DynamiX, 2003

I wrote this program for fun to teach students some principles of nonlinear dynamics with regards to one-dimensional chains of “atoms” with nonlinear interatomic potential. It allows to define structure of a chain (initial displacements, boundary conditions, interatomic potential) and watch how the system evolves in time. This process can be saved, and then played as a “video” for demonstration purposes. For the program interface, I used an analogy of a “media player”:

DynamiX interface

The program itself can be downloaded here. The zip-file contains a Windows executable file, a demo “video” and several files with various initial conditions.

Observation of a Chaotic Breather

One of the interesting experiments you can do with DynamiX is to observe an interesting physics concept described in [1] as a Chaotic Breather. In this experiment, the energy is initially uniformly distributed along the chain in a pi-mode (the neighboring atoms are out of phase by half wavelength), but over time it localizes and that leads to formation of a Chaotic Breather – a localization of energy which basically accumulates all the energy of a chain and travels along it chaotically.

Evolution of local energy of FPU-beta chain, with initial conditions corresponding to pi-mode

For this experiment, you would need a chain which consists of 128 atoms and integration of the chain can take some time even on modern-day machines. So to save you on precious computer time, the program is accompanied with the “video file” which has that experiment already recorded in DynamiX format.

That’s how chaotic breather borns, lives and dies

I may describe in a bit more detail how to use DynamiX to properly enjoy this amazing experiment at some later time.

[1] T.Cretegny et al, Physica D 121 ,1998, 109-126

Product Details
Name: DynamiX, download (5 Mb)
Programming languages used: Object Pascal
Methods for integration of equations of motion: Runge-Kutta and Euler
Type: standalone desktop app for Windows
Framework/Platform: Delphi
Budget: 3+ man-months
Release: June 2003.