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Full-Text Articles in Physical Sciences and Mathematics
Localized Breathing Modes In Granular Crystals With Defects, G Theocharis, M Kavousanakis, Pg Kevrekidis, C Daraio, Ma Porter, Ig Kevrekidis
Localized Breathing Modes In Granular Crystals With Defects, G Theocharis, M Kavousanakis, Pg Kevrekidis, C Daraio, Ma Porter, Ig Kevrekidis
Mathematics and Statistics Department Faculty Publication Series
We study localized modes in uniform one-dimensional chains of tightly packed and uniaxially compressed elastic beads in the presence of one or two light-mass impurities. For chains composed of beads of the same type, the intrinsic nonlinearity, which is caused by the Hertzian interaction of the beads, appears not to support localized, breathing modes. Consequently, the inclusion of light-mass impurities is crucial for their appearance. By analyzing the problem’s linear limit, we identify the system’s eigenfrequencies and the linear defect modes. Using continuation techniques, we find the solutions that bifurcate from their linear counterparts and study their linear stability in …
Two-Dimensional Paradigm For Symmetry Breaking: The Nonlinear Schroumldinger Equation With A Four-Well Potential, C Wang, G Theocharis, Pg Kevrekidis, N Whitaker, Kjh Law, Dj Frantzeskakis, Ba Malomed
Two-Dimensional Paradigm For Symmetry Breaking: The Nonlinear Schroumldinger Equation With A Four-Well Potential, C Wang, G Theocharis, Pg Kevrekidis, N Whitaker, Kjh Law, Dj Frantzeskakis, Ba Malomed
Mathematics and Statistics Department Faculty Publication Series
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are analyzed. Selective “static” features of the model are examined in the context of nonlinear waves including rotobreathers and kinklike solitary waves. We also explore “dynamic” features of the model concerning the resonant transfer of energy and the role of moving intrinsic localized modes in the process.
Two-Component Nonlinear Schrodinger Models With A Double-Well Potential, C Wang, Pg Kevrekidis, N Whitaker, Ba Malomed
Two-Component Nonlinear Schrodinger Models With A Double-Well Potential, C Wang, Pg Kevrekidis, N Whitaker, Ba Malomed
Mathematics and Statistics Department Faculty Publication Series
We introduce a model motivated by studies of Bose–Einstein condensates (BECs) trapped in double-well potentials. We assume that a mixture of two hyperfine states of the same atomic species is loaded in such a trap. The analysis is focused on symmetry-breaking bifurcations in the system, starting at the linear limit and gradually increasing the nonlinearity. Depending on values of the chemical potentials of the two species, we find numerous states, as well as symmetry-breaking bifurcations, in addition to those known in the single-component setting. These branches, which include all relevant stationary solutions of the problem, are predicted analytically by means …