OxPDE Lunchtime Seminar
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Thu, 28/01/2010 12:30 |
François Genoud (OxPDE, University of Oxford) |
OxPDE Lunchtime Seminar  |
Gibson 1st Floor SR |
| I will present in detail the celebrated theories of Onsager (1949) and Maier-Saupe (1958) explaining the phenomenon of long-range orientational order in nematic liquid crystals. The models are not rigorous from the mathematical viewpoint and my talk will stay at the formal level. If time permits, I will suggest directions towards a rigorous mean-field theory. | |||
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Thu, 04/02/2010 12:30 |
Myoungjean Bae (Northwestern University, USA) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| One of important subjects in the study of transonic flow is to understand a global structure of flow through a convergent-divergent nozzle so called a de Laval nozzle. Depending on the pressure at the exit of the de Laval nozzle, various patterns of flow may occur. As an attempt to understand such a phenomenon, we introduce a new potential flow model called 'non-isentropic potential flow system' which allows a jump of the entropy across a shock, and use this model to rigorously prove the unique existence and the stability of transonic shocks for a fixed exit pressure. This is joint work with Mikhail Feldman. | |||
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Thu, 11/03/2010 14:30 |
Radu Ignat (Université Paris-Sud 11) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| The aim of this talk is to analyze energy functionals concentrated on the jump set of 2D vector fields of unit length and of vanishing divergence. The motivation of this study comes from thin-film micromagnetics where these functionals correspond to limiting wall-energies. The main issue consists in characterizing the wall-energy density (the cost function) so that the energy functional is lower semicontinuous (l.s.c.). The key point resides in the concept of entropies due to the scalar conservation law implied by our vector fields. Our main result identifies appropriate cost functions associated to certain sets of entropies. In particular, certain power cost functions lead to l.s.c. energy functionals. A second issue concerns the existence of minimizers of such energy functionals that we prove via a compactness result. A natural question is whether the viscosity solution is a minimizing configuration. We show that in general it is not the case for nonconvex domains. However, the case of convex domains is still open. It is a joint work with Benoit Merlet, Ecole Polytechnique (Paris). | |||
