Local: Sala C119
Palestrante: Marcos Cossarini (IMPA)
Título: Discrete geometry of surfaces towards the filling area conjecture
Resumo: In 1983, Gromov conjectured that the hemisphere has smallest area among Riemannian surfaces that fill isometrically a circle of given length. We discuss the history of the problem and present a discrete version, where a cycle graph of length 2n is filled isometrically by a combinatorial square-celled surface with the least possible number of cells, conjectured to be n(n-1)/2. The discrete problem is equivalent to Gromov's filling area conjecture, as extended by Ivanov to admit filling surfaces with self-reverse Finsler metrics, because every such continuous metric can be replaced by a square-celling whose lengths and areas approximate the original values as precisely as desired (quasi-isometrically with arbitrarily good additive and multiplicative constants).
Palestrante: Diego Sanhueza
Local: Sala C116
Palestrante: Fernando Pereira Duda(COPPE-UFRJ)
Título: Continuum mechanics of polymer gels
Resumo: A polymer gel is a two-component material composed of an elastic cross-linked polymer network and a fluid that permeates the interstices of the network. Such materials exhibit unusual and complex phenomena as a result of the coupling between large deformation and fluid permeation.
In this talk, we apply the methods of continuum mechanics to describe the mutual interaction between large deformation and fluid permeation in polymer gels. The basic tenet here is the conceptual view of this body as a platform for two interdependent phenomena: a macroscopic (mechanical) phenomenon due to the deformation of the network and a microscopic (chemical) phenomenon due to the permeation of the fluid through the network. Applications of the theory are provided within the context of volumetric phase transition, cavitation, and pressure-driven fluid flow through a gel-filled channel.