Based on the three keywords, mathematical modeling, numerical simulations and mathematical analysis, we are intending to establish methods for understanding natural science and life phenomena from a mathematical point of view. Mathematical models are tools for mimicking the real phenomena in terms of equations. By performing numerical simulations, we can reproduce the phenomena on the computer, and by logically understanding the phenomena on the computer, we can know the essential mechanism underlying the real phenomena. In addition, mathematical analysis can extract universal mathematical structure from the real phenomena, which can provide us with a common understanding of the essential mechanism of different phenomena.
We are now collaborating with many investigators in various fields. Among them, the work of mathematical modeling for barrier of epidermis is a collaboration with a cosmetics company, and the analysis of skin barrier in this work is expected to be applicable to anti-aging and skin diseases. On the other hand, in the fields of biology we are investigating the cleavage of eggs, the locomotion of amoebas and the polarity of cells from a mathematical modeling point of view. In addition, we are investigating pattern formations in reaction diffusion systems and the movement of droplets using the useful methods, such as the calculation of bifurcation structure and the discrete variational method. These investigations lead to the development of mathematical tools in these fields, and are one of the important subjects of our laboratory.
- Kobayashi, H. Kitahata, and M. Nagayama, “Model for calcium-mediated reduction of structural fluctuations in epidermis”, Physical Review E 92, 022709 (2015).
- Nakata, M. Nagayama, H. Kitahata, N. J. Suematsu and T. Hasegawa, “Physicochemical design and analysis of self-propelled objects that are characteristically sensitive to interfacial environments, Physical Chemistry Chemical Physics, 7, 10326-10338 (2015).
- Kobayashi, Y. Sanno, A. Sakai, Y. Sawabu, M. Tsutsumi, M. Goto, H. Kitahata, S. Nakata, J. Kumamoto, M. Denda and M. Nagayama, “Mathematical modeling of calcium waves induced by mechanical stimulation in keratinocytes” PLoS ONE 9(3), e92650. (2014).
- Ayukawa, M. Akiyama, J.L. Mummery-Widmer, T. Stoeger, J. Sasaki, J.A. Knoblich, H. Senoo, T. Sasaki, and M. Yamazaki, Dachsous-Dependent Asymmetric Localization of Spiny-Legs Determines Planar Cell Polarity Orientation in Drosophila. Cell Reports, 8(2), 610 – 621 (2014).
- Ginder, S. Omata and K. Svadlenka. “A variational method for multiphase volume-preserving interface motions” , Journal of Computational and Applied Mathematics, 257, 157–179 (2014).