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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 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.

Theoretical Analysis of Pattern Dynamics to Understand Structural Formation in Materials Science

The structure of materials plays a significant role in determining their physical properties and functions. Understanding pattern dynamics is essential not only for understanding how the physical properties appear, but also for gaining insight about the creation of novel materials. We are working on the analysis of pattern dynamics from a theoretical point of view, and are also developing machine learning techniques to estimate mathematical models from data.

Theoretical Analysis of Pattern Dynamics to Understand Structural Formation in Materials Science

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.

Numerical and experimental sporadic flames

Mechanism of Instability and Route to Turbulence of Vortical Flows

Many flows are subjected to instability by which small disturbances grow and cause turbulent flow. The route to turbulent flows and the structures and patterns which emerge in the process depend crucially on the nature of the flow. We study the mechanism of various types of flows and the route to turbulence both theoretically and with numerical simulations.

Mechanism of Instability and Route to Turbulence of Vortical Flows