PARALLEL SIMULATIONS OF SPIRAL
AND SCROLL WAVE
INTERACTION IN EXCITABLE MEDIA
Dr. Roman M. Zaritski
Research in collaboration with Dr. Arkady Pertsov (SUNY Upstate Medical University).
Below is a brief description of this project.
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Examples of excitable media include cardiac tissue and numerous chemical
and biological systems.
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Excitable media are known to support persistent rotating vortices of excitation
that emit spiral (in 2D) or scroll (in 3D) waves.
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The question is how multiple spiral or scroll waves interact with each
other (both short-term and asymptotically).
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Although a simple FitzHugh-Nagumo model is used, because of
the size of the domain (to accommodate large number of interacting
spirals or scrolls) and the number of time steps (to determine the
asymptotic behavior), the problem is very computationally intensive.
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To reduce the simulation time, and to make use of the available
parallel resources, a simple "domain slicing" algorithm is used
to parallelize the FHN simulations.
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The rectangular domain is sliced into rectangular strips. Each available
processor takes care of one such strip. For each time step each processor
updates unknown functions on the corresponding strip, then the neighboring
processors exchange the common boundary information using message passing
(MPI).
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Two challenges in this study are large data files and visualization of
collected data.
Techniques for spiral tip and scroll filament detection, with
subsequent MPEG compression, have been developed. This reduces
data file sizes by hundreds of times and makes playing "movies" easy.
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Simulations on a simple rectangle led to unexpected results, such
as the formation and persistence of spiral triplets:
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The simulations on a torus (i.e. on a rectangle with special boundary
conditions) also led to unexpected results, resembling crystallization
domains:
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Examples of 2D MPEG Movies (750x1500 gridsize, 8 hrs of GALAXY cluster time,
spiral tips are displayed):
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In 3D, intermittent formation of triple filament strands
was discovered:
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Examples of 3D simulation Movies (300x300x200 gridsize, over 1 week of
GALAXY cluster time, scroll filaments are displayed):
