Aaryn Tonita, B.Sc.

Department of physics and Astronomy

6224 Agricultural Rd.

Vancouver BC

V6T 1Z1

 

 

Office phone: 1-604-822-2095

atonita@physics.ubc.ca

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Research

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Feb 1

Feb 28

Mar 16

This is the current state of my research and intentions as of the date selected.

Current State:

1. Working program:
   • adaptively polygonizes a parametric curve to minimize open angle between two consecutive line segments, currently uses random numbers so that no two approximations are alike.
   • using a galerkin finite element method, computes general relativistic initial data for axisymmetric spacetime using the above curve as a generator for a marginally trapped surface of revolution.
   • uses bisection method to find point on the actual parametric curve that is closest to a given boundary point on the approximating polygon
2. Parameters:
   • theta0 = opening angle criteria, the closer this is to pi or 180 degrees, the more accurate the approximating polygon will be.
   • hmax = "maximum size" of a given finite element, problems occur if this is taken too small
   • grade = maximum ratio of the areas of two adjacent elements
   • rmax = radius at which the discretization truncates spacetime.
3. Interface:
   • program is called either from the command line (usage statement is included) or from a perl script which reads a config file and reads the above parameters.
4. Specification of curve:
   • hard coded in source code and specified through the make file.

To do:

1. On the program
   • consider unimplementing random number generator in adaptive polygonisation.
   • clean up source code and add comments
2. Specification of curve:
   • Implement a perl script to automatically switch curves and make binary
3. Physics:
   • Implement an apparent horizon finder.
   • use the apparent horizon to place a lower limit on the mass, compute the ADM mass for an upper limit.
   • run a large number of various shaped apparent horizons.
4. Writing:
   • begin outline phase of thesis writing