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Nonlinearity with Disorder
In the past three decades there has been enormous progress in identifying the essential role that nonlinearity plays in physical systems, including supporting soliton-like solutions and self-trapped sxcitations such as polarons. during the same period, similarly impressive progress has occurred in understanding the effects of disorder in linear quantum problems, especially regarding Anderson localization arising from impurities, random spatial structures, stochastic applied fields, and so forth. These striking consequences of disorder, noise and nonlinearity frequently occur together in physical systems. Yet there have been only limited attempts to develop systematic techniques which can inc...
Disorder and Nonlinearity
ill the past three decades there has been enonnous progress in identifying the es sential role that "nonlinearity" plays in physical systems. Classical nonlinear wave equations can support localized, stable "soliton" solutions, and nonlinearities in quantum systems can lead to self-trapped excitations, such as polarons. Since these nonlinear excitations often dominate the transport and response properties of the systems in which they exist, accurate modeling of their effects is essential to interpreting a wide range of physical phenomena. Further, the dramatic de velopments in "deterministic chaos", including the recognition that even simple nonlinear dynamical systems can produce seemingly ...
Proton Transfer in Hydrogen-Bonded Systems
Charge transport through the transfer of protons between molecules has long been recognized as a fundamental process, which plays an important role in many chemical reactions. In particular, proton transfer through Hydrogen (H-) bonds has been identified as the main mechanism, via which many bio logical functions are performed and many properties of such basic substances as proteins and ice can be understood. In this volume, several of these important aspects of the H-bond are rep resented. As the division in different sections already indicates, present day research in proton teansfer in biochemistry, biology, and the physics of water and ice remains highly active and very exciting. Nearly ...
Interplay of Quantum Mechanics and Nonlinearity
This book presents an in-depth study of the discrete nonlinear Schrödinger equation (DNLSE), with particular emphasis on spatially small systems that permit analytic solutions. In many quantum systems of contemporary interest, the DNLSE arises as a result of approximate descriptions despite the fundamental linearity of quantum mechanics. Such scenarios, exemplified by polaron physics and Bose-Einstein condensation, provide application areas for the theoretical tools developed in this text. The book begins with an introduction of the DNLSE illustrated with the dimer, development of fundamental analytic tools such as elliptic functions, and the resulting insights into experiment that they all...
Davydov’s Soliton Revisited
Proceedings of a NATO ARW held in Thisted, Denmark, July 30-August 5, 1989
Fluctuation Phenomena: Disorder And Nonlinearity - Proceedings Of The International Workshop
This book addresses the issues of nonlinearity and disorder. It covers mathematical and numerical techniques as well as applications of nonlinearity and disorder. The analysis of continuous and discrete systems is also shown.
Stairway to the Mind
Human consciousness has perplexed philosophers, artists and scientists for centuries. Some hold it to be purely physical, while others believe it transcends the material world. Now comes a book that offers a new perspective - based entirely on evidence from the natural sciences - whereby materialism and dualism co-exist. The author - a distinguished pioneer of nonlinear dynamics - bases his argument on a hierarchical view of mental organization; a stairway. Atoms give rise to molecules, neurons form the brain and individual consciousness leads to shared culture. All steps are needed to complete the picture and each level derives from the previous one. The book shows specialists how each of their fields adds to the overall picture, while providing general readers with an introduction to this investigation.
International Conference on Singular Behavior and Nonlinear Dynamics, Samos, Greece, 18-26 August 1988
The two volumes of these Proceedings contain recent results and some review articles on major topics of Nonlinear Dynamical Systems: Chaos, Solitons, Bifurcations, Qualitative and Quantitative aspects of nonlinear phenomena that were presented at the International Conference of Samos. The first volume is devoted to theoretical analysis while the second contains a wealth of applied results from Solid State Physics, Fluid Mechanics, Josephson junctions, Optical Fibers and Biological systems. The major aim of the organizers was to bring together mathematicians and physicists from both the Coherent (solitonic) and Chaotic aspects of Nonlinear Dynamics as well as some more traditional theorists of Dynamical Systems.
