Special Session 23: New trends in pattern formations and dynamics for dissipative systems and related topics

Reaction-diffusion type modeling of the self-propelled motion.

Masaharu Nagayama
Hokkadio University
Japan
Co-Author(s):    Natsume Motohashi, Hiroyuki Kitahata, Yasuaki Kobayashi, Ken-Ichi Nakamura, Koya Sakakibara, Keisuke Takasao, Harunori Monobe
Abstract:
A mathematical model was developed that included self-propelled objects in motion with deformation, such as droplets, and self-propelled objects without deformation, such as camphor. This study represents the self-propelled object by a volume-conserving Phase-Field equation derived from the $L^2$ gradient flow. The self-propelled object shape during motion is successfully controlled depending on the parameters included in the model equations. Moreover, adding a spatially inhomogeneous function to the potential term made it possible to represent the self-propelled object motion in elliptical and dumbbell shapes.