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TANAKA Yoshitaro 准教授

TANAKA, Yoshitaro Associate Professor

Research Projects

I am interested in the formation of various patterns observed in nature, and I am researching their mechanisms and the mathematical structures underlying them. Motivated by the mechanisms of pattern formation, I propose mathematical models and perform numerical calculations and analyses of these models. In my research, I deal with reaction-diffusion systems and evolution equations with nonlocal interactions and integral nuclei (nonlocal evolution equations) in relation to the arrangement of flowers in plants, body surface patterns in animals, and the development of the visual center in orangutans.

The appeal of research

The natural world is full of diverse patterns, and while they may appear complex at first glance, we can find order and rules within them. We can observe labyrinthine and dotted patterns on the skin of giraffes and pandas, and geometric patterns in the flowers of plants like sunflowers. Organisms around us spontaneously form complex tissues and organs. I believe the appeal of this research lies in being able to formalize these phenomena using mathematics and mathematically understand the mechanisms and processes behind pattern formation. Furthermore, the ability to construct new mathematical theories motivated by an understanding of these phenomena is another fascinating aspect of this research.

Achievements

Awards

• June 2024 September, 2024 　Received the Japan Society for Industrial and Applied Mathematics Best Author Award (Paper Category)(Related page)
• June 2021 March, 2021 　I received the Mathematical Society of Japan's Encouragement Award for Applied Mathematics.(Related page)
• June 2016 July, 2016 　I won the top prize in the Student Paper Competition at the 11th AIMS Conference.
• June 2014 July, 2014 　I was selected as a finalist in the Student Paper Competition at the 10th AIMS Conference.
• June 2011 October, 2011 　I received the Outstanding Poster Award at the MIMS Symposium on Phenomenological Mathematics.
• June 2011 September, 2011 　I received the Best Poster Award at the 21st Annual Meeting of the Japanese Society for Mathematical Biology.

Major publications and papers

• (Refereed) S.-I. Ei, H. Ochiai, Y. Tanaka, Method of fundamental solutions for Neumann problems of the modified Helmholtz equation in disk domains, Journal of Computational and Applied Mathematics, 402, 113795 (2022)
• (Refereed) S.-I. Ei, H. Ishii, S. Kondo, T. Miura, Y. Tanaka, Effective nonlocal kernels on Reaction-diffusion networks, Journal of Theoretical Biology, 509, 110496 (2021)
• (Refereed) S.-I. Ei, H. Ishii, M. Sato, Y. Tanaka, M. Wang, T. Yasugi, A continuation method for spatially discretized models with nonlocal interactions conserving size and shape of cells and lattices, Journal of Mathematical Biology, Springer, 81, pp981–1028 (2020)
• (Refereed) H. Ninomiya, Y. Tanaka, H. Yamamoto, Reaction-diffusion approximation of nonlocal interactions using Jacobi polynomials, accepted in Japan Journal of Industrial and Applied Mathematics, Springer, 2017
• (Refereed) Y. Tanaka, H. Yamamoto, H. Ninomiya, Mathematical approach to nonlocal interactions using a reaction-diffusion system, Development Growth and Differentiation, 59, a special issue: Mathematics, Physics, and Engineering in Biology, pp 388-395 (2017)
• (Refereed) H. Ninomiya, Y. Tanaka, H. Yamamoto, Reaction, diffusion and non-local interaction, J. Math. Biol., Springer, 75, 1203–1233 (2017)
• (Refereed) Tanaka, Y, Mimura, M, Ninomiya, H: “A reaction diffusion model for understanding phyllotactic formation”, Japan Journal of Industrial and Applied Mathematics, Springer, 33, pp183-205 (2016)