ProbatoriosFacultaddeCienciasMy name is Rosa Maria Vargas Magaña I recently (August 2017) received my Ph.D. in Mathematical Sciences from the Universidad Nacional Autónoma de México at (IIMAS), working on non-local shallow water wave models over variable topography under the supervision of Dr. Panayotis Panayotaros
My principal research interests are: Nonlinear waves, Hamiltonian systems, Surface water waves, Pseudo-dierential operators, Numerical analysis, Fluid dynamics, Geophysical and Engineering applications.
In my doctoral dissertation, I proposed a Hamiltonian non-local shallow water wave model for flow over variable topography using the Hamiltonian formulation of the free surface potential flow introduced by Zakharov-Craig-Sulem. I then approximated the Dirichlet-Neumann (DN) operator for the Laplacian in the fluid domain appearing in the kinetic energy part of the Hamiltonian.
Explicit expressions for the DN operator for variable depth were derived by Craig, Guyenne, Nicholls, Sulem and other authors. Nevertheless, such expressions are complicated when strong variations of topography are considered. The model proposed in my dissertation is a simple approximation to the DN operator that involves a pseudo-dierential operator which has the same structural features of the DN operator for variable depth. This leads to a bidirectional nonlocal Whitham-Boussinesq-type shallow water wave model for variable topography that can be used for 2-D and 3-D flow.
With my collaborators, we published three articles :
- Linear guided modes for channels with constant cross section and approximate Dirichlet-Neumann operators. LinearmodesforchannelsandapproxDNoperatorsLinearmodesforchannelsandapproxDNoperators
- A Whitham-Boussinesq long wave model for variable topography with P. Panayotaros. (Wave Motion, vol.65, pp.156-174, 2016.)
Ph. D Thesis: Nonlocal shallow water wave models over variable topography Advisor: Panayotis Panayotaros
Master thesis: “Planar Cantor sets with Hausdor dimension greater than one
with projections in all directions with positive Lebesgue measure” (In Spanish)“Constelaciones en el plano : Sombras que engañan a los observadores“.
Advisor : Dr. Héctor Méndez LangoReview
Bachelor thesis: (In Spanish) “Aspectos dinámicos y topológicos de la herradura de Smale”
Advisors : Dr. Héctor Méndez Lango & Dr. Jefferson Edwin King Dávalos
My Curriculum Vitae is available CV2019
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