**Intorduction of Laboratory of Mathematical modeling**

Capturing natural phenomena from the viewpoint of the mathematical sciences

With mathematical modeling, numerical computation, and mathematical analysis forming the foundation of our research, we aim to understand biological and other natural phenomena from the perspective of the mathematical sciences.

Mathematical modeling is the imitation of phenomena through numerical formulae. By replicating phenomena on a computer via numerical computations, one can unearth the essential mechanisms hidden within the phenomenon. Moreover, mathematical analysis makes it possible to establish general mathematical structures for the target phenomenon. These structures enable one to give a common understanding to the underlying mechanisms of numerous phenomena.

The nature of our research also includes joint work with other groups working in the field of experimentation. In particular, our mathematical modeling of the skin barrier function is collaboration with researchers in industry and, through our analysis, we are expecting applications of our research related to antiaging and to the treatment of skin diseases.

Also in mathematical biology, we study models for cleavage (cell division), and the locomotion of amoeba cells. In addition, we work on the mathematical analysis of Physarum, planar cell polarity, and gait transitions in quadrupeds—the latter studies are expected to see practical use in the robotic engineering of biological motions.

We are also studying the motion of liquid droplets, bubbles, and volume-constrained multiphase flows. This subject is approached by using variational techniques and is also tied to the development of fast numerical methods for solving the corresponding partial differential equations. Additionally, by using numerical techniques for global bifurcation structures, we investigate pattern formation in reaction-diffusion systems.

Research Topics

Mathematical analysis of self-propelled materials.

Mathematical analysis of epidermal structures and skin diseases.

Formulation of biological models.

Mathematical analysis of self-propelled phenomenon using minimizing movements.

Pattern formation in reaction-diffusion systems