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Past research

List of papers

List of talks

Research topics I am working on now


Source: M. Heiss et al., SPIE 2013
Wetting and dynamics of surfaces with anisotropic energies
A problem important in crystal growth or development of materials with nanostructures such as nanowires. The aim is to mathematically understand motion of interfaces with energy depending on the orientation of the interface, and to develop efficient numerical methods for its simulation.
This is joint work with X. Xu and Y. Di (Chinese Academy of Sciences).
  • Short explanation is here.

Hyperbolic mean curvature flow
With E. Ginder (Meiji University)
Hyperbolic interface evolution
Evolution of interfaces of hyperbolic type, such as curvature accelerated motion, have only started being studied, although it applies to many areas from water waves to string theory. We are analyzing such problems from the mathematical and numerical point of view.
This is joint work with E. Ginder (Meiji U.) and R. Mohammad (Kyoto U.).
  • Short explanation is here.

Cellular pattern formation
With R. Mohammad (Kyoto U.)
Modeling of cellular rearrangement in morphogenesis
In many cases epithelial morphogenesis can be modeled by the motion of interfacial networks. In this research we are interested in elucidating the principles behind the mysterious morphogenesis phenomenon but also in mathematical and numerical aspects related to motion of interfacial networks with nonconstant surface tensions. In particular, we are interested in the analysis of the coupled model between interface motion and time-dependent chemical field.
This is joint work with R. Mohammad (Kyoto U.), H. Togashi (Kobe U.), H. Murakawa (Kyushu U.) and A. Rey (ENSTA ParisTech).

Kinks in Mg85Zn7Y8
Source: K. Hagihara et al., Mater. Lett. 2018
Mathematical modeling of kink formation in mille-feuille structured metallic materials
When alloys of magnesium and rare earth metals are compressed, kinks (wedge-like structures) are formed, which leads to a significant strengthening of the material. The mathematical problem here is to reveal the mechanism behind formation of such kind of unexpected microstructure and its role in the strengthening process. Our plan is to use variational approach via a multi-well energy with interfacial terms.
This is joint work within the JSPS Grant-in-Aid for Scientific Research on Innovative Areas.

Simulation of moving filaments
Analysis of co-dimension 2 geometrical motions
When we want to understand motion of vortex rings in fluid or motion of dislocation and disclinations in materials, it is necessary to think of motions of 1-dimensional curves in 3-dimensional space. I would like to answer the following questions about motion of such filaments in case when topological changes occur: How to define the motion mathematically in the parabolic and hyperbolic cases? How to design an efficient numerical algorithm for their simulation?

COPD simulation
Simulation of COPD disease
We try to understand the mechanism of the development of the lung disease called COPD through mathematicl modeling.
This is joint research with professors Atsuyasu Sato, Susumu Sato and Naoya Tanabe (Kyoto U., Medical faculty).