Download or read book Symmetry Phase Modulation and Nonlinear Waves written by Thomas J. Bridges and published by Cambridge University Press. This book was released on 2017-07-03 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridges studies the origin of Korteweg-de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.
Download or read book Symmetry Phase Modulation and Nonlinear Waves written by Thomas J. Bridges and published by Cambridge University Press. This book was released on 2017-07-03 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Download or read book Controllable Nonlinear Waves in Graded Index Waveguides GRIN written by Thokala Soloman Raju and published by Springer Nature. This book was released on with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonconservative Stability Problems of Modern Physics written by Oleg N. Kirillov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-03-08 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated revision gives a complete and topical overview on Nonconservative Stability which is essential for many areas of science and technology ranging from particles trapping in optical tweezers and dynamics of subcellular structures to dissipative and radiative instabilities in fluid mechanics, astrophysics and celestial mechanics. The author presents relevant mathematical concepts as well as rigorous stability results and numerous classical and contemporary examples from non-conservative mechanics and non-Hermitian physics. New coverage of ponderomotive magnetism, experimental detection of Ziegler’s destabilization phenomenon and theory of double-diffusive instabilities in magnetohydrodynamics.
Download or read book Geometry of the Phase Retrieval Problem written by Alexander H. Barnett and published by Cambridge University Press. This book was released on 2022-05-05 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solution to this class of problems. Written for mathematicians, physicists and engineers working in image analysis and reconstruction, this book introduces a conceptual, geometric framework for the analysis of these problems, leading to a deeper understanding of the essential, algorithmically independent, difficulty of their solutions. Using this framework, the book studies standard algorithms and a range of theoretical issues in phase retrieval and provides several new algorithms and approaches to this problem with the potential to improve the reconstructed images. The book is lavishly illustrated with the results of numerous numerical experiments that motivate the theoretical development and place it in the context of practical applications.
Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 1107 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Download or read book Parity time Symmetry and Its Applications written by Demetrios Christodoulides and published by Springer. This book was released on 2018-11-28 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive review of the state-of-the-art theoretical and experimental advances in linear and nonlinear parity-time-symmetric systems in various physical disciplines, and surveys the emerging applications of parity-time (PT) symmetry. PT symmetry originates from quantum mechanics, where if the Schrodinger operator satisfies the PT symmetry, then its spectrum can be all real. This concept was later introduced into optics, Bose-Einstein condensates, metamaterials, electric circuits, acoustics, mechanical systems and many other fields, where a judicious balancing of gain and loss constitutes a PT-symmetric system. Even though these systems are dissipative, they exhibit many signature properties of conservative systems, which make them mathematically and physically intriguing. Important PT-symmetry applications have also emerged. This book describes the latest advances of PT symmetry in a wide range of physical areas, with contributions from the leading experts. It is intended for researchers and graduate students to enter this research frontier, or use it as a reference book.
Download or read book Discrete Variational Problems with Interfaces written by Roberto Alicandro and published by Cambridge University Press. This book was released on 2023-12-31 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many materials can be modeled either as discrete systems or as continua, depending on the scale. At intermediate scales it is necessary to understand the transition from discrete to continuous models and variational methods have proved successful in this task, especially for systems, both stochastic and deterministic, that depend on lattice energies. This is the first systematic and unified presentation of research in the area over the last 20 years. The authors begin with a very general and flexible compactness and representation result, complemented by a thorough exploration of problems for ferromagnetic energies with applications ranging from optimal design to quasicrystals and percolation. This leads to a treatment of frustrated systems, and infinite-dimensional systems with diffuse interfaces. Each topic is presented with examples, proofs and applications. Written by leading experts, it is suitable as a graduate course text as well as being an invaluable reference for researchers.
Download or read book Spaces of Measures and their Applications to Structured Population Models written by Christian Düll and published by Cambridge University Press. This book was released on 2021-10-07 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.
Download or read book Multivariate Approximation written by V. Temlyakov and published by Cambridge University Press. This book was released on 2018-07-19 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained presentation of multivariate approximation from classical linear approximation to contemporary nonlinear approximation.
Download or read book Mathematical Modelling of the Human Cardiovascular System written by Alfio Quarteroni and published by Cambridge University Press. This book was released on 2019-05-09 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are important when solving problems with high complexity, which would otherwise be out of reach.
Download or read book Numerical Bifurcation Analysis of Maps written by I︠U︡riĭ Aleksandrovich Kuznet︠s︡ov and published by Cambridge University Press. This book was released on 2019-03-28 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combines a systematic analysis of bifurcations of iterated maps with concrete MATLAB® implementations and applications.
Download or read book Quasi Interpolation written by Martin Buhmann and published by Cambridge University Press. This book was released on 2022-03-03 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Delve into an in-depth description and analysis of quasi-interpolation, starting from various areas of approximation theory.
Download or read book The Christoffel Darboux Kernel for Data Analysis written by Jean Bernard Lasserre and published by Cambridge University Press. This book was released on 2022-04-07 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible overview introduces the Christoffel-Darboux kernel as a novel, simple and efficient tool in statistical data analysis.
Download or read book Operator Adapted Wavelets Fast Solvers and Numerical Homogenization written by Houman Owhadi and published by Cambridge University Press. This book was released on 2019-10-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although numerical approximation and statistical inference are traditionally covered as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. This book explores these connections from a game and decision theoretic perspective, showing how they constitute a pathway to developing simple and general methods for solving fundamental problems in both areas. It illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, fast solvers, and Gaussian processes. This perspective reveals much of their essential anatomy and greatly facilitates advances in these areas, thereby appearing to establish a general principle for guiding the process of scientific discovery. This book is designed for graduate students, researchers, and engineers in mathematics, applied mathematics, and computer science, and particularly researchers interested in drawing on and developing this interface between approximation, inference, and learning.
Download or read book Fundamentals and Applications of Nonlinear Nanophotonics written by Nicolae C. Panoiu and published by Elsevier. This book was released on 2023-09-18 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals and Applications of Nonlinear Nanophotonics includes key concepts of nonlinear nanophotonics, computational and modeling techniques to design these materials, and the latest advances. This book addresses the scientific literature on nanophotonics while most existing books focus almost exclusively on the linear aspects of light-matter interaction at the nanoscale. Sections cover nonlinear optics of sub-wavelength photonic nanostructured materials, review nonlinear optics of bound-states in the continuum, nonlinear optics of chiral plasmonic metasurfaces, nonlinear hyperbolic nanomaterials, nonlinear topological photonics, plasmonic lattice solitons, and more. This book is suitable for academics and industry professionals working in the discipline of materials science, engineering and nanotechnology. Discusses advances in nonlinear optics research such as plasmonics, topological photonics and emerging materials Reviews the latest computational methods to model and design nonlinear photonic materials Introduces key principles of advanced concepts in nonlinear optics of bound-states in a continuum and symmetries in nonlinear nano-optics
Download or read book Odyssey of Light in Nonlinear Optical Fibers written by Kuppuswamy Porsezian and published by CRC Press. This book was released on 2017-12-19 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications presents a collection of breakthrough research portraying the odyssey of light from optical solitons to optical rogue waves in nonlinear optical fibers. The book provides a simple yet holistic view on the theoretical and application-oriented aspects of light, with a special focus on the underlying nonlinear phenomena. Exploring the very frontiers of light-wave technology, the text covers the basics of nonlinear fiberoptics and the dynamics of electromagnetic pulse propagation in nonlinear waveguides. It also highlights some of the latest advances in nonlinear optical fiber technology, discussing hidden symmetry reductions and Ablowitz–Kaup–Newell–Segur (AKNS) hierarchies for nonautonomous solitons, state-of-the-art Brillouin scattering applications, backpropagation, and the concept of eigenvalue communication—a powerful nonlinear digital signal processing technique that paves the way to overcome the current limitations of traditional communications methods in nonlinear fiber channels. Key chapters study the feasibility of the eigenvalue demodulation scheme based on digital coherent technology by throwing light on the experimental study of the noise tolerance of the demodulated eigenvalues, investigate matter wave solitons and other localized excitations pertaining to Bose–Einstein condensates in atom optics, and examine quantum field theory analogue effects occurring in binary waveguide arrays, plasmonic arrays, etc., as well as their ensuing nonlinear wave propagation. Featuring a foreword by Dr. Akira Hasegawa, the father of soliton communication systems, Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications serves as a curtain raiser to usher in the photonics era. The technological innovations at the core of the book form the basis for the next generation of ultra-high speed computers and telecommunication devices.
