Pattern formation in Reaction-Diffusion systems.

Summary

Pattern forming in complex system has numerous applications in science and technology. One application, for instance, is their abilities to generate and propagate a respond to a small stimulus from the environment in a fast and reliable fashion. Reaction-diffusion system, as an excitable media, has two stable rest and excited states. Perturbations larger than the threshold may cause a large response, while small perturbations and noise decay immediately. Super-threshold perturbations lead via diffusion to propagation of fast reaction-diffusion waves that transmit information in a reliable fashion. Propagation of action potential in response to a small change in potential of the neural membrane, is a good example of this ability in neural networks of the brain!

Cellular patterns

Oscillatory patterns

Achievements

• Developed finite difference C++ codes for large-scale parallel computing, achieved 10x speedup
• Programmed shell, Matlab, and Python scripts to collect, transfrom, and visualize unstructured grid simulation data files
• Specialized and optimized the pre-existing Adaptive Mesh Refinement (AMR) code for simulations of heat/mass transfer in 2D & 3D, (2 orders of magnitude speedup & reduced the computational cost and memory usage)