nature |
| Total Pages | : 361 |
| Release | : 2021-11-22 |
| Genre | : Mathematics |
| ISBN | : 9811600619 |
This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell’s equations in periodic structures. The fundamental importance of the fields is clear, since they are related to technology with significant applications in optics and electromagnetics. The book provides both introductory materials and in-depth discussion to the areas in diffractive optics that offer rich and challenging mathematical problems. It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics, and engineering disciplines as well.
| Author | : Alain Bensoussan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 410 |
| Release | : 2011-10-26 |
| Genre | : Mathematics |
| ISBN | : 0821853244 |
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.
| Author | : Avner Friedman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461384540 |
This is the seventh volume in the series "Mathematics in Industrial Prob lems. " The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level;" that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on the seminar presentations and on questions raised in subse quent discussions. Each chapter is devoted to one of the talks and is self contained. The chapters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in previous volumes, as well as references to papers in which such solutions have been published. The speakers in the Seminar on Industrial Problems have given us at the IMA hours of delight and discovery. My thanks to David K. Lambert (Gen eral Motors Research and Development), David S.
| Author | : Jean-Claude Nedelec |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 356 |
| Release | : 2001-03-30 |
| Genre | : Computers |
| ISBN | : 9780387951553 |
Acoustic and electromagnetic waves underlie a range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. This book, written by an international researcher, presents some of the research in a complete way. It is useful for graduate students in mathematics, physics, and engineering.
| Author | : Ivan Graham |
| Publisher | : Walter de Gruyter |
| Total Pages | : 328 |
| Release | : 2013-10-14 |
| Genre | : Mathematics |
| ISBN | : 3110282283 |
This book is the third volume of three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" taking place in Linz, Austria, October 3-7, 2011. This book surveys recent developments in the analysis of wave propagation problems. The topics covered include aspects of the forward problem and problems in inverse problems, as well as applications in the earth sciences. Wave propagation problems are ubiquitous in environmental applications such as seismic analysis, acoustic and electromagnetic scattering. The design of efficient numerical methods for the forward problem, in which the scattered field is computed from known geometric configurations is very challenging due to the multiscale nature of the problems. Even more challenging are inverse problems where material parameters and configurations have to be determined from measurements in conjunction with the forward problem. This book contains review articles covering several state-of-the-art numerical methods for both forward and inverse problems. This collection of survey articles focusses on the efficient computation of wave propagation and scattering is a core problem in numerical mathematics, which is currently of great research interest and is central to many applications in energy and the environment. Two generic applications which resonate strongly with the central aims of the Radon Special Semester 2011 are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements, and as a component in larger weather/climate prediction models in numerical weather forecasting. As an example of the second application, inverse problems in wave propagation in heterogeneous media arise in the problem of imaging the subsurface below land or marine deposits. The book records the achievements of Workshop 3 "Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment". It brings together key numerical mathematicians whose interest is in the analysis and computation of wave propagation and scattering problems, and in inverse problems, together with practitioners from engineering and industry whose interest is in the applications of these core problems.
| Author | : Heinrich G. W. Begehr |
| Publisher | : World Scientific |
| Total Pages | : 1557 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 981238572X |
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
| Author | : Heinrich G W Begehr |
| Publisher | : World Scientific |
| Total Pages | : 1557 |
| Release | : 2003-08-04 |
| Genre | : Mathematics |
| ISBN | : 9814485233 |
The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
| Author | : K.-H. Hoffmann |
| Publisher | : Birkhäuser |
| Total Pages | : 290 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034881487 |
Interest in the area of control of systems defined by partial differential Equations has increased strongly in recent years. A major reason has been the requirement of these systems for sensible continuum mechanical modelling and optimization or control techniques which account for typical physical phenomena. Particular examples of problems on which substantial progress has been made are the control and stabilization of mechatronic structures, the control of growth of thin films and crystals, the control of Laser and semi-conductor devices, and shape optimization problems for turbomachine blades, shells, smart materials and microdiffractive optics. This volume contains original articles by world reknowned experts in the fields of optimal control of partial differential equations, shape optimization, numerical methods for partial differential equations and fluid dynamics, all of whom have contributed to the analysis and solution of many of the problems discussed. The collection provides a state-of-the-art overview of the most challenging and exciting recent developments in the field. It is geared towards postgraduate students and researchers dealing with the theoretical and practical aspects of a wide variety of high technology problems in applied mathematics, fluid control, optimal design, and computer modelling.
| Author | : Gang Bao |
| Publisher | : SIAM |
| Total Pages | : 349 |
| Release | : 2001-01-01 |
| Genre | : Science |
| ISBN | : 9780898717594 |
This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.
| Author | : Siegfried Janz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 304 |
| Release | : 2006-01-12 |
| Genre | : Technology & Engineering |
| ISBN | : 9781402041655 |
The contributions to this book constitute an excellent record of many key issues and scientific problems in planar lightwave circuit research. There are detailed overviews of experimental and theoretical work in high index contrast waveguide systems, micro-optical resonators, nonlinear optics, and advanced optical simulation methods, as well as articles describing emerging applications of integrated optics for medical and biological applications.
