Juliane Fonseca de Oliveira
University of Porto, Portugal
Title: Dimensionality of pattern formation in symmetric physical systems
Biography
Biography: Juliane Fonseca de Oliveira
Abstract
In the study of pattern formation in symmetric physical systems a 3-dimensional structure in thin domains is often modelled as 2-dimensional one. As a contrast, in this talk we use the full 3-dimensionality of the problem to give a theoretical interpretation and possibly decide whether the pattern seen in such systems naturally occur in either 2- or 3- dimension. For this purpose, we are concerned with functions in 3-dimention that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. In particular, we introduce a formalism to explain how the study of bifurcation theory, in the context of symmetries, is applied to the theory of projection we present.