Collective Dynamics of Weakly Coupled Nonlinear Periodic Structures
Collective Dynamics of Weakly Coupled Nonlinear Periodic Structures

Author: Diala Bitar

Publisher:

Published: 2017

Total Pages: 216

ISBN-13:

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Although the dynamics of periodic nonlinear lattices was thoroughly investigated in the frequencyand time-space domains, there is a real need to perform profound analysis of the collectivedynamics of such systems in order to identify practical relations with the nonlinear energy localizationphenomenon in terms of modal interactions and bifurcation topologies. The principal goal ofthis thesis consists in exploring the localization phenomenon for modeling the collective dynamicsof periodic arrays of weakly coupled nonlinear resonators.An analytico-numerical model has been developed in order to study the collective dynamics ofa periodic coupled nonlinear oscillators array under simultaneous primary and parametric excitations,where the bifurcation topologies, the modal interactions and the basins of attraction havebeen analyzed. Arrays of coupled pendulums and electrostatically coupled nanobeams under externaland parametric excitations respectively were considered. It is shown that by increasing thenumber of coupled oscillators, the number of multimodal solutions and the distribution of the basinsof attraction of the resonant solutions increase. The model was extended to investigate the collectivedynamics of periodic nonlinear 2D arrays of coupled pendulums and spherical particles underbase excitation, leading to additional features, mainly larger bandwidth and important vibrationalamplitudes. A second investigation of this thesis consists in identifying the solitons associated tothe collective nonlinear dynamics of the considered arrays of periodic structures and the study oftheir stability.

Collective Dynamics of Nonlinear and Disordered Systems
Collective Dynamics of Nonlinear and Disordered Systems

Author: Günter Radons

Publisher: Springer Science & Business Media

Published: 2005-01-12

Total Pages: 402

ISBN-13: 9783540213833

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Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

Encyclopedia of Nonlinear Science
Encyclopedia of Nonlinear Science

Author: Alwyn Scott

Publisher: Routledge

Published: 2006-05-17

Total Pages: 1107

ISBN-13: 1135455589

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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.

Nonlinearities in Periodic Structures and Metamaterials
Nonlinearities in Periodic Structures and Metamaterials

Author: Cornelia Denz

Publisher: Springer

Published: 2010-03-11

Total Pages: 299

ISBN-13: 3642020666

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Optical information processing of the future is associated with a new generation of compact nanoscale optical devices operating entirely with light. Moreover, adaptive features such as self-guiding, reconfiguration and switching become more and more important. Nonlinear devices offer an enormous potential for these applications. Consequently, innovative concepts for all-optical communication and information technologies based on nonlinear effects in photonic-crystal physics and nanoscale devices as metamaterials are of high interest. This book focuses on nonlinear optical phenomena in periodic media, such as photonic crystals, optically-induced, adaptive lattices, atomic lattices or metamaterials. The main purpose is to describe and overview new physical phenomena that result from the interplay between nonlinearities and structural periodicities and is a guide to actual and future developments for the expert reader in optical information processing, as well as in the physics of cold atoms in optical lattices.

Design and Modeling of Mechanical Systems—III
Design and Modeling of Mechanical Systems—III

Author: Mohamed Haddar

Publisher: Springer

Published: 2017-11-25

Total Pages: 1225

ISBN-13: 3319666975

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This book offers a collection of original peer-reviewed contributions presented at the 7th International Congress on Design and Modeling of Mechanical Systems (CMSM’2017), held in Hammamet, Tunisia, from the 27th to the 29th of March 2017. It reports on both research findings, innovative industrial applications and case studies concerning mechanical systems and related to modeling and analysis of materials and structures, multiphysics methods, nonlinear dynamics, fluid structure interaction and vibroacoustics, design and manufacturing engineering. Continuing on the tradition of the previous editions, this proceedings offers a broad overview on the state-of-the art in the field and a useful resource for academic and industry specialists active in the field of design and modeling of mechanical systems. CMSM’2017 was jointly organized by two leading Tunisian research laboratories: the Mechanical, Modeling and Manufacturing Laboratory of the National Engineering School of Sfax and the Mechanical Engineering Laboratory of the National Engineering School of Monastir..

Dynamical Systems in Neuroscience
Dynamical Systems in Neuroscience

Author: Eugene M. Izhikevich

Publisher: MIT Press

Published: 2010-01-22

Total Pages: 459

ISBN-13: 0262514206

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Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.