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DTSTAMP:20260606T111404Z
SUMMARY:Junior Analysis Seminar: Carles Falcó (Oxford)
DESCRIPTION:Title\nNonlocal models of cell-cell adhesion and their Cahn-Hil
 liard approximation\nAbstract\n\nCell-cell adhesion is one the most fundam
 ental mechanisms regulating collective cell migration during tissue develo
 pment\, homeostasis and repair\, allowing cell populations to self-organis
 e and eventually form and maintain complex tissue shapes. Adhesive forces 
 are highly linked to the cell geometry and often\, continuum models repres
 ent these by nonlocal attractive interactions.\nIn this talk\, I will expl
 ain how such models can be approximated by Cahn-Hilliard type equations in
  the limit of short-range interactions. The resulting model is a local agg
 regation-diffusion equation\, resembling a thin-film type equation\, and n
 umerical simulations in one and two dimensions reveal that it still shows 
 the diversity of patterns observed both in experiments and in previously u
 sed nonlocal models. Moreover\, this local equation can be written as grad
 ient flow with respect to the 2-Wasserstein metric\, which motivates the u
 se of variational methods to prove existence. The existence results also r
 ely on a bound from below of the associated free energy functional\, which
  is given by a suitable functional inequality. Finally\, I will discuss ge
 neralisations of the existence theory to the case of systems of interactin
 g populations.\n\nPlease note that the seminar will take place in person i
 n room 642 of Huxley Building.\n\nClick here to get to the Junior Analysis
  Seminar webpage.
URL:https://www.imperial.ac.uk/events/166102/junior-analysis-seminar-carles
 -falco-oxford/
DTSTART;TZID=Europe/London:20231004T140000
DTEND;TZID=Europe/London:20231004T150000
LOCATION:642\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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