Linear local modes induced by intrinsic localized modes in a monatomic chain

Abstract

A theory is developed to describe the effect of an intrinsic localized mode (ILM) on small vibrations in a monatomic chain with hard quartic anharmonicity. One prediction is the appearance in the chain of linear local modes nearby the ILM. To check this result, MD calculations of vibrations under strong local excitation are carried through with high precision. The results fully confirm the prediction.

Bifurcation dynamics of a perturbed intrinsic localized mode in a driven micromechanical array

“…This is opposite to the case studied in Ref. [8] where an ILM has even symmetry. In our cantilever array, an excitation of the even LLM causes a lateral vibrational motion of the ILM at the difference frequency between the ILM and the LLM.…”

“…[8] Since the ILM in the cantilever array is odd shaped, the most localized LLM has even symmetry. This is opposite to the case studied in Ref.…”

“…[1][2][3][4] These nonlinear localized modes have attracted attention both because of fundamental interest and also because of possible practical applications. [5][6][7][8][9][10][11][12][13][14][15][16][17][18] Experimentally, a stationary ILM can be maintained in steady state using a driver to compensate for damping. [5][6][7] In this state the ILM is frequency locked, and a so called auto-resonance (AR) state is achieved where the driver frequency controls the ILM amplitude.…”

Standing and Moving Discrete Breathers with Frequencies Above the Phonon Spectrum

“…Therefore not only the frequency but also the shape of the mode described by (9.4) coincides with that of the DB. We emphasize that V MF does not describe the effect of the DB on phonons which time-dependence is essentially different [17,18]. Equation (9.4) is analogous to the equation which describes local dynamics of a lattice with static defect: the matrix v nn determining the perturbation of the lattice is an analog of the matrix describing the perturbation induced by the defect.…”

“…The number of the actual bond amplitudes may be still reduced taking into account the symmetry of the considered DB, thus only a few amplitudes must be found self-consistently in the real calculations. Using the presented theory, DBs have been calculated for some model systems [16][17][18]36] and have been predicted for Ni and Nb [10]. Below we apply it to discuss DBs with the frequencies above the top of the phonon band.…”