14 research outputs found
Aspects of Discrete Breathers and New Directions
We describe results concerning the existence proofs of Discrete Breathers
(DBs) in the two classes of dynamical systems with optical linear phonons and
with acoustic linear phonons. A standard approach is by continuation of DBs
from an anticontinuous limit. A new approach, which is purely variational, is
presented. We also review some numerical results on intraband DBs in random
nonlinear systems. Some non-conventional physical applications of DBs are
suggested. One of them is understanding slow relaxation properties of glassy
materials. Another one concerns energy focusing and transport in biomolecules
by targeted energy transfer of DBs. A similar theory could be used for
describing targeted charge transfer of nonlinear electrons (polarons) and, more
generally, for targeted transfer of several excitations (e.g. Davydov soliton).Comment: to appear in the Proceedings of NATO Advanced Research Workshop
"Nonlinearity and Disorder: Theory and Applications",
Tashkent,Uzbekistan,October 1-6, 200
Nonlinear Localization in Metamaterials
Metamaterials, i.e., artificially structured ("synthetic") media comprising
weakly coupled discrete elements, exhibit extraordinary properties and they
hold a great promise for novel applications including super-resolution imaging,
cloaking, hyperlensing, and optical transformation. Nonlinearity adds a new
degree of freedom for metamaterial design that allows for tuneability and
multistability, properties that may offer altogether new functionalities and
electromagnetic characteristics. The combination of discreteness and
nonlinearity may lead to intrinsic localization of the type of discrete
breather in metallic, SQUID-based, and symmetric metamaterials. We
review recent results demonstrating the generic appearance of breather
excitations in these systems resulting from power-balance between intrinsic
losses and input power, either by proper initialization or by purely dynamical
procedures. Breather properties peculiar to each particular system are
identified and discussed. Recent progress in the fabrication of low-loss,
active and superconducting metamaterials, makes the experimental observation of
breathers in principle possible with the proposed dynamical procedures.Comment: 19 pages, 14 figures, Invited (Review) Chapte
PT-Symmetric Dimer in a Generalized Model of Coupled Nonlinear Oscillators
Abstract In the present work, we explore the case of a general PT -symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrödinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations