טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentVeremkroit Michael
SubjectAnalytic Exploration of Discrete Breathers in a
Forced-Damped Klein-Gordon Type Chain
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

Discrete Breathers (DB, coined also intrinsic localized models-ILM) are localized excitations in spatially extended discrete systems. These systems are translationally invariant, implying the absence of disorder or defects. They are solutions of a variety of underlying nonlinear lattice models. These special solutions are typically characterized as time-periodic and spatially localized.

Nonlinearity and discreteness, key properties of a lattice which can support the existence of a discrete breather, are inherent to many systems in nature, such as crystals and molecules, but also to artificial systems e.g. Bose-Einstein condensates, Josephson Junctions, optical devices or micromechanical devices.

The purpose of this research is to analyze forced-damped nonlinear coupled oscillators in an infinite 1-D chain. We suggest an analytical approximation for the discrete breather. The approximation is based on the idea that the nonlinearity is taken into account only in the central part of the breather; the tails are treated as linear excitations. This idea allows drastic reduction of the dimensionality and allows one to obtain tractable analytical expressions. The analysis is based on Harmonic Balance method. This method allows prediction of possible response regimes of the system, and predicts the existence of a DB under a specific set of parameters. The results are verified by means of numerical simulations. Using the numerical model, it is possible to justify the approximations made in the analytical procedure. The analytical model successfully predicts the response regimes, as one stays far enough from the boundaries of DB existence zone in the space of parameters.