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The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems. This book provides some recent advances in the investigation of numerical approximations of the stochastic Maxwell equations via structure-preserving algorithms. It presents an accessible overview of the construction and analysis of structure-preserving algorithms with an emphasis on the preservation of geometric structures, physical properties, and asymptotic behaviors of the stochastic Maxwell equations. A friendly introduction to the simulation of the stochastic Maxwell equations with some structure-preserving algorithms is provided using MATLAB for the reader’s convenience. The objects considered in this book are related to several fascinating mathematical fields: numerical analysis, stochastic analysis, (multi-)symplectic geometry, large deviations principle, ergodic theory, partial differential equation, probability theory, etc. This book will appeal to researchers who are interested in these topics.

Numerical analysis. --- Probabilities. --- Differential equations. --- Numerical Analysis. --- Probability Theory. --- Differential Equations. --- Equacions de Maxwell

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This book explores generalized Lorenz–Mie theories when the illuminating beam is an electromagnetic arbitrary shaped beam relying on the method of separation of variables. Although it particularly focuses on the homogeneous sphere, the book also considers other regular particles. It discusses in detail the methods available for evaluating beam shape coefficients describing the illuminating beam. In addition it features applications used in many fields such as optical particle sizing and, more generally, optical particle characterization, morphology-dependent resonances and the mechanical effects of light for optical trapping, optical tweezers and optical stretchers. Furthermore, it provides various computer programs relevant to the content. In the last years many new developments took place so that a new edition became necessary. This new book now incorporates solutions for many more particle shapes and morphologies, various kinds of illuminating beams, and also to mechanical effects of light, whispering-gallery modes and resonances, and optical particle characterization techniques. In addition, the new book considers localized approximations, on the renewal of the finite series technique, on a new categorization of optical forces, and the study of Bessel beams, Mathieu beams, Laguerre-Gauss beams, frozen waves.

Topological groups. --- Lie groups. --- Fluid mechanics. --- Electrodynamics. --- Telecommunication. --- Topological Groups and Lie Groups. --- Engineering Fluid Dynamics. --- Classical Electrodynamics. --- Microwaves, RF Engineering and Optical Communications. --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Communication --- Information theory --- Telecommuting --- Dynamics --- Hydromechanics --- Continuum mechanics --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Electrodinàmica --- Mecànica de fluids --- Equacions de Maxwell

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Differential equations, Partial. --- Partial differential equations --- Equacions en derivades parcials --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Karman --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica) --- Equacions de Von Kármán

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Equacions en derivades parcials --- Differential equations, Partial. --- Partial differential equations --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Kármán --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica)

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Mathematical analysis. --- Equacions en derivades parcials --- EDPs --- Equació diferencial en derivades parcials --- Equacions diferencials en derivades parcials --- Equacions diferencials parcials --- Equacions diferencials --- Dispersió (Matemàtica) --- Equació d'ona --- Equació de Dirac --- Equació de Fokker-Planck --- Equació de Schrödinger --- Equacions de Navier-Stokes --- Equacions de Hamilton-Jacobi --- Equacions de Maxwell --- Equacions de Monge-Ampère --- Equacions de Von Kármán --- Equacions diferencials el·líptiques --- Equacions diferencials hiperbòliques --- Equacions diferencials parabòliques --- Equacions diferencials parcials estocàstiques --- Funcions harmòniques --- Laplacià --- Problema de Cauchy --- Problema de Neumann --- Teoria espectral (Matemàtica) --- 517.1 Mathematical analysis --- Mathematical analysis