Date of Award


Document Type


Degree Name

Master of Science (MS)


College of Science and Mathematics


Computer Science

Thesis Sponsor/Dissertation Chair/Project Chair

Roman M. Zaritski

Committee Member

Dajin Wang

Committee Member

Carl E. Bredlau


Spiral waves have been observed and studied in a variety of biological, physical and chemical systems, known as excitable media. The most famous examples of excitable media include cardiac tissue, the Belousov-Zhabotinsky chemical reaction, and aggregation of starving slime mold amoeba.

It had been shown previously that spiral waves could self-organize into multi- armed spirals. A 3D analog of a 2D spiral wave is called a scroll wave. It rotates around a 1D imaginary tube known as a filament. A later study based on the so-called Puschino model has reported formation of multi-armed scroll waves in 3D. But a question of whether multi-armed scroll waves are a common property of excitable medium or just an artifact of that particular model remained unanswered.

To answer this question we investigated the spontaneous formation and stability of multi-armed scroll waves based on four alternative mathematical models. Most often we used a simple Decoupled Parallel Programming (DPP) approach, starting multiple non-communicating concurrent jobs on multiple available CPUs, corresponding to different parameter values. Isolated scroll ring, evolving into much more complex turbulent patterns, was used as the initial condition.

We observed self-organization of spiral turbulence into multi-armed scroll waves in all four considered models. The presented results may be relevant to the cardiac defibrillation research.

This study has been made possible by the exclusive use of the on-site high- performance 64-CPU “Parallel Monster” cluster: with a close to 64-fold speed-up, it has helped reduce the simulation time for a single set of experiments from over one year to under one week.

File Format