"Singular limit analysis to reaction diffusion systems with applications to biological problems"
講演者 三村 昌泰 / 広島大学大学院
The purpose of this talk is to investigate the singular limit of reaction-diffusion systems, or more precisely the fast reaction limit of ecological and biological systems. It often turns out that such systems converge to new limiting systems, which described by free boundary problems, nonlinear diffusion systems and cross-diffusions. As an application of the fast reaction limit, we discuss the relationship between Turing’s instability and cross-diffusion induced instability.
京都駅前セミナー 招聘講演 15:10－16:00
座長：岩見真吾 / 九州大学大学院 理学研究院生物科学部門
"Bridging a mesoscopic inhomogeneity to macroscopic performance of amorphous materials in the framework of the phase field modeling"
講演者 西浦 廉政 / 北海道大学
One of the big challenges in materials science is to bridge microscopic or mesoscopic properties to macroscopic performance such as fracture toughness. This is particularly interesting for the amorphous materials such as epoxy resins because their micro/meso structures are difficult to characterize so that any information connecting different scales would be extremely useful. At the process level, the polymerization rate can be changed experimentally that influences a lot over the performance of materials, however, it is known that the maximum toughness does not always appear at the maximum polymerization rate, which suggests that some differences in the micro/meso-scopic structure affect the macroscopic property behind. The goal of my talk is to present a framework to bridge a mesoscopic observation of X-ray CT and the criterion of fracture toughness, which is computable in the framework of the phase field modeling. First we classify the data of the X-ray image with different polymerization rate by using two different methods: one is SVD and the other is persistent homology. Secondly we compute a crack propagation of each sample and evaluated a scalar value called the effective toughness (ET) via J-integral, which is one of the good candidates indicating a toughness of material. It turns out that ET reflects the performance of each sample and consistent with the experimental results. There remains many open problems and my presentation is the first step toward our final goal. This is a joint work with Edgar Avalos, Shuangqaun Xie, and Kazuto Akagi of Tohoku University.
［ JST MIRAI 共催 ］
"Mathematical sciences are expanding & cooperating with other sciences"
坂上 貴之 / 京都大学
岩見真吾 / 九州大学
At one time, mathematical sciences were essentially ignored by other communities, but in the last 10 years it has become an important subject to aid several material and life sciences area. Mathematical sciences including applied mathematics and mathematical biology in tandem with rigorous real data, offers an opportunity to cooperate with other sciences. In our symposium collaborating with JST MIRAI projects heading by Sakajo and Iwami, we would like to show how mathematical sciences are expanding and improve our life with examples of quantitative data analysis.
"Topological Flow Data Analysis: Theory and applications" 坂上 貴之 / 京都大学大学院 理学研究科
"Theory, software, and applications of persistent homology" 大林 一平 / 理化学研究所 革新知能統合研究センター
"Multiscale mathematical model for quantative data analysis in life sciences" 岩見 真吾 / 九州大学大学院 理学研究院生物科学部門
"A mathematical framework for inferring consensus formation in biological processes" 中岡 慎治 / 北海道大学 先端生命科学部