Wave propagation and pattern formation phenomena in biological models
Tuesday, June 15 at 09:30am (PDT)Tuesday, June 15 at 05:30pm (BST)Wednesday, June 16 01:30am (KST)
Bogdan Kazmierczak (Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland), Je-Chiang Tsai (Department of Mathematics, National Tsing Hua University, Taiwan)
Pattern formation is a fundamental phenomenon ubiquitous in many branches of natural sciences, like physics, chemistry, geography, biology, and also in social sciences. It is a paradigm that pattern formation processes are a sine qua non condition for life origin, because they enable the formation of germ layers, tissues and then highly specified organs, like skin, bones, brain or heart. Moreover, similar spatial patterning occur inside cells as a result of, e.g. response to external stimuli. It is thus extremely intriguing to design mathematical models which are able to explain, how (and under what conditions) the spatial patterns can be developed. Very often the patterning phenomena are carried out via traveling waves, which can be pinned (stopped), in particular, due to geometrical properties, like a local curvature of the boundary or growth of the region. Biological models leading to formation of patterns and/or wave propagation can shed an explanatory light and provide a lot information about the evolution and the final (asymptotic) states of the systems corresponding to many phenomena in embryology, virus spreading or tumour dynamics.