Superdiffusive Transport And Energy Localization In Disordered Granular Crystals
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| Total Pages | : |
| Release | : 2016 |
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We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition. Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.
| Author | : Christopher Chong |
| Publisher | : Springer |
| Total Pages | : 100 |
| Release | : 2018-03-29 |
| Genre | : Science |
| ISBN | : 3319778846 |
This book summarizes a number of fundamental developments at the interface of granular crystals and the mathematical and computational analysis of some of their key localized nonlinear wave solutions. The subject presents a blend of the appeal of granular crystals as a prototypical engineering tested for a variety of diverse applications, the novelty in the nonlinear physics of its coherent structures, and the tractability of a series of mathematical and computational techniques to analyse them. While the focus is on principal one-dimensional solutions such as shock waves, traveling waves, and discrete breathers, numerous extensions of the discussed patterns, e.g., in two dimensions, chains with defects, heterogeneous settings, and other recent developments are discussed. The emphasis on the subject was motivated by models in condensed matter physics, ferroelectrics, high energy physics, and statistical mechanics, leading to developments in mathematical analysis, numerical computation and insights on the physical aspects of the model. The book appeals to researchers in the field, as well as for graduate and advanced undergraduate students. It will be of interest to mathematicians, physicists and engineers alike.
| Author | : E. Silin̦š |
| Publisher | : American Institute of Physics |
| Total Pages | : 466 |
| Release | : 1994 |
| Genre | : Science |
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Market: Specialists, researchers, and students in solid-state physics, materials science, electronics, chemical physics, organic and physical chemistry, and molecular biophysics. This monograph focuses on the interaction processes of excitons and charge carriers with the local environment, including the polarization and localization phenomena and the formation of polaronic quasi- particles. Transport phenomena are discussed and directly correlated with interaction dynamics, which actually determine the time- and temperature-dependent transiton of charge carriers and excitons from a coherent to a diffusive mode of motion.
| Author | : Yoon Young Kim |
| Publisher | : Springer Nature |
| Total Pages | : 395 |
| Release | : 2023-08-01 |
| Genre | : Science |
| ISBN | : 9819902053 |
This book serves as an introductory text for students and engineers with limited knowledge of metamaterials (and elastic waves). This text begins with the most straightforward vibrating systems, such as single and 2-DOF spring-mass systems. It examines the observed phenomena in 2-DOF systems in an unconventional manner to prepare the reader for research on metamaterials. After presenting wave phenomena in an infinitely connected spring-mass system, an elastic bar, a continuous version of an infinite system, is analyzed. This instructional strategy, which progresses from the discrete model to the continuous model, facilitates efficient comprehension of wave and metamaterial concepts. Using continuous and discrete one-dimensional models, bending waves and their manipulation through metamaterials are also discussed. In the latter chapters of this book, advanced readers are introduced to the fundamental wave phenomena in two-dimensional media and wave manipulation using metamaterials, such as mode-converting transmission. As wave phenomena are the fundamental phenomena in vibrating structures, those interested in acoustics and vibration would gain a great deal of knowledge from this book, as the material covered in it offers a very different perspective on oscillatory phenomena than what is typically found in books on acoustics and vibration. Because this book presents a new technique for manipulating waves using metamaterials, engineers and scientists who work with (ultra)sounds and structural vibrations would find it very useful for expanding their knowledge of relevant topics.
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| Total Pages | : 1812 |
| Release | : 1992 |
| Genre | : Physics |
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| Author | : Kurt Binder |
| Publisher | : World Scientific |
| Total Pages | : 562 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 9814350176 |
This book gives a pedagogical introduction to the physics of amorphous solids and related disordered condensed matter systems. Important concepts from statistical mechanics such as percolation, random walks, fractals and spin glasses are explained. Using these concepts, the common aspects of these systems are emphasized, and the current understanding of the glass transition and the structure of glasses are concisely reviewed. This second edition includes new material on emerging topics in the field of disordered systems such as gels, driven systems, dynamical heterogeneities, growing length scales etc. as well as an update of the literature in this rapidly developing field.
| Author | : Ngoc Son Nguyen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 247 |
| Release | : 2013-07-06 |
| Genre | : Science |
| ISBN | : 3642392989 |
The extension of collision models for single impacts between two bodies, to the case of multiple impacts (which take place when several collisions occur at the same time in a multibody system) is a challenge in Solid Mechanics, due to the complexity of such phenomena, even in the frictionless case. This monograph aims at presenting the main multiple collision rules proposed in the literature. Such collisions typically occur in granular materials, the simplest of which are made of chains of aligned balls. These chains are used throughout the book to analyze various multiple impact rules which extend the classical Newton (kinematic restitution), Poisson (kinetic restitution) and Darboux-Keller (energetic or kinetic restitution) approaches for impact modelling. The shock dynamics in various types of chains of aligned balls (monodisperse, tapered, decorated, stepped chains) is carefully studied and shown to depend on several parameters: restitution coefficients, contact stiffness ratios, elasticity coefficients (linear or nonlinear force/ indentation relation), and kinetic angles (that depend on the mass ratios). The dissipation and the dispersion of kinetic energy during a multiple impact are mandatory modelling, and are quantified with suitable indices. Particular attention is paid to the ability of the presented laws to correctly predict the wave effects in the chains. Comparisons between many numerical and experimental results are shown, as well as comparisons between four different impact laws in terms of their respective abilities to correctly model dissipation and dispersion of energy.
| Author | : Marco Baldovin |
| Publisher | : Springer |
| Total Pages | : 133 |
| Release | : 2021-08-21 |
| Genre | : Science |
| ISBN | : 9783030511722 |
Recent experimental evidence about the possibility of "absolute negative temperature" states in physical systems has triggered a stimulating debate about the consistency of such a concept from the point of view of Statistical Mechanics. It is not clear whether the usual results of this field can be safely extended to negative-temperature states; some authors even propose fundamental modifications to the Statistical Mechanics formalism, starting with the very definition of entropy, in order to avoid the occurrence of negative values of the temperature tout-court. The research presented in this thesis aims to shed some light on this controversial topic. To this end, a particular class of Hamiltonian systems with bounded kinetic terms, which can assume negative temperature, is extensively studied, both analytically and numerically. Equilibrium and out-of-equilibrium properties of this kind of system are investigated, reinforcing the overall picture that the introduction of negative temperature does not lead to any contradiction or paradox.
| Author | : Martin H. Sadd |
| Publisher | : Academic Press |
| Total Pages | : 432 |
| Release | : 2018-03-31 |
| Genre | : Technology & Engineering |
| ISBN | : 0128116498 |
Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries: kinematics of motion and deformation; force and stress measures; and general principles of mass, momentum and energy balance. The book then moves beyond other books by dedicating several chapters to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity. Linear multiple field problems of thermoelasticity, poroelasticity and electoelasticity are also presented. Discussion of nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials are also given. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Offers a thorough, concise and organized presentation of continuum mechanics formulation Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study Features extensive use of exercises, providing more material for student engagement and instructor presentation
| Author | : Vladimir V. Uchaikin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 400 |
| Release | : 2013-07-09 |
| Genre | : Science |
| ISBN | : 3642339115 |
The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular. Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian) in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.
