This book addresses the issue of non-linear problems that have dominated the forefront of physics. To analyse these problems, it is necessary to develop mathematical methods to match new concepts. In this connection, for the first time in a long time, the same key notions have attracted the attention of physicists and mathematicians. This book discusses how the role of such excitations in essentially non-linear systems is similar to that of harmonic oscillations and waves in linear physical models.
Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "complete integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifica tion schemes. The draw upon widely different sections of mathematics.
Synergetics is the quantitative study of multicomponent systems that exhibit nonlinear dynamics and cooperativity. This book specifically considers basic models of the nonlinear dynamics of molecular systems and discusses relevant applications in biological physics and the polymer sciences. Emphasis is placed on specific solutions to the dynamical equations that correspond to the coherent formation of spatial-temporal structures, such as solitons, kinks and breathers, in particular. The emergence of these patterns in molecular structures provides a variety of information on their structural properties and plays a significant part in energy transfer processes, topological defects, dislocations, and related structure transitions. Real media, in which solitons take the form of solitary waves, are also considered. In this context, the formation of nonlinear waves in a continuous medium described by nonlinear equations is associated with spontaneous breaking of the local symmetry of the homogeneous system, which produces a range of interesting phenomena. A particular feature of this text is its combination of analytic and computational strategies to tackle difficult nonlinear problems at the molecular level of matter.
This book is a state-of-the-art review on the Physics of Emergence. The challenge of complexity is to focus on the description levels of the observer in context-dependent situations. Emergence is not only an heuristic approach to complexity, but it also urges us to face a much deeper question ? what do we think is fundamental in the physical world?This volume provides significant and pioneering contributions based on rigorous physical and mathematical approaches ? with particular reference to the syntax of Quantum Physics and Quantum Field Theory ? dealing with the bridge-laws and their limitations between Physics and Biology, without failing to discuss the involved epistemological features.Physics of Emergence and Organization is an interdisciplinary source of reference for students and experts whose interests cross over to complexity issues.
This workshop in nonlinear dynamics and mathematical physics, organized by the Italian Nuclear Energy Agency (ENEA) in Bologna, is intended to give an updated overview of modern trends in the field of nonlinear dynamics with emphasis on applications to physics, quantum theory, plasma physics and fluid dynamics, optics and electrodynamics, computer simulation and neural networks.
This volume contains papers based on the workshop OC Energy and Information Transfer in Biological Systems: How Physics Could Enrich Biological UnderstandingOCO, held in Italy in 2002. The meeting was a forum aimed at evaluating the potential and outlooks of a modern physics approach to understanding and describing biological processes, especially regarding the transition from the microscopic chemical scenario to the macroscopic functional configurations of living matter. In this frame some leading researchers presented and discussed several basic topics, such as the photon interaction with biological systems also from the viewpoint of photon information processes and of possible applications; the influence of electromagnetic fields on the self-organization of biosystems including the nonlinear mechanism for energy transfer and storage; and the influence of the structure of water on the properties of biological matter."
A review of energy transfer mechanisms and luminescence measurements of efficiency of electronic excitation energy transfer in synthetic bichromophoric molecules, polymers and bio-polymers. It is devoted mainly to contradictions and alternative viewpoints.
This volume contains papers based on the workshop “Energy and Information Transfer in Biological Systems: How Physics Could Enrich Biological Understanding”, held in Italy in 2002. The meeting was a forum aimed at evaluating the potential and outlooks of a modern physics approach to understanding and describing biological processes, especially regarding the transition from the microscopic chemical scenario to the macroscopic functional configurations of living matter. In this frame some leading researchers presented and discussed several basic topics, such as the photon interaction with biological systems also from the viewpoint of photon information processes and of possible applications; the influence of electromagnetic fields on the self-organization of biosystems including the nonlinear mechanism for energy transfer and storage; and the influence of the structure of water on the properties of biological matter.
A coherent introduction to the complete range of soliton theory including Hirota's method and Backlund transformations. Details physical applications of soliton theory with chapters on the peculiar wave patterns of the Andaman Sea, atmospheric phenomena, general relativity and Davydov solitons. Contains testing for full integrability, a discussion of the Painlevé technique, symmetries and conservation law.
This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
