Department of Pattern Dynamics Analysis
Department Head: Professor Yuji Hattori
We promote collaboration between mathematics and other scientific fields by focusing on pattern dynamics that appear in natural and social phenomena and analyzing them mathematically. For example, we work on the pattern dynamics of reaction-diffusion systems and their applications to material science, as well as the pattern dynamics of flow fields and their applications to environmental and biological phenomena.
Pattern dynamics of reaction-diffusion systems and their applications to material science
Pattern dynamics in material science are closely related to the properties of materials and the realization of new, useful properties of them. We contribute to the creation of new materials and the discovery of functions of existing materials by analyzing pattern dynamics from various mathematical standpoints.
Construction of the unified combustion limit theory based on space experiments and pattern dynamics analysis of peculiar flames
We are planning experiments to be conducted in space at the international space station, in the Japanese module “KIBO”, in order to construct a unified combustion limit theory, which will comprehensively cover both peculiar “flame ball” phenomena and ordinary flames.
To analyze and create a numerical model for the transition from ordinary flame to flame ball, international collaborative research with Far Eastern Federal University, in Russia, is ongoing. Transition from ordinary flame to flame ball will be addressed experimentally where ordinary flame is decisively obtained by governing equations, whereas flame balls are essentially pattern formation problems.
The pattern dynamics of flow fields and their applications to biomedical problems
There are various flows in the human body, such as blood flow, the flow of cerebrospinal fluid, and expiratory flows, which have unique space-time patterns that are closely related to our health conditions. Collaborative research between mathematics and biology and/or clinical medicine will be performed to analyze the patterns arising in these flow fields.