Speaker
Maria Aguareles

Description In this talk we will provide a description for rigidly rotating spirals in some Fizhugh-Nagumo systems based on the fact that one of the unknowns develops abrupt jumps in some regions of the space. The core of the spiral is delimited by these regions and in particular we assume that there is an inner circle where the system remains at equilibrium while the spiral rotates. The description of the spirals is made using a mixture of asymptotic and rigorous arguments and we will present several open problems whose rigorous solution would provide in the general question of the persistence of spiral wave patterns.

Speaker
Álvaro Kohn Luque

Description During embryonic vasculogenesis, the earliest mechanism of blood vessel morphogenesis, isolated vascular cell progenitors called angioblasts assemble into a characteristic network pattern. So far, however, the mechanisms underlying the coalescence and patterning of angioblasts remain unclear. In this talk, I will discuss a number of mathematical and computational approaches to model and simulate early vascular patterning. Particular attention will be paid to describe a hybrid cell based model that we use to explore the dynamics of network formation as well as the role of cell shape and cell density in this process. I will conclude by discussing some experimental validation efforts carried out so far as well as other related studies still in progress.

Speaker
Robert Castelo

Speaker
Ruben Requejo

Speaker
Ivan Santamaría Holek

Description In this talk we present a novel model to describe and explain the contribution of higher order multipoles and different relaxation mechanisms to non-Debye dielectric relaxation. The model is formulated using mesoscopic nonequilibrium thermodynamics that leads to a Fokker–Planck description incorporating memory effects through integral relations containing memory kernels. A connection with fractional Fokker–Planck descriptions is established. The model is developed in terms of the evolution equations for the first two moments of the distribution function that are used to calculate the expressions for the complex susceptibilities in terms of the frequency and the wave number. Different memory kernels are considered and used to compare with and interpret experiments of dielectric relaxation in different glassy systems.