Relativity

The last major remaining test of Einstein's Theory of Relativity, and the holy grail of modern relativity, is the direct detection of gravitational waves. Even beyond probing and elucidating the fundamental nature of space and time, gravitational wave detection will give us a new window on the universe and usher in a new era in astronomy.
Gravitational waves are propagating ripples in space-time (an artist's rendition is pictured on the right; image taken from the LISA website).

My research involves studying what happens when two black holes collide.
Because gravity waves are weak, and because they must travel great distances to reach our detectors on Earth, an ideal source of detectable waves is a cataclysmic gravitational event, such as the collision of two black holes. Understanding what happens when two black holes collide has been an elusive problem.
My approach is novel in that I'm using a state-of-the-art finite element technique with rational spline basis functions and a nonlinear cutting plane solver, with which I hope to achieve computational results that were previously out-of-reach.

Gravity waves were first indirectly observed in the Nobel prize-winning work by Hulse and Taylor in the 1970's. Modern detectors are being built to detect them directly, such as LIGO at Caltech, LISA by NASA and ESA, and others around the world like VIRGO in Italy.

My advisors on this project are Professor Richard Matzner and Professor Tom Hughes.

Chaos

Nonlinear Dynamics is more popularly known as "Chaos Theory".

I work with the Granular Media group. We study the complex motions of granular media (such as sand). The long term goal is to develop a statistical mechanical description of granular media, including temperature, entropy, phase transitions, and so on.
My project aims to measure granular temperature and it utilizes speckle visibility spectroscopy, which involves shining a laser through the medium to probe the motion of the particles within.

My advisor on this project is Professor Harry Swinney

Astrophysics & Cosmology

The ultimate goal of this research is to answer a question that has existed as long as civilization: How did we get here? More specifically, how did the universe evolve from the time of the Big Bang into the galactic and extra-galactic structure it has today? What are the origins of galaxies? And, what role do dark matter and radiation play?
This project in particular investigates the influence that radiation had on the early universe during the period of reionization. This is done by incorporating radiative transfer into an astrophysical gas dynamics simulation.
The image at right, generated by Marcelo Alvarez, is the simulation's depiction of the web-like large scale structure in the universe.

This work is supervised by Professor Paul Shapiro.

At TAC, I worked with the Berkeley Astrophysical Fluid Dynamics group on supercomputer (courtesy of the San Diego Supercomputing Center) simulations of star formation, and in particular wanted to answer: Why are binary star systems so common?
The image at right is a real-world example of a star-forming region, the Orion Nebula. This photo was taken by the Hubble Space Telescope.

This work was supervised by Professor Chris McKee.

Graphics & Simulation

Currently, I am interested in physically-based simulation and their applications to special effects and computer games. My current work focuses on developing a method for simulating smoke. Methods already exist to quickly and realistically simulate the complicated vortices and details of smoke, for example the image at right which is taken from work by Ron Fedkiw. I am also interested in animations of water, fire, and cloth; see Fedkiw's page for more examples.
One shortcoming in current smoke animation methods is their inability to resolve details at a fine enough level to allow smoke to seep through a crack. I'm looking into developing a hybrid method that will do this.

This work is supervised by Professor Okan Arikan

The image at right, inspired both by Picasso's "Taureau (seri)" painting ("series of bulls") and by Garland and Heckbert's seminal paper on the topic, was generated by my software. The first image is the original model, with 5804 polygons. The next image is the output after simplification to 994 polygons, and the third image has only 532 polygons. Notice the similarity in appearance despite a factor-of-10 reduction in complexity! The last two images have 248 and 64 polygons, respectively.

That project was supervised by Pankaj Agarwal.

Fall 2008

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Fall 2003

Brazilian Jiu-jitsu & Martial Arts

If you are looking to start training in the Austin area, I've compiled this list of schools and clubs.

For the record, I do not think violence is an acceptable means to resolving conflict (see Safeplace below). However, I think self-defense is a vital skill (I encourage everyone to get involved, including women), and I believe that the sport of physical combat can be both challenging and exciting without necessitating anger or hatred for your opponent (actually in my experience it fosters a comraderie with and respect for your opponent that can only be acheived by pitting your wits and strength head to head against his). Martial arts is not only the most physically demanding activity I've ever tried, but it involves a great deal of quick thinking, emotional calm under stress, quick wits, and strategy. If you want to challenge yourself and strengthen your body, mind, and spirit, I highly recommend martial arts!

Safeplace

Outdoors

• Rock Climbing
  There are many excellent places to climb in Austin. Enchanted Rock Online has information about where to climb in Central Texas, and puts out a guidebook that lists all climbing walls and routes.
• Waterskiing
  I've been doing this almost as long as I've been walking, and I've competed in a few competitions. My events are slalom and jump (slalom depicted at right). I once was a member of the Duke Waterski Team and later the Texas Waterski Team.
• Hiking and Backpacking
  Austin affords you many opportunities to get outside and go hiking without even leaving the city limits. The Austin Outside Guide is a nice resource, as is the City of Austin Parks and Recreation Department. In particular, this page from Parks and Recreation has links to two great maps of Town Lake (pdf) and the Barton Creek Greenbelt (pdf).

Living with Disabilities