Experimental and numerical exploration of intrinsic localized modes in an atomic lattice

Abstract

This review focuses attention on the experimental studies of intrinsic localized modes (ILMs) produced in driven atomic lattices. Production methods involve the application of modulational instability under carefully controlled conditions. One experimental approach is to drive the atomic lattice far from equilibrium to produce ILMs, the second is to apply a driver of only modest strength but nearby in frequency to a plane wave mode so that a slow transformation from large amplitude standing waves to ILMs takes place. Since, in either case, the number of ILMs produced is small, the experimental observation tool appropriate for this task is four-wave mixing. This nonlinear detection technique makes use of the nonlinearity associated with an ILM to enhance its signal over that produced by the more numerous, but linear, spin waves. The final topic deals with numerical simulations of a nonlinear nanoscale atomic lattice where the new feature is running ILMs.

Discrete breathers in a realistic coarse-grained model of proteins

“…Recently, it has been shown that band-edge normal modes (NMs) can be continued to nonlinear localized vibrations of high energy termed Discrete Breathers (DBs) [15], also known as intrinsic localized modes [17]. DBs are time-periodic, spatially localized solutions emerging generically in discrete networks of nonlinear oscillators [18,19], that have been also observed experimentally in many systems [19,20,21,22].…”

Optimal entrainment with smooth, pulse, and square signals in weakly forced nonlinear oscillators

“…(48) and (49), and are continuous, as proved in Appendix F. Moreover, ∂T p (∆φ,λ) ∂λ = β⟨|Z(θ ) + λ| β−1 ⟩ > 0 for any ∆φ from Eq. (51f).…”

“…(2). This idea seems rather reasonable, since stable ILMs (elliptic breathers) in finitedimensional Hamiltonian systems are generically characterized as periodic solutions in the center of KAM tori [47], and the dynamics around such periodic solutions would be reduced to the phase controlling discrete breathers, which gives a hint for understanding emerging interesting experimental results such as [48].…”

Intrinsic localized modes in two-dimensional vibrations of crystalline pillars and their application for sensing

“…23,[25][26][27] The coefficients for the individual beam can be derived from the nonlinear Euler-Bernoulli beam theory. If u is measured as a fraction of cross-section w x , for example, then b 1 =a 1 $ C 1 w 2 x =L 2 , with the non-dimensionalized prefactor C 1 depending on the normalization of w x chosen, typically being of order 1.…”

“…Since then, ILMs have then been found in a wide variety of structures and there has been substantial interest in the theoretical analysis and practical applications of ILMs. [17][18][19][20][21][22][23][24][25][26][27][28][29] In general, most of these works have concentrated on the analysis of the oscillations being described by one variable. In particular case of ILM in cantilever arrays, the one-dimensionality of vibrations was enforced by designing the experiments with the cantilever thickness in the direction of vibration to be much smaller than in the other direction.…”