Influence of obstacles on the shape and speed of excitation waves

Niklas Manz

Obstacles

A collection of three images that shows the predicted front evolution behind obstacles with different shapes, different sizes, and different arrangements.

This project had been started by Alex Gould as his 2016 NSF-REU summer research project. The starting point was a 2015 published theoretical work regarding the influence of obstacles on the propagation speeds of reaction-diffusion waves (Wang, Tan, and Lou, Influence of obstacles on the propagation speeds of nonlinear waves driven by curvature, Physica A 425, 41-49, 2015). The authors investigated the influence of the sizes of squares and differently elongated rhombuses on the front speed behind the obstacles.

Alex wrote a JAVA program to recreate the published numerical results and improved the resolution of their findings. In addition, he compared the wave behavior around sharp obstacles (squares and rhombuses) with smooth obstacles (circles and ellipses) and suggested improvements to the program. The average wave velocity through the system v depends on the shape (see, for example Case 1 vs. Case 4 in Fig. 4) and size (see, for example, Case 1 to Case 4 in Fig. 6) of the obstacles. We need to run some more simulations in smaller size-steps as the transition from ‘effect on v’ to ‘no effect = undisturbed v’ is pretty abrupt and we need to investigate the transition region in more detail.

We also plan to obtain experimental results. Alex got some preliminary results with 3D-printed molds but we need to improve the smoothness of the system by using different 3D-printing techniques and companies and/or using very fine computer numerical controlled (CNC) drilling machines.