Research Institute for Electronic Science, Hokkaido University


LAST UPDATE 2017/02/25

  • 研究者氏名
    Researcher Name

    長山雅晴 Masaharu NAGAYAMA
    教授 Professor
  • 所属
    Professional Affiliation

    Research Institute for Electronic Science, Hokkaido University

    Mathematical Modeling Lab.
  • 研究キーワード
    Research Keywords

    Mathematical modeling
    Reaction-diffusion systems
    Numerical simulations
    Numerical bifurcation analysis
Research Subject
Mathematical modeling and analysis of nonlinear phenomena

研究の背景 Background


Through a combination of mathematical modeling, numerical simulation and analysis of concrete phenomena, the mathematical sciences provide a framework for extracting underlying structures which can be used in understanding the common and essential mechanisms of various phenomena. Here, mathematical modeling of the phenomena is of great importance and a main hurdle lies in establishing appropriate methodologies for its analysis.

研究の目標 Outcome


The main objective of our research is to provide theoretical clarification of mechanisms giving rise to different nonlinear phenomena. Here we utilize methods of mathematical modeling, simulation and analysis. Concrete examples include: the self-driven motion of particles and liquid droplets, division and motion of biological cells, waves observed in developmental processes, nuclear motions observed in mouse brain development, formulation of homeostasis in the epidermal barrier function, and combustion synthesis reactions. We also develop numerical methods for analyzing mathematical models.

研究図Research Figure

Fig.1. Numerical results regarding the mathematical model for self-driven motions. (i) translational motion of a circular camphor disk (ii) motion of pinwheel-shaped camphor (iii) rotational motion of a comma-shaped camphor. Fig.2. Numerical result of the mathematical model for epidermal structure. Even if the shape of the skin changes, the structure of the keratin cells is maintained. Fig.3. Numerical simulation of a combustion wave arising in our model for combustion synthesis

文献 / Publications

Physica D, 272, 39-50 (2014), PLoS ONE 9(3): e92650 (2014), J. Materials Synthesis and Processing 9(3), 153-163 (2001)