Photonic Crystals Mathematical Analysis And Numerical Approximation
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Photonic Crystals Mathematical Analysis And Numerical Approximation
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Author : Willy Dörfler
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-18
Photonic Crystals Mathematical Analysis And Numerical Approximation written by Willy Dörfler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-18 with Mathematics categories.
This book concentrates on the mathematics of photonic crystals, which form an important class of physical structures investigated in nanotechnology. Photonic crystals are materials which are composed of two or more different dielectrics or metals, and which exhibit a spatially periodic structure, typically at the length scale of hundred nanometers. In the mathematical analysis and the numerical simulation of the partial differential equations describing nanostructures, several mathematical difficulties arise, e. g., the appropriate treatment of nonlinearities, simultaneous occurrence of continuous and discrete spectrum, multiple scales in space and time, and the ill-posedness of these problems. This volume collects a series of lectures which introduce into the mathematical background needed for the modeling and simulation of light, in particular in periodic media, and for its applications in optical devices.
Mathematical Modeling In Optical Science
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Author : Gang Bao
language : en
Publisher: SIAM
Release Date : 2001-01-01
Mathematical Modeling In Optical Science written by Gang Bao and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Science categories.
This volume addresses recent developments in mathematical modeling in three areas of optical science: diffractive optics, photonic band gap structures, and waveguides. Particular emphasis is on the formulation of mathematical models and the design and analysis of new computational approaches. The book contains cutting-edge discourses on emerging technology in optics that provides significant challenges and opportunities for applied mathematicians, researchers, and engineers.
The Holodeck
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Author : Michael Cloran
language : en
Publisher: Xlibris Corporation
Release Date : 2020-02-07
The Holodeck written by Michael Cloran and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-07 with Science categories.
This book is about a requirements specification for a Holodeck at a proof of concept level. In it I introduce optical functions for a optical processor and describe how they map to a subset of the Risc-V open instruction set. I describe how parallelism could be achieved. I then describe a possible layered approach to an optical processor motherboard for the datacenter and for a personal Holodeck. I describe Volumetrics in brief and show how its evolution to Holodeck volumetrics could be done with bend light technology and the possibility of solidness to touch. I describe in detail the architecture of a Holodeck covering several approaches to Holodecks from static scene to scrolling scene to multi-user same complex to networked multi-user Holodecks.
Advanced Studies In Nonlinear Dynamical Systems
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Author : Dumitru Baleanu
language : en
Publisher: Springer Nature
Release Date : 2025-05-06
Advanced Studies In Nonlinear Dynamical Systems written by Dumitru Baleanu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-06 with Science categories.
This book is a compilation of select chapter from the 2023 International Conference on Nonlinear Science and Complexity. It presents recent advancements, discoveries, and ongoing research in various facets of nonlinear science and complexity. The book covers a broad scope of topics, including nonlinear dynamical systems, complex systems, quantum sensing, and mathematical approaches in biological and economic models. Key subspecialties addressed include nonlinear differential equations, modeling of nonlinear processes in diverse fields such as biology and economics, and innovative computational techniques. Each chapter contributes unique insights into its respective field, providing theoretical analyses, practical applications, and numerical simulations to advance the understanding of complex nonlinear phenomena.
Mixed Finite Element Methods And Applications
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Author : Daniele Boffi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-02
Mixed Finite Element Methods And Applications written by Daniele Boffi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.
Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.
Numerical Approximations Of Stochastic Maxwell Equations
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Author : Chuchu Chen
language : en
Publisher: Springer Nature
Release Date : 2024-01-04
Numerical Approximations Of Stochastic Maxwell Equations written by Chuchu Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-04 with Mathematics categories.
The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems. This book provides some recent advances in the investigation of numerical approximations of the stochastic Maxwell equations via structure-preserving algorithms. It presents an accessible overview of the construction and analysis of structure-preserving algorithms with an emphasis on the preservation of geometric structures, physical properties, and asymptotic behaviors of the stochastic Maxwell equations. A friendly introduction to the simulation of the stochastic Maxwell equations with some structure-preserving algorithms is provided using MATLAB for the reader’s convenience. The objects considered in this book are related to several fascinating mathematical fields: numerical analysis, stochastic analysis, (multi-)symplectic geometry, large deviations principle, ergodic theory, partial differential equation, probability theory, etc. This book will appeal to researchers who are interested in these topics.
Photonic Crystals
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Author : John D. Joannopoulos
language : en
Publisher: Princeton University Press
Release Date : 2011-10-30
Photonic Crystals written by John D. Joannopoulos and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-30 with Science categories.
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers. Extensively revised and expanded Features improved graphics throughout Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding Provides an introduction to coupled-mode theory as a powerful tool for device design Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.
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.
Advances In Photonic Crystals
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Author : Vittorio Passaro
language : en
Publisher: BoD – Books on Demand
Release Date : 2013-02-13
Advances In Photonic Crystals written by Vittorio Passaro and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-13 with Technology & Engineering categories.
This book collects chapters on different theoretical and experimental aspects of photonics crystals for Nanophotonics applications. It is divided in two parts - a theoretical section and an experimental and applicative section. The first part includes chapters developing several numerical methods for analysis and design of photonic crystal devices, such as 2D ring resonators for filters, single and coupled nanobeam cavities, birefringence in photonic crystal cavities, threshold analysis in photonic crystal lasers, gap solitons in photonic crystals, novel photonic atolls, dynamic characteristics of photonic crystal filters. The second part focuses on some aspects of photonic crystals fabrication and relevant applications, such as nitrogen defect technology in diamond, silicon nitride free standing membranes, photonic crystals structures in silicon, photonic crystals for optical sensing.
Compatible Spatial Discretizations
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Author : Douglas N. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-26
Compatible Spatial Discretizations written by Douglas N. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-26 with Mathematics categories.
The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.