About me

ProbatoriosFacultaddeCienciasFotoyoMy 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 :

  1. Linear guided modes for channels with constant cross section and approximate Dirichlet-Neumann operators. LinearmodesforchannelsandapproxDNoperatorsCaptura de pantalla 2019-02-24 a la(s) 17.56.48LinearmodesforchannelsandapproxDNoperators

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  2. A Whitham-Boussinesq long wave model for variable topography                         with  P. Panayotaros. (Wave Motion, vol.65, pp.156-174, 2016.)SWgauss
  3. Constelaciones en el plano   with H. Méndez Lango (Miscelanea Matematica 55 65-88, 2012.) [here]Const1


Theses:

Ph. D Thesis: Nonlocal shallow water wave models over variable topography        PORTADATESIS      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“.TesinaCara
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 DávalosHerradura2


My Curriculum Vitae is available CV2019Captura de pantalla 2019-02-24 a la(s) 18.29.39

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