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Next: Bibliography Up: DISCRETE BREATHER ANIMATION Previous: Introduction

Description

In the applet you can choose the type of potentials and set the value of needed coefficients $V_i$ and $W_i$ in (2) and (3). After that, it is possible to set an initial profile of displacement (and/or velocities by changing the showing panel) by pressing the left mouse button and dragging the circle. During this process the coordinates of the circle will be displayed. When you finish, you can check the value of amplitude just by pressing the left mouse button under the circle. If you did something wrong and would like to set a new profile, you can just press "Reset" button (or "Reset all") to set all amplitudes (and velocities) to zero. Each panel has its own value of maximum visible amplitude. But it can be changed by typing approapriate value and pressing the button "Set new max. value". It can be changed also during simulation. Initially the Morse potential is chosen with the linear coupling $W_1=0.05$. The profile of displacement and velocities is set to the DB state with the frequency $\Omega_b=0.85$. When you press "Start" button, the animation starts.

The fourth order Runge-Kutta method is used with the time step $dt=0.01$. The simulation can be interrupted at any time by pressing "Stop" button and start over again. It is possible to stop the simulation and change some parameters such as potentials (value of coupling in order to obtain the breather via anticontinuous limit), time of integration $Dt$ between frames. The Newton method can be used to obtain DB state. For this the desired frequency of the breather $\Omega_b$ should be given and good approximation to the initial shape. Note, that it should be outside of the phonon spectrum (5) and not in resonance with it for all harmonics $k\Omega_b\neq\omega_q$, where $k$ is integer.


next up previous
Next: Bibliography Up: DISCRETE BREATHER ANIMATION Previous: Introduction
Andrey Miroshnchenko 2003-01-15