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Human Mathematical Sciences Lab
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The lab studies mathematical modeling, translating the motion of droplets and cells into equations.
AboutAbout the lab
Seeing phenomena through mathematics.
The lab studies methods for understanding natural and biological phenomena from the viewpoint of mathematical sciences.
A mathematical model imitates a phenomenon with equations, and when it is reproduced on a computer through numerical computation, the mechanisms hidden in the phenomenon become visible.
Adding mathematical analysis makes it possible to extract mathematical structures shared by different phenomena.
The lab investigates the motion of droplets and particles, the barrier function of the epidermis, and the motion of cells, in collaboration with experimental groups and companies.
Key terms
- Mathematical model
- A description of how a phenomenon works, expressed in equations. It is run on a computer to reproduce the phenomenon.
- Reaction-diffusion system
- Equations that describe how substances spread while reacting. Patterns such as stripes and spots appear.
- Finite element method
- A method that divides an object into small elements and finds approximate solutions of equations on a computer.
NewsLab news
A paper by Assistant Professor Ishii and colleagues is published in Journal of Fixed Point Theory and Applications
A paper by Project Assistant Professor Chiba and colleagues is published in Physica A: Statistical Mechanics and its Applications
A paper by Assistant Professor Ishii and colleagues is published in Journal of Mathematical Biology
Prof. Nagayama receives the Mimura Prize in Mathematical Sciences of Phenomena
A paper by Assistant Professor Ishii is featured in a press release
ResearchResearch themes
The lab builds mathematical models of nonlinear and biological phenomena and works on their mathematical analysis. It also carries out joint research with companies, including the Hitachi-Hokudai Lab, aiming to connect mathematical sciences with society.
*Illustrative imageMathematical sciences of self-propelled systems
In collaboration with experimental groups, the lab builds mathematical models of systems that move while changing themselves and their surroundings, and studies them with computer-assisted analysis that incorporates numerical bifurcation computation and similar methods. The subjects have ranged from camphor particles moving through changes in surface tension to the interaction of multiple droplets in a reaction-diffusion field.
*Illustrative imageMathematical modeling of epidermal structure
The lab is building a mathematical model of the barrier function of the skin's epidermis, as joint research with a company. Mathematical analysis of the barrier function is expected to be applicable to anti-aging measures and measures against skin diseases.
*Illustrative imageNumerical analysis of partial differential equations
This research proposes how to carry out numerical computation for problems that existing software cannot compute, and shows how good those methods are. It investigates the mathematical properties of the finite difference method, the finite element method, the discontinuous Galerkin method and others.
*Illustrative imageNonlocal effects and pattern formation
The lab works on reaction-diffusion systems with nonlocal effects, in which states at distant locations influence each other, and aims to clarify how patterns are formed from them. Taking peristalsis of the esophagus as an example, it has built a mathematical model and worked on a theoretical explanation of the phenomenon.
MembersFaculty
The lab's members consist of faculty, doctoral, master's and undergraduate students, visiting researchers, and technical assistants.As of 2026
- ProfessorMasaharu Nagayama
- Associate ProfessorYuki Ueda
- Assistant ProfessorHiroshi Ishii
- Project Assistant ProfessorKosuke Sugita
- Project Assistant ProfessorYumihiko Sanno
- Project Assistant ProfessorYuki Chiba
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Diplora strigosa” LASZLO ILYES (laszlo-photo) from Cleveland, Ohio, USA / CC BY 2.0 (cropped)
- Mathematical sciences of self-propelled systems: “Aqua Spout” JJ Harrison (https://www.jjharrison.com.au/) / CC BY-SA 3.0 (cropped)
- Mathematical modeling of epidermal structure: “Normal Epidermis and Dermis with Intradermal Nevus 10x-cropped” Normal_Epidermis_and_Dermis_with_Intradermal_Nevus_10x.JPG: Kilbad derivative work: Fama Clamosa (talk) / Public domain (cropped)
- Numerical analysis of partial differential equations: “Fictitious domain method simulation” Greegg0 / CC0 (cropped)
- Nonlocal effects and pattern formation: “Giant Puffer fish skin pattern” Chiswick Chap / CC BY-SA 3.0 (cropped)
- Related lab (Mathematical Sciences Lab (Sakai)): “3Dpercolation” David Adams / CC BY 3.0 (cropped)
- Related lab (Analysis (Kubo) Lab): “Surface waves” Roger McLassus / CC BY-SA 3.0 (cropped)
- Related lab (Nakano Lab): “Hurricane Isabel from ISS” Image courtesy of Mike Trenchard, Earth Sciences & Image Analysis Laboratory, NASA Johnson Space Center. / Public domain (cropped)
- Related lab (Mathematical Sciences (Masaki) Lab): “Baltic Sea Wave (Cien Water)” Marek Nowocień / CC BY 2.5 (cropped)
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