Friday, March 26, 2004

Travis Garrett: Spring 2004 Research Summary.

I am still working on my first large project, a 3-D computer simulation of a binary star inspiral using a co-rotating reference frame and a scalar gravity approximation (Watt&Misner gr-qc/9910032). I think the code is almost finished: the evolution for the individual spherical components works well (the hardest part probably being transparent boundary conditions - always some numerical reflection), and the synthesis code works well also. The primary problem is getting the proper evolution of the system since it depends on very delicate spatial derivatives (evolving using geodesics...). I am trying to get around this through several different approximation methods and I suspect I will be successful soon. When I am I will write my first paper on it, and go on to have my prelim. The PhD project will be on the same problem, only using tensor fields. I want to write at least 4 papers in my remaining 2 years here, at least a couple on the main research I describe here, but a couple of shorter ones also - talking to Martin Bojowald I have some ideas on evolving through singularities using a discrete mesh at the Planck scale (and as a relativitist I should have some grounding in quantum loop gravity, which I'm studying now), on a similar line I'm looking at Jack's work on quantum foam, might be good for a quick paper, and I also still have an interest in evolving large systems of particles - like globular clusters or colliding galaxies, and have some code written for those, might get a quick paper out on those also. I'm also 60% the way through a formal write-up of Statistical Metaphsyics, where I derive being an observer from all mathematical structures, although I'm not sure where I'd publish it (but Max Tegmark thinks I should publish it somewhere, perhaps a philosophy journal). In any case, I've got a lot to do.

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