Tournus Magali – Groupe de Travail Guide d’ondes, milieux stratifiés et problèmes inverses (GOMS)

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Date(s) - 28 février 2018

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Title :Estimating the division rate and kernel in the fragmentation equation.Biological application : Amyloid fibrils fragmentation. Abstract :The question is to determine what is the effect of a turbulent agitation on the fragmentation rate (what is the probability that a fibril of given length breaks apart ?) and fragmentation kernel (where a fibril is more likely to break apart ?) in a suspension of proteins of amyloid types.The talk will be composed with two parts. In the first part, I will focus on the new experiments which were performed at Kent University, and on how the data they provide can be used. On the second part, I will focus on the well-posedness of the inverse problem. In particular, I aim to detail the theoretical recontruction formula we obtain for the fragmentation kernel. One of the delicate points is to prove that the Mellin transform of the asymptotic profile never vanishes, which is done using the Wiener-Hopf representation.[