Symmetry Phase Modulation And Nonlinear Waves
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| Author | : Thomas J. Bridges |
| Publisher | : Cambridge University Press |
| Total Pages | : 240 |
| Release | : 2017-07-03 |
| Genre | : Science |
| ISBN | : 1108101321 |
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.
| Author | : Thomas J. Bridges |
| Publisher | : Cambridge University Press |
| Total Pages | : 239 |
| Release | : 2017-07-03 |
| Genre | : Mathematics |
| ISBN | : 1107188849 |
Bridges studies the origin of Korteweg-de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.
| Author | : Thokala Soloman Raju |
| Publisher | : Springer Nature |
| Total Pages | : 85 |
| Release | : |
| Genre | : |
| ISBN | : 9819704413 |
| Author | : Oleg N. Kirillov |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 548 |
| Release | : 2021-03-08 |
| Genre | : Science |
| ISBN | : 3110655403 |
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.
| Author | : Alexander H. Barnett |
| Publisher | : Cambridge University Press |
| Total Pages | : 321 |
| Release | : 2022-05-05 |
| Genre | : Mathematics |
| ISBN | : 1009007785 |
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.
| Author | : Demetrios Christodoulides |
| Publisher | : Springer |
| Total Pages | : 579 |
| Release | : 2018-11-28 |
| Genre | : Science |
| ISBN | : 9811312478 |
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.
| Author | : Roberto Alicandro |
| Publisher | : Cambridge University Press |
| Total Pages | : 276 |
| Release | : 2023-12-31 |
| Genre | : Mathematics |
| ISBN | : 1009298801 |
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.
| Author | : Christian Düll |
| Publisher | : Cambridge University Press |
| Total Pages | : 322 |
| Release | : 2021-10-07 |
| Genre | : Mathematics |
| ISBN | : 1009020471 |
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.
| Author | : V. Temlyakov |
| Publisher | : Cambridge University Press |
| Total Pages | : 551 |
| Release | : 2018-07-19 |
| Genre | : Computers |
| ISBN | : 1108428754 |
Self-contained presentation of multivariate approximation from classical linear approximation to contemporary nonlinear approximation.
| Author | : Alfio Quarteroni |
| Publisher | : Cambridge University Press |
| Total Pages | : 291 |
| Release | : 2019-05-09 |
| Genre | : Mathematics |
| ISBN | : 1108570534 |
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.
