1. Collaboration with clinical medicine

We are collaborating with physicians to find solutions to medical problems based on mathematical science. This research is supported as a CREST project by the Japan Science and Technology Agency (JST). Our targets include the following. This project will contribute to high-performance clinical diagnoses through construction of decision-making tools including mathematical modeling, simulation technology, statistical analysis, image processing, and inverse analysis.

2. Mathematical approach to environmental problems

We are collaborating with environmental scientists, agricultural scientists, limnologists and many other scientists and engineers working to resolve environmental issues. Here also, our main tools are mathematical modeling and numerical simulations, which can be powerful tools for ascertaining behaviors related to environmental problems. Our targets include the following. In addition to domestic collaboration, we are collaborating with researchers from the Finnish Environment Institute supported by the Japan Society for the Promotion of Science (JSPS).

3. Numerical simulation methods

Widely various numerical methods are used, such as finite element, finite difference, and finite volume methods. We are working out the most appropriate means of simulations depending on the targeted problems. The whole procedure from mathematical modeling to programming by C, Python, FORTRAN, etc. via discretization processes, should be connected seamlessly. Our targets, in addition to #1 and #2 above, include flows around candles, flows around rotating rugby footballs, and sound fields around obstacles.

4. Scientific visualization methods

Because the results of computational simulations are rows of numerical values, visualization techniques have been important tools for use with computational simulations. Scientists have been presenting visualizations of their results obtained using 1D graphs, 2D contour lines, 3D contour surfaces and volume rendering techniques, 2D/3D vector arrows, 2D/3D passive particle paths, etc. including photo-realistic rendering techniques and ray-tracing algorithms mainly developed in computer graphics (CG) fields. In recent years, a new generation of scientific visualization techniques called "virtual reality" has been proposed. Several such technologies exist such as 3D/4D (3D + time axis) stereoscopic vision on screens with and without special eyewear. We are applying several visualization techniques in our daily research work and are finding ways of producing comprehensible renditions of our numerical results.