Mathematical And Computational Methods In Photonics And Phononics
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Mathematical And Computational Methods In Photonics And Phononics
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Author : Habib Ammari
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-10-15
Mathematical And Computational Methods In Photonics And Phononics written by Habib Ammari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-15 with Mathematics categories.
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 Methods In Liquid Crystal Optics And Lens Design
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Author : Eric Stachura
language : en
Publisher: Springer Nature
Release Date : 2024-08-20
Mathematical Methods In Liquid Crystal Optics And Lens Design written by Eric Stachura and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-20 with Mathematics categories.
Freeform lens design has numerous applications in imaging, aerospace, and biomedicine. Due to recent advancements in precision cutting and grinding, the manufacturing of freeform optical lenses with very high precision is now possible. However, there is still a significant lack of mathematical literature on the subject, and essentially none related to liquid crystals. Liquid crystals are appealing for use in imaging due to their flexibility and unique electro-optical properties. This book fills a gap in mathematical literature and attracts focus to liquid crystals for freeform lens design. It provides a rigorous mathematical perspective on liquid crystal optics, focusing on ray tracing in the geometric optics regime. A mathematical foundation is set to study lens design and ray tracing problems in liquid crystals. Additionally, it addresses absolute instruments, which are devices that image without any optical aberrations. These instruments cannot be designed through transformation optics, and until recently, only a handful of examples were known. Mathematically, this is a largely untapped area of research, yet the applications are profound. Finally, the book describes several open directions, revealing the richness of the intersection of liquid crystal optics and mathematical analysis. The content of this book will prove invaluable for researchers of mathematical optics as well as those interested in liquid crystal theory, in addition to those mathematics graduate students aiming to understand the physical basis of light propagation in liquid crystals
Applied Analysis Of Composite Media
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Author : Piotr Drygas
language : en
Publisher: Woodhead Publishing
Release Date : 2019-10-22
Applied Analysis Of Composite Media written by Piotr Drygas and has been published by Woodhead Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-22 with Computers categories.
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.
Metamaterial Analysis And Design
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Author : Habib Ammari
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-11-06
Metamaterial Analysis And Design written by Habib Ammari and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-06 with Mathematics categories.
Metamaterials are advanced composite materials which have exotic and powerful properties. Their complicated microstructures make metamaterials challenging to model, requiring the use of sophisticated mathematical techniques. This book uses a from-first-principles approach (based on boundary integral methods and asymptotic analysis) to study a class of high-contrast metamaterials. These mathematical techniques are applied to the problem of designing graded metamaterials that replicate the function of the cochlea.
Maximal Function Methods For Sobolev Spaces
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Author : Juha Kinnunen
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-02
Maximal Function Methods For Sobolev Spaces written by Juha Kinnunen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-02 with Education categories.
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.
Numerical Algorithms For Number Theory Using Pari Gp
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Author : Karim Belabas
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-23
Numerical Algorithms For Number Theory Using Pari Gp written by Karim Belabas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-23 with Education categories.
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
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Author : J. Scott Carter
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-15
Diagrammatic Algebra written by J. Scott Carter and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-15 with Mathematics categories.
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.
Hopf Algebras And Galois Module Theory
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Author : Lindsay N. Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-11-10
Hopf Algebras And Galois Module Theory written by Lindsay N. Childs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-10 with Education categories.
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.
Perverse Sheaves And Applications To Representation Theory
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Author : Pramod N. Achar
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-27
Perverse Sheaves And Applications To Representation Theory written by Pramod N. Achar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-27 with Education categories.
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.
Asymptotic Geometric Analysis Part Ii
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Author : Shiri Artstein-Avidan
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-13
Asymptotic Geometric Analysis Part Ii written by Shiri Artstein-Avidan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-13 with Mathematics categories.
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.