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

Abstract

Surface acoustic wave band gaps in a diamond-based two-dimensional locally resonant phononic crystal for high frequency applicationsWe present a complete analysis on the possibility of exciting and observing the intrinsic localized modes (ILMs) in a crystalline linear array of nano pillars. We discuss the nano-fabrication techniques for these arrays and visualization procedures to observe the real-time dynamics. As a consequence, we extend previous models to the study of two dimensional vibrations to be consistent with these restrictions. For these pillars, the elastic properties and hence the dynamics depend on the pillar's shape and the orientation of the crystal axes. We show that ILMs do form in the system, but their stability, defect pinning, and reaction to friction strongly depend on the crystals properties, with the optimal dynamics only achieved in a rather small region of the parameter space. We also demonstrate fabrication techniques for these pillars and discuss the applications of these pillar arrays to sensing. V C 2012 American Institute of Physics. [http://dx.

Reduced systems for Intrinsic Localized Modes on an infinite oscillator array

“…Another interesting direction will be to extend the results of this system to two-dimensional oscillations of pillars as described in [2]. We believe that such a system, which must necessarily involve involving six canonical variables (one position x and two amplitudes A and B for out-of-plane and in-plane oscillations, and the corresponding momenta), should provide a consistent low-dimensional description of ILM behaviour.…”

“…Realistic numbers in the literature [2] yield the force of dissipation on the k-th oscillator as ∼ γu k where γ ∼ 10 −4 . One could try to insert the averaging ansatz (1) directly into the total dissipation rate k −γu 2 k and compute the dissipation force; however, in our opinion, such approach is inconsistent.…”

Simplified models for Intrinsic Localized Mode dynamics

“…For the purpose of this manuscript, we shall only consider one dimensional deflection of oscillators. As we discuss in [24], to accurately model nano mechanical arrays, one needs to consider two dimensional vibrations, but this is left for future consideration. For now, define u n be the deflection of the nth pillar.…”

“…The scaling of ILM-based sensors to nanoscale presents several challenges, the most important being impossibility of visualization of motion using any light of near-visible spectrum. We refer the reader to our recent paper [24] for the discussion of challenges of nanoscale dynamics, methods of solutions and some theory behind visualization of the dynamics of nano pillar arrays.…”

Intrinsic localized modes of a classical discrete anisotropic Heisenberg ferromagnetic spin chain

“…However, to our knowledge exact analytic solutions of these excitations are very limited in these models. Our main objective in this paper is to obtain a class of exact analytic solutions of ILMs of a classical one-dimensional discrete anisotropic Heisenberg ferromagnetic chain including external magnetic fields, which one can then search experimentally [18]. The classical anisotropic spin systems are of significant physical interest, e.g.…”