Localized Excitations In Nonlinear Complex Systems
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Localized Excitations In Nonlinear Complex Systems
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Author : Ricardo Carretero-González
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-19
Localized Excitations In Nonlinear Complex Systems written by Ricardo Carretero-González 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 2013-11-19 with Science categories.
The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.
Localized Excitations In Nonlinear Complex Systems Lencos 09
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Author : Ricardo Carretero-González
language : en
Publisher:
Release Date : 2011
Localized Excitations In Nonlinear Complex Systems Lencos 09 written by Ricardo Carretero-González and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Nonlinear Systems Vol 2
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Author : Juan F. R. Archilla
language : en
Publisher: Springer
Release Date : 2017-12-21
Nonlinear Systems Vol 2 written by Juan F. R. Archilla and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-21 with Science categories.
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction arrays, waveguide arrays, photonic crystals and optical fibers. Nonlinear excitations are inherent to Bose-Einstein Condensates, constituting an excellent benchmark for testing their properties and providing a pathway for future discoveries in fundamental physics.
A Mathematical Modeling Approach From Nonlinear Dynamics To Complex Systems
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Author : Elbert E. N. Macau
language : en
Publisher: Springer
Release Date : 2018-06-14
A Mathematical Modeling Approach From Nonlinear Dynamics To Complex Systems written by Elbert E. N. Macau and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-14 with Technology & Engineering categories.
This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls. · Introduces new concepts for understanding and modeling complex systems; · Explains risk reduction management in complex systems; · Examines the symmetry group approach to understanding complex systems; · Illustrates the relation between transient chaos and crises.
Mathematical Modelling
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Author : Hemen Dutta
language : en
Publisher: American Mathematical Society
Release Date : 2023-07-07
Mathematical Modelling written by Hemen Dutta and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-07 with Mathematics categories.
This volume is a collection of chapters that present key ideas and theories, as well as their rigorous applications, required for the development of mathematical models in areas such as travelling waves, epidemiology, the chemotaxis system, atrial fibrillation, and vortex nerve complexes. The techniques, methodologies and approaches adopted in this book have relevance in several other fields including physics, biology, and sociology. Each chapter should also assist readers in comfortably comprehending the related and underlying ideas. The companion volume (Contemporary Mathematics, Volume 786) is devoted to principle and theory.
Nonlinear Waves
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Author : M D Todorov
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2018-09-18
Nonlinear Waves written by M D Todorov and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-18 with Science categories.
The Boussinesq equation is the first model of surface waves in shallow water that considers the nonlinearity and the dispersion and their interaction as a reason for wave stability known as the Boussinesq paradigm. This balance bears solitary waves that behave like quasi-particles. At present, there are some Boussinesq-like equations. The prevalent part of the known analytical and numerical solutions, however, relates to the 1d case while for multidimensional cases, almost nothing is known so far. An exclusion is the solutions of the Kadomtsev-Petviashvili equation. The difficulties originate from the lack of known analytic initial conditions and the nonintegrability in the multidimensional case. Another problem is which kind of nonlinearity will keep the temporal stability of localized solutions. The system of coupled nonlinear Schroedinger equations known as well as the vector Schroedinger equation is a soliton supporting dynamical system. It is considered as a model of light propagation in Kerr isotropic media. Along with that, the phenomenology of the equation opens a prospect of investigating the quasi-particle behavior of the interacting solitons. The initial polarization of the vector Schroedinger equation and its evolution evolves from the vector nature of the model. The existence of exact (analytical) solutions usually is rendered to simpler models, while for the vector Schroedinger equation such solutions are not known. This determines the role of the numerical schemes and approaches. The vector Schroedinger equation is a spring-board for combining the reduced integrability and conservation laws in a discrete level. The experimental observation and measurement of ultrashort pulses in waveguides is a hard job and this is the reason and stimulus to create mathematical models for computer simulations, as well as reliable algorithms for treating the governing equations. Along with the nonintegrability, one more problem appears here - the multidimensionality and necessity to split and linearize the operators in the appropriate way.
Quodons In Mica
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Author : Juan F. R. Archilla
language : en
Publisher: Springer
Release Date : 2015-07-31
Quodons In Mica written by Juan F. R. Archilla and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-31 with Technology & Engineering categories.
This book presents the current knowledge about nonlinear localized travelling excitations in crystals. Excitations can be vibrational, electronic, magnetic or of many other types, in many different types of crystals, as silicates, semiconductors and metals. The book is dedicated to the British scientist FM Russell, recently turned 80. He found 50 years ago that a mineral mica muscovite was able to record elementary charged particles and much later that also some kind of localized excitations, he called them quodons, was also recorded. The tracks, therefore, provide a striking experimental evidence of quodons existence. The first chapter by him presents the state of knowledge in this topic. It is followed by about 18 chapters from world leaders in the field, reviewing different aspects, materials and methods including experiments, molecular dynamics and theory and also presenting the latest results. The last part includes a personal narration of FM Russell of the deciphering of the marks in mica. It provides a unique way to present the science in an accessible way and also illustrates the process of discovery in a scientist's mind.
Normal Modes And Localization In Nonlinear Systems
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Author : Alexander F. Vakakis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Normal Modes And Localization In Nonlinear Systems written by Alexander F. Vakakis 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 2013-06-29 with Science categories.
The nonlinear normal modes of a parametrically excited cantilever beam are constructed by directly applying the method of multiple scales to the governing integral-partial differential equation and associated boundary conditions. The effect of the inertia and curvature nonlin earities and the parametric excitation on the spatial distribution of the deflection is examined. The results are compared with those obtained by using a single-mode discretization. In the absence of linear viscous and quadratic damping, it is shown that there are nonlinear normal modes, as defined by Rosenberg, even in the presence of a principal parametric excitation. Furthermore, the nonlinear mode shape obtained with the direct approach is compared with that obtained with the discretization approach for some values of the excitation frequency. In the single-mode discretization, the spatial distribution of the deflection is assumed a priori to be given by the linear mode shape ¢n, which is parametrically excited, as Equation (41). Thus, the mode shape is not influenced by the nonlinear curvature and nonlinear damping. On the other hand, in the direct approach, the mode shape is not assumed a priori; the nonlinear effects modify the linear mode shape ¢n. Therefore, in the case of large-amplitude oscillations, the single-mode discretization may yield inaccurate mode shapes. References 1. Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A., Nonnal Modes and Localization in Nonlinear Systems, Wiley, New York, 1996.
Synergetics Of Molecular Systems
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Author : Lev N. Lupichev
language : en
Publisher: Springer
Release Date : 2014-08-19
Synergetics Of Molecular Systems written by Lev N. Lupichev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-19 with Science categories.
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.
Reviews Of Nonlinear Dynamics And Complexity
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Author : Heinz Georg Schuster
language : en
Publisher: John Wiley & Sons
Release Date : 2010-07-06
Reviews Of Nonlinear Dynamics And Complexity written by Heinz Georg Schuster and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-06 with Science categories.
Written in a style that breaks the barriers between the disciplines, this monograph enables researchers from life science, physics, engineering, or chemistry to access the most recent results in a common language. The resulting review character of this project sets it apart from specialized journals, and allows each volume to respond quickly to new developments. This third volume contains new topics ranging from chaotic computing, via random dice tossing and stochastic limit-cycle oscillators, to a number theoretic example of self-organized criticality, wave localization in complex networks and anomalous diffusion. A first-class board of international scientists advises the editor, such that the carefully selected and invited contributions represent the latest and most relevant findings.