Seminars & Colloquia Calendar

Abstract: One of the dreams of materials scientists is to make a novel materials through the design of atomistic scale, however most of the modern composite materials is very heterogeneous in order to make it strong via network structure like epoxy resin matrix with carbon fibers used in the aircraft. Those are far from crystal structure nor completely random so that it is not apriori clear what type of mathematical concepts is appropriate to describe it, especially medium-range structure. As for the static profile, recent statistical methods as well as topological approach TDA clarify some aspects of it. On the other hand, the performance of the materials, especially its dynamic robusness against mechanical stress remains open and still heavily depends on trials and errors in the laboratories. The difficulty lies in that, firstly the lack of good macroscopic mathematical model to describe dynamical processes, secondly it is not clear how to implement the microscopic heterogeneity into the macroscopic model, thirdly how to extract an appropriate mathematical descriptor that can measure and predict the strength of it and even allows us to design novel materials. I would like to present a case study in this direction in the context of cracking phenomena for brittle materials. The stage is still early phase, however it suggests many interesting questions and challenge not only for for materials scientists but for mathematicians.