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Interested in getting involved in computational research? Interested in computers, math, or black holes? My research brings together all three of these fields and there's much work to do:

*nonlinear models (ODEs)*--Besides gravity, there are a number of mathematical models that are quite interesting and require computational modeling to really understand them. These models are a bit simpler than gravity, and yet their phenomena are not well understood. Examples include Q-Balls, Skyrmions, the Faddeev-Skyrme model for Hopf solitons, monopoles, domain walls, and strings. For some of these models, once can find particular solutions with certain symmetries by numerically solving ordinary differential equations (ODEs).

*nonlinear models (PDEs)*--One sees ODEs in introductory calculus, and PDEs (partial DEs) generally aren't introduced until the third semester with vector calculus. Though more ambitious, solving PDEs allows one to model the evolution of various models. There are also mathematical questions (e.g. of global existence) with a variety of geometrically motivated models and with the nonlinear Schroedinger Equation.

*exploring parameter space*--We have codes capable of modeling neutron stars and black holes with magnetic fields, and there are a huge number of scenarios to explore by running the code over and over. It takes someone to look at the results, interpret them, and re-run with different parameters. This by-passes much of the nitty-gritty in terms of the mathematical equations and the programming, but still requires gaining experience working with numerical data and understanding physics from noise and error.

*distributed computing*--supercomputers these days generally consist of large numbers of individual "computers" networked together. To be able to treat them as a single machine for computing purposes, one needs to be able to write software that "talks" to its constituent pieces. I do this with something called message passing interface (MPI) and also OpenMP. The recent advent of parallel computing using graphics processors has much potential using the industry standard OpenCL. I have not yet explored this possibility, and it would be nice to work with a student to help figure out how it works with my needs.

Last updated June 8, 2013. |
Copyright 2000-2014 S.L. Liebling |

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