I am a PhD. graduate student interested in using computers to understand the dynamics of complicated partial differential equations in 2+1 and 3+1 dimensions. My supervisor is Matthew Choptuik.
I was born in Mexico city in 1973. I received my
B.Sc. in Physics in 2002 from the National University of Mexico (UNAM). I am completing my
Ph.D studies in Physics at the University
of British Columbia, in Vancouver, Canada. My research and skills
have benefited from several internships since my undergraduate years (CERN, Summer
Program 1996),
more
recently
at
the
Max-Planck
Institute for Gravitational Physics, in Golm, Germany (2008) and The
Perimeter
Institute
for
Theoretical
Physics (2010) in Waterloo,
Canada. Before starting my doctoral studies I worked as a Linux server
specialist at my home university's Institute
for
Mathematical
Research,
and later at Hewlett
Packard
Mexico.
My PhD. research project consists in the study of dynamics of certain type of solutions to the equations of motion of non-linear classical field theories. The scattering of solitons and their time-dependent evolution in a non-integrable classical or quantum field theory remains an intractable and difficult problem. This is where numerical methods offer an effective tool to deal with the complexity of the equations, which require sophisticated algorithms and extensive runtime and storage resources. Independently of their physical applications, the non-linear nature of the solutions provides a rich phenomenology, interesting in its own right.
These problems are expressed as hyperbolic time-dependent non-linear partial differential equations (PDEs) in 2 and 3 spatial dimensions, supplemented by suitable boundary conditions. To solve them, we apply finite difference techniques and iterative relaxation methods such as Newton-Gauss-Seidel. However, the physical domain spans over several time and space scales. The appropriate optimization of computational resources is achived by means of parallel adaptive mesh refinement (PAMR) techniques. They implement a hierarchy of meshes with different resolutions, concentrating resources on areas with high phenomenology using a modified Berger-Oliger algorithm.benjamin at phas.ubc.ca Mon Jan 2 08:29:52 PST 2012