The building blocks of mathematical morphogenesis were put
several decades ago in the seminal works of Turing and Eden. Their goal
was understanding how a macroscopic structure, in particular one
breaking the initial homogeneity, could arise out of a multiplicity of
simple interactions. While the approach of Turing implied the use of
reaction-diffusion equations, Eden concentrated on a probabilistic
abstraction of a developing cell colony. In particular, he studied the
architecture of a lattice cell colony to which new cells were added
following certain probabilistic rules. The objective was studying the
asymptotic colony profile. The original Eden problem can be greatly
generalized by means of the use of stochastic partial differential
equations. They allow a systematic study of the properties of the colony
periphery, particularly of the interface fluctuations. In this talk we
will summarize our recent progress in this field, concentrating on the
properties of the realizations of the stochastic growth process. Our
goal is unveiling under which conditions the developing radial cluster
asymptotically weakly converges to the concentrically propagating
spherically symmetric profile.
Coffee and cookies will be served 15 minutes before the start of the seminar
Detalles de contacto:
Ernesto M. Nicola Contact form