Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics - G. F. Roach, I. G. Stratis, A. N. Yannacopoulos

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics (eBook)

G. F. Roach, I. G. Stratis, A. N. Yannacopoulos (Autoren)

eBook Download: EPUB

2012
400 Seiten
Princeton University Press (Verlag)
978-1-4008-4265-0 (ISBN)

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

G. F. Roach is professor emeritus in the Department of Mathematics and Statistics at the University of Strathclyde. I. G. Stratis is professor in the Department of Mathematics at the National and Kapodistrian University, Athens. A. N. Yannacopoulos is professor in the Department of Statistics at the Athens University of Economics and Business.

Erscheint lt. Verlag	4.3.2012
Reihe/Serie	Princeton Series in Applied Mathematics
Reihe/Serie	Princeton Series in Applied Mathematics
Verlagsort	Princeton
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Chemie ► Physikalische Chemie
	Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik
	Technik ► Elektrotechnik / Energietechnik
Schlagworte	Addition • Applied mathematics • Approximation • A priori estimate • asymptotic expansion • AtkinsonЗilcox expansion theorem • auxiliary elliptic problems • backward stochastic evolution equations • Banach space • Basis (linear algebra) • Beltrami fields • bilinear form • Bochner integral • boundary controllability • boundary integral equation • Boundary value problem • Calculation • chirality • chiral material • Chiral Media • coefficient • combination • compact embeddings • Compact operator • Compact space • complex electromagnetic media • complex media • constitutive relations • Controllability • controllability problem • convolution • Decompositions • Derivative • Differentiable function • differential equation • Differential Equations • Differential operator • Dimension (vector space) • Directional derivative • dispersive media • Divergence Theorem • dyadics • Eigenfunction • eigenvalue problems • Eigenvalues and Eigenvectors • Electrical Engineering • Electric Field • electric flux density • electromagnetic complex media • Electromagnetic field • Electromagnetic fields • electromagnetic media • Electromagnetic radiation • electromagnetics • electromagnetic waves • electromagnetic wave scattering • electromagnetism • elliptic operator • Embedding • Equation • Ergodicity • estimation • Euclidean Vector • evolution family approach • evolution operators • evolution problems • existential quantification • exterior problems • Exterior (topology) • Faedo-Galerkin approach • finite-dimensional approximation • finite-dimensional space • Finite Element Method • Fixed point approach • Fourier transform • Frequency • frequency domain • function space • function spaces • generalised integral transforms • general scattering theorem • Geometry • handedness • Helmholtz equation • Herglotz wave functions • Hermitian adjoint • hilbert space • Hilbert Uniqueness method • homogenisation • homogenisation problem • homogenised media • homogenised system • infinite Frchet differentiability • Initial Condition • Initial Value Problem • integral equation • integral transform • integro-differential equation • integrodifferential equations • integrodifferential evolution equation • interior domain problem • inverse problem • Laplace transform • Lebesgue measure • Linear combination • Linearity • Linear map • magnetic flux density • Mathematical Analysis • Mathematical Modelling • Mathematical Optimization • Mathematical Theory • Maxwell Equations • Maxwell operator • Maxwell's equations • nonlinearity • Nonlinear Model • nonlinear PDEs • nonlinear phenomena • Nonlinear problems • nonlinear system • Notation • Numerical analysis • operators • Optical Theorem • optimal control • Parameter • partial differential equation • PDEs • penetrable obstacle • Perfect conductor • perfectly conducting obstacle • Periodic Media • Physics • plane electromagnetic waves • Polarization (waves) • polynomial • probability measure • Probability space • Prolegomena to Any Future Metaphysics • Quantity • random bianisotropic media • random coefficients • random complex electromagnetic media • random complex medium • Random field • Random Variable • reciprocity principle • scattering • scattering problems • scattering process • scattering theories • scattering theory • scientific notation • Self-adjoint operator • Semigroup • semigroup approach • semigroup arguments • semigroup-based approach • Sobolev Space • solvability • Spaces • Special case • spectral theory • standard differential • Stochastic Calculus • stochastic complex electromagnetic media • stochastic integrodifferential equations • Stochasticity • Stochastic process • subsequence • Subset • Summation • Surface integral • Theorem • theory • Time • time domain • time-harmonic electromagnetic wave • time-harmonic problems • Trace operator • trace operators • two-scale approach • two-scale expansion • Unit vector • Variable (mathematics) • variational formulation • Vector analysis • Vector field • wave equation • wave function • Wave Motions • wavenumber • Wave operators • Weak convergence (Hilbert space) • Weak formulation • well posedness • Wiener chaos approach • Wiener process • Without loss of generality
ISBN-10	1-4008-4265-4 / 1400842654
ISBN-13	978-1-4008-4265-0 / 9781400842650

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