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Mathematical And Computational Methods In Photonics And Phononics
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Book Synopsis Mathematical and Computational Methods in Photonics and Phononics by : Habib Ammari
Download or read book Mathematical and Computational Methods in Photonics and Phononics written by Habib Ammari and published by American Mathematical Soc.. This book was released on 2018-10-15 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic metamaterials and metasurfaces. Throughout this book, the authors demonstrate the power of layer potential techniques for solving challenging problems in photonics and phononics when they are combined with asymptotic analysis. This book might be of interest to researchers and graduate students working in the fields of applied and computational mathematics, partial differential equations, electromagnetic theory, elasticity, integral equations, and inverse and optimal design problems in photonics and phononics.
Book Synopsis Mathematical and Computational Methods in Photonics and Phononics by : Habib Ammari
Download or read book Mathematical and Computational Methods in Photonics and Phononics written by Habib Ammari and published by . This book was released on 2018 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fields of photonics and phononics encompass the fundamental science of light and sound propagation and interactions in complex structures, as well as its technological applications. This book reviews new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods to address challenging problems in photonics and phononics. An emphasis is placed on analyzing sub-wavelength resonators, super-focusing and super-resolution of electromagnetic and acoustic waves, photonic and phononic crystals, electromagnetic cloaking, and electromagnetic and elastic me.
Book Synopsis Numerical Methods in Photonics by : Andrei V. Lavrinenko
Download or read book Numerical Methods in Photonics written by Andrei V. Lavrinenko and published by CRC Press. This book was released on 2018-09-03 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation and modeling using numerical methods is one of the key instruments in any scientific work. In the field of photonics, a wide range of numerical methods are used for studying both fundamental optics and applications such as design, development, and optimization of photonic components. Modeling is key for developing improved photonic devices and reducing development time and cost. Choosing the appropriate computational method for a photonics modeling problem requires a clear understanding of the pros and cons of the available numerical methods. Numerical Methods in Photonics presents six of the most frequently used methods: FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green’s function, and FEM. After an introductory chapter outlining the basics of Maxwell’s equations, the book includes self-contained chapters that focus on each of the methods. Each method is accompanied by a review of the mathematical principles in which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATLAB® is used throughout the text. This book provides a solid basis to practice writing your own codes. The theoretical formulation is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools.
Book Synopsis Mathematical Optics by : Vasudevan Lakshminarayanan
Download or read book Mathematical Optics written by Vasudevan Lakshminarayanan and published by CRC Press. This book was released on 2018-10-08 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics. Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics. Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers. Part VI introduces super-resolution imaging and differential geometric methods in image processing. As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book’s figures are available at www.crcpress.com.
Book Synopsis Applied Mathematical Problems in Geophysics by : Massimo Chiappini
Download or read book Applied Mathematical Problems in Geophysics written by Massimo Chiappini and published by Springer Nature. This book was released on 2022-07-23 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This CIME Series book provides mathematical and simulation tools to help resolve environmental hazard and security-related issues. The contributions reflect five major topics identified by the SIES (Strategic Initiatives for the Environment and Security) as having significant societal impact: optimal control in waste management, in particular the degradation of organic waste by an aerobic biomass, by means of a mathematical model; recent developments in the mathematical analysis of subwave resonators; conservation laws in continuum mechanics, including an elaboration on the notion of weak solutions and issues related to entropy criteria; the applications of variational methods to 1-dimensional boundary value problems, in particular to light ray-tracing in ionospheric physics; and the mathematical modelling of potential electromagnetic co-seismic events associated to large earthquakes. This material will provide a sound foundation for those who intend to approach similar problems from a multidisciplinary perspective.
Book Synopsis Recent Trends in Computational Photonics by : Arti Agrawal
Download or read book Recent Trends in Computational Photonics written by Arti Agrawal and published by Springer. This book was released on 2017-11-01 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the recent cutting-edge work on computational methods in photonics and their applications. The latest advances in techniques such as the Discontinuous Galerkin Time Domain method, Finite Element Time Domain method, Finite Difference Time Domain method as well as their applications are presented. Key aspects such as modelling of non-linear effects (Second Harmonic Generation, lasing in fibers, including gain nonlinearity in metamaterials), the acousto-optic effect, and the hydrodynamic model to explain electron response in nanoplasmonic structures are included. The application areas covered include plasmonics, metamaterials, photonic crystals, dielectric waveguides, fiber lasers. The chapters give a representative survey of the corresponding area.
Book Synopsis Analytical and Computational Methods in Scattering and Applied Mathematics by : Fadil Santosa
Download or read book Analytical and Computational Methods in Scattering and Applied Mathematics written by Fadil Santosa and published by CRC Press. This book was released on 2019-05-07 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Ralph Kleinman was director of the Center for the Mathematics of Waves and held the UNIDEL Professorship of the University of Delaware. Before his death in 1998, he made major scientific contributions in the areas of electromagnetic scattering, wave propagation, and inverse problems. He was instrumental in bringing together the mathematic
Book Synopsis Applied Analysis of Composite Media by : Piotr Drygas
Download or read book Applied Analysis of Composite Media written by Piotr Drygas and published by Woodhead Publishing. This book was released on 2019-11-05 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Analysis of Composite Media: Analytical and Computational Approaches presents formulas and techniques that can used to study 2D and 3D problems in composites and random porous media. The main strength of this book is its broad range of applications that illustrate how these techniques can be applied to investigate elasticity, viscous flow and bacterial motion in composite materials. In addition to paying attention to constructive computations, the authors have also included information on codes via a designated webpage. This book will be extremely useful for postgraduate students, academic researchers, mathematicians and industry professionals who are working in structured media. Provides a uniform, computational methodology that can be applied to the main classes of transport and elastic problems by using a combination of exact formulae, advanced simulations and asymptotic methods Includes critical phenomena in transport and elastic problems for composites and porous media Applies computational methodology to biological structures Presents computer protocols/algorithms that can be used for materials design
Book Synopsis Maximal Function Methods for Sobolev Spaces by : Juha Kinnunen
Download or read book Maximal Function Methods for Sobolev Spaces written by Juha Kinnunen and published by American Mathematical Soc.. This book was released on 2021-08-02 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
Book Synopsis Maxwell’s Equations in Periodic Structures by : Gang Bao
Download or read book Maxwell’s Equations in Periodic Structures written by Gang Bao and published by Springer Nature. This book was released on 2021-11-22 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Algorithms for Number Theory: Using Pari/GP by : Karim Belabas
Download or read book Numerical Algorithms for Number Theory: Using Pari/GP written by Karim Belabas and published by American Mathematical Soc.. This book was released on 2021-06-23 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex L L-functions. For each task, many algorithms are presented, such as Gaussian and doubly-exponential integration, Euler-MacLaurin, Abel-Plana, Lagrange, and Monien summation. Each algorithm is given in detail, together with a complete implementation in the free Pari/GP system. These implementations serve both to make even more precise the inner workings of the algorithms, and to gently introduce advanced features of the Pari/GP language. This book will be appreciated by anyone interested in number theory, specifically in practical implementations, computer experiments and numerical algorithms that can be scaled to produce thousands of digits of accuracy.
Book Synopsis Diagrammatic Algebra by : J. Scott Carter
Download or read book Diagrammatic Algebra written by J. Scott Carter and published by American Mathematical Society. This book was released on 2021-12-15 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.
Book Synopsis Asymptotic Geometric Analysis, Part II by : Shiri Artstein-Avidan
Download or read book Asymptotic Geometric Analysis, Part II written by Shiri Artstein-Avidan and published by American Mathematical Society. This book was released on 2021-12-13 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a continuation of Asymptotic Geometric Analysis, Part I, which was published as volume 202 in this series. Asymptotic geometric analysis studies properties of geometric objects, such as normed spaces, convex bodies, or convex functions, when the dimensions of these objects increase to infinity. The asymptotic approach reveals many very novel phenomena which influence other fields in mathematics, especially where a large data set is of main concern, or a number of parameters which becomes uncontrollably large. One of the important features of this new theory is in developing tools which allow studying high parametric families. Among the topics covered in the book are measure concentration, isoperimetric constants of log-concave measures, thin-shell estimates, stochastic localization, the geometry of Gaussian measures, volume inequalities for convex bodies, local theory of Banach spaces, type and cotype, the Banach-Mazur compactum, symmetrizations, restricted invertibility, and functional versions of geometric notions and inequalities.
Book Synopsis Perverse Sheaves and Applications to Representation Theory by : Pramod N. Achar
Download or read book Perverse Sheaves and Applications to Representation Theory written by Pramod N. Achar and published by American Mathematical Soc.. This book was released on 2021-09-27 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.
Book Synopsis Hopf Algebras and Galois Module Theory by : Lindsay N. Childs
Download or read book Hopf Algebras and Galois Module Theory written by Lindsay N. Childs and published by American Mathematical Soc.. This book was released on 2021-11-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.
Book Synopsis Maximal Cohen–Macaulay Modules and Tate Cohomology by : Ragnar-Olaf Buchweitz
Download or read book Maximal Cohen–Macaulay Modules and Tate Cohomology written by Ragnar-Olaf Buchweitz and published by American Mathematical Society. This book was released on 2021-12-16 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.
Book Synopsis Ridge Functions and Applications in Neural Networks by : Vugar E. Ismailov
Download or read book Ridge Functions and Applications in Neural Networks written by Vugar E. Ismailov and published by American Mathematical Society. This book was released on 2021-12-17 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.
