Mathematical And Computational Methods In Photonics And Phononics

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Mathematical and Computational Methods in Photonics and Phononics

Habib Ammari,Brian Fitzpatrick,Hyeonbae Kang,Matias Ruiz,Sanghyeon Yu,Hai Zhang
Mathematical and Computational Methods in Photonics and Phononics Book PDF

Author : Habib Ammari,Brian Fitzpatrick,Hyeonbae Kang,Matias Ruiz,Sanghyeon Yu,Hai Zhang
Publisher : American Mathematical Soc.
Page : 509 pages
File Size : 41,8 Mb
Release : 2018-10-15
Category : Photonics
ISBN : 9781470448004

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Mathematical and Computational Methods in Photonics and Phononics by Habib Ammari,Brian Fitzpatrick,Hyeonbae Kang,Matias Ruiz,Sanghyeon Yu,Hai Zhang Pdf

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.

Mathematical and Computational Methods in Photonics and Phononics

Habib Ammari
Mathematical and Computational Methods in Photonics and Phononics Book PDF

Author : Habib Ammari
Publisher : Unknown
Page : 522 pages
File Size : 52,8 Mb
Release : 2018
Category : Electronic
ISBN : 1470449099

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Mathematical and Computational Methods in Photonics and Phononics by Habib Ammari Pdf

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.

Numerical Methods in Photonics

Andrei V. Lavrinenko,Jesper Lægsgaard,Niels Gregersen,Frank Schmidt,Thomas Søndergaard
Numerical Methods in Photonics Book PDF

Author : Andrei V. Lavrinenko,Jesper Lægsgaard,Niels Gregersen,Frank Schmidt,Thomas Søndergaard
Publisher : CRC Press
Page : 362 pages
File Size : 53,7 Mb
Release : 2018-09-03
Category : Science
ISBN : 9781466563896

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Numerical Methods in Photonics by Andrei V. Lavrinenko,Jesper Lægsgaard,Niels Gregersen,Frank Schmidt,Thomas Søndergaard Pdf

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.

Mathematical Optics

Vasudevan Lakshminarayanan,María L. Calvo,Tatiana Alieva
Mathematical Optics Book PDF

Author : Vasudevan Lakshminarayanan,María L. Calvo,Tatiana Alieva
Publisher : CRC Press
Page : 630 pages
File Size : 49,8 Mb
Release : 2018-10-08
Category : Science
ISBN : 9781439869611

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Mathematical Optics by Vasudevan Lakshminarayanan,María L. Calvo,Tatiana Alieva Pdf

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.

Applied Mathematical Problems in Geophysics

Massimo Chiappini,Vincenzo Vespri
Applied Mathematical Problems in Geophysics Book PDF

Author : Massimo Chiappini,Vincenzo Vespri
Publisher : Springer Nature
Page : 211 pages
File Size : 52,8 Mb
Release : 2022-07-23
Category : Mathematics
ISBN : 9783031053214

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Applied Mathematical Problems in Geophysics by Massimo Chiappini,Vincenzo Vespri Pdf

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.

Applied Analysis of Composite Media

Piotr Drygas,Simon Gluzman,Vladimir Mityushev,Wojciech Nawalaniec
Applied Analysis of Composite Media Book PDF

Author : Piotr Drygas,Simon Gluzman,Vladimir Mityushev,Wojciech Nawalaniec
Publisher : Woodhead Publishing
Page : 372 pages
File Size : 44,9 Mb
Release : 2019-11-05
Category : Computers
ISBN : 9780081026700

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Applied Analysis of Composite Media by Piotr Drygas,Simon Gluzman,Vladimir Mityushev,Wojciech Nawalaniec Pdf

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

Analytical and Computational Methods in Scattering and Applied Mathematics

Fadil Santosa,Ivar Stakgold
Analytical and Computational Methods in Scattering and Applied Mathematics Book PDF

Author : Fadil Santosa,Ivar Stakgold
Publisher : CRC Press
Page : 292 pages
File Size : 42,9 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9780429525087

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Analytical and Computational Methods in Scattering and Applied Mathematics by Fadil Santosa,Ivar Stakgold Pdf

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

Maximal Function Methods for Sobolev Spaces

Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Maximal Function Methods for Sobolev Spaces Book PDF

Author : Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 40,7 Mb
Release : 2021-08-02
Category : Education
ISBN : 9781470465759

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Maximal Function Methods for Sobolev Spaces by Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas Pdf

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.

Maxwell’s Equations in Periodic Structures

Gang Bao,Peijun Li
Maxwell s Equations in Periodic Structures Book PDF

Author : Gang Bao,Peijun Li
Publisher : Springer Nature
Page : 361 pages
File Size : 50,5 Mb
Release : 2021-11-22
Category : Mathematics
ISBN : 9789811600616

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Maxwell’s Equations in Periodic Structures by Gang Bao,Peijun Li Pdf

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.

Numerical Algorithms for Number Theory: Using Pari/GP

Karim Belabas,Henri Cohen
Numerical Algorithms for Number Theory Using Pari GP Book PDF

Author : Karim Belabas,Henri Cohen
Publisher : American Mathematical Soc.
Page : 429 pages
File Size : 40,5 Mb
Release : 2021-06-23
Category : Education
ISBN : 9781470463519

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Numerical Algorithms for Number Theory: Using Pari/GP by Karim Belabas,Henri Cohen Pdf

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.

Diagrammatic Algebra

J. Scott Carter,Seiichi Kamada
Diagrammatic Algebra Book PDF

Author : J. Scott Carter,Seiichi Kamada
Publisher : American Mathematical Society
Page : 365 pages
File Size : 44,9 Mb
Release : 2021-12-15
Category : Mathematics
ISBN : 9781470466718

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Diagrammatic Algebra by J. Scott Carter,Seiichi Kamada Pdf

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.

Asymptotic Geometric Analysis, Part II

Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman
Asymptotic Geometric Analysis Part II Book PDF

Author : Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman
Publisher : American Mathematical Society
Page : 645 pages
File Size : 48,8 Mb
Release : 2021-12-13
Category : Mathematics
ISBN : 9781470463601

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Asymptotic Geometric Analysis, Part II by Shiri Artstein-Avidan,Apostolos Giannopoulos,Vitali D. Milman Pdf

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.

Perverse Sheaves and Applications to Representation Theory

Pramod N. Achar
Perverse Sheaves and Applications to Representation Theory Book PDF

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 49,9 Mb
Release : 2021-09-27
Category : Education
ISBN : 9781470455972

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Perverse Sheaves and Applications to Representation Theory by Pramod N. Achar Pdf

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.

Hopf Algebras and Galois Module Theory

Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood
Hopf Algebras and Galois Module Theory Book PDF

Author : Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 52,6 Mb
Release : 2021-11-10
Category : Education
ISBN : 9781470465162

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Hopf Algebras and Galois Module Theory by Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood Pdf

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.

Maximal Cohen–Macaulay Modules and Tate Cohomology

Ragnar-Olaf Buchweitz
Maximal Cohen Macaulay Modules and Tate Cohomology Book PDF

Author : Ragnar-Olaf Buchweitz
Publisher : American Mathematical Society
Page : 175 pages
File Size : 50,7 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781470453404

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Maximal Cohen–Macaulay Modules and Tate Cohomology by Ragnar-Olaf Buchweitz Pdf

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.