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A Scattering
In Highland Scotland in 1850, Catriona lives life to the rhythm of seasons and Gaelic songs, until a dramatic change of circumstance forces her to fight for everyone and everything she loves. Years later Rose, an artist, trying to make sense of her fractured family and her own restlessness, searches among the ruins of a deserted landscape.Does the answer lie in the injustices of the past?Set on a remote Scottish hillside, during the Highland Clearances, A Scattering follows Rose and Catriona, who are from different centuries, but share a secret and a common enemy. Interweaving the story of a crofting community with a rich Gaelic culture, and one set in present-day Scotland, it explores the effect the clearances had not only on the people and culture but also on later generations, until one woman finds a way to break the cycle.
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A Scattering and Anniversary
A Scattering and Anniversary
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A Scattering of Blue Light
A Scattering of Blue Light
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Maxwell Equation: Inverse Scattering In Electromagnetism
How can one determine the physical properties of the medium or the geometrical properties of the domain by observing electromagnetic waves?To answer this fundamental problem in mathematics and physics, this book leads the reader to the frontier of inverse scattering theory for electromagnetism.The first three chapters, written comprehensively, can be used as a textbook for undergraduate students.Beginning with elementary vector calculus, this book provides fundamental results for wave equations and Helmholtz equations, and summarizes the potential theory.It also explains the cohomology theory in an easy and straightforward way, which is an essential part of electromagnetism related to geometry.It then describes the scattering theory for the Maxwell equation by the time-dependent method and also by the stationary method in a concise, but almost self-contained manner.Based on these preliminary results, the book proceeds to the inverse problem for the Maxwell equation.The chapters for the potential theory and elementary cohomology theory are good introduction to graduate students.The results in the last chapter on the inverse scattering for the medium and the determination of Betti numbers are new, and will give a current scope for the inverse spectral problem on non-compact manifolds.It will be useful for young researchers who are interested in this field and trying to find new problems.
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Scattering of Waves : Theory and Applications
Scattering of waves from material objects and abstract potentials is a large part of modern mathematical physics with wide applications from geophysics and medical imaging to relatively recent near-field physics and technology making almost unrestricted imaging resolution possible.These have led to profound advancements in scattering and inverse scattering theories.Scattering of Waves: Theory and Applications explores the underlying concepts, physics and mathematics of wave scattering and wave field structures and self-consistently introduces a range of topics in scalar acoustics and quantum and vector electromagnetic scattering. Features:A unified and comprehensive presentation of Laplace, Poisson, Helmholtz and wave equations, d'Alembert's solution, Poisson's spherical means, Hadamard's method of descent and the equations of Euler-Poisson-Darboux and Kirchoff, their revealing physical imports and connections with Huygen's principle.Also included are Maxwell's equations, gauges, energy and momentum conservations. A concise introduction to the concepts of domain differentiation, angular spectrum, principal volume and cavity definition used in the derivations. Extensive treatments of Green's functions and tensors, delta derivatives, transverse delta function, point approximation of electromagnetic Green's tensor, distributional calculations of the mixed derivatives of scalar Green's function and the depolarizing dyadic. An in-depth presentation of the integral method in scattering and the Huygen-Fresnel, Fresnel-Kirchoff and Helmholtz integral representations of the scattered fields.Also provided a comprehensive historical antecedents alongside modern quantitative development. Extensive discussions of time dependent and stationary formal scattering theory; resolvent, Green and wave operators, S and T matrices; detailed compilations of numerous operator relations and identities; scattering amplitude; its properties and Fourier transform relation with T-matrix. Detailed derivations of the optical theorem; field equivalence principles; physics and mathematics of evanescent waves and near-field implications of the derived expressions. Expressions are mostly derived explicitly and whenever possible, from more than a single perspective. Often, there arise controversies among experts on some derivations and interpretations.These are brought out whenever they appear for the reader to form his or her own opinion. Primarily aimed at advanced students of physics, engineering and applied mathematics, this text will also be valuable to researchers and faculties in electromagnetics, acoustics and quantum mechanics.
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Scattering Amplitudes in Quantum Field Theory
This open access book bridges a gap between introductory Quantum Field Theory (QFT) courses and state-of-the-art research in scattering amplitudes.It covers the path from basic definitions of QFT to amplitudes, which are relevant for processes in the Standard Model of particle physics.The book begins with a concise yet self-contained introduction to QFT, including perturbative quantum gravity.It then presents modern methods for calculating scattering amplitudes, focusing on tree-level amplitudes, loop-level integrands and loop integration techniques.These methods help to reveal intriguing relations between gauge and gravity amplitudes and are of increasing importance for obtaining high-precision predictions for collider experiments, such as those at the Large Hadron Collider, as well as for foundational mathematical physics studies in QFT, including recent applications to gravitational wave physics.These course-tested lecture notes include numerous exercises with solutions.Requiring only minimal knowledge of QFT, they are well-suited for MSc and PhD students as a preparation for research projects in theoretical particle physics.They can be used as a one-semester graduate level course, or as a self-study guide for researchers interested in fundamental aspects of quantum field theory.
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Brillouin Scattering Part 2 : Volume 110
Brillouin Scattering, Part Two, Volume 110 in the Semiconductors and Semimetal series, marks the centenary of Leon Brillouin’s seminal 1922 paper which provided a detailed theory on the effect that now bears his name. Sections in this new release include Optical Fiber Sensors Based on Stimulated Brillouin scattering, Brillouin-based RF frequency sources, SBS for Microwave Photonics (MWP), Engineerable Brillouin processes for integrated photonics, SBS in optical communication systems - the good, the bad and the ugly, Slow light, dynamic gratings and light storage, Non-reciprocity in Brillouin scattering, Electromechanical Brillouin Scattering, and Brillouin light scattering for studying mechanics of biological systems. Stimulated Brillouin Scattering (SBS) is the strongest third order nonlinearity and plays an important role in contemporary science and applications, particularly lasers, communications, fiber optics and basic physics.This volume provides different perspectives on current technological contexts of SBS in a range of different application areas, including sensing, communications, radar, imaging and information storage.
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Inverse Acoustic and Electromagnetic Scattering Theory
The inverse scattering problem is central to many areas of science and technology such as radar, sonar, medical imaging, geophysical exploration and nondestructive testing.This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves.In this fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions.Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added.
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