2018-06-11 Seminar Report

Prof. Yasumasa Nishiura gave a lecture at iTHEMS Colloquium which was taken place June 7th. His lecture was entitled "On the interplay between intrinsic and extrinsic instabilities of spatially localized patterns" and various patterns emerge from rather simple sets of differential equations were introduced. According to the lecture, spatially localized dissipative structures are observed in various fields, such as neural signaling, chemical reactions, discharge patterns, granular materials, vegetated landscapes, binary convection and block copolymer nanoparticles. Now, while these patterns are much simpler than single living cells, yet they seem to inherit several characteristic "living state" features, such as generation of new patterns, self-replication, switching to new dynamics via collisions and adaptive morphological changes to environments. Prof. Nishiura explained that these behaviors stem from an interplay between the intrinsic instability of each localized pattern and the strength of external signals. The global geometric interrelation amongst all relevant solution branches of a corresponding system with approximate unfolding parameters was explored. He argued that a global geometric structure formed by all relevant solution branches gives us much more insight rather than conventional PDE approaches. The theme of the lecture was most pertinent to iTHEMS colloquium and the audience was fascinated by the power of the mathematical insight applied to varied subjects and phenomena.

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