Areas of Interest
Publication and Citation List
View the slides from my April 2003 colloquium at NCSU. I gave a similar talk at the November 2003 SESAPS meeting. Some of my recent research involves the Variational Integrator approach to numerical modeling, as applied to general relativity. I gave a talk on this subject at theYorkfest conference, which took place at Cornell University in July 2004 in honor of Jimmy York's 65th birthday. I gave another talk on numerical relativity and variational integrators in the NCSU Physics Department's Theory Seminar. Here is a short talk on the conformal-traceless decomposition of the gravitational field presented at the Eastern Gravity Meeting in March 2005.
The ground based interferometer gravitational wave detectors LIGO and VIRGO are now operating and should reach their design sensitivities in one or two years. Development is underway by NASA and the European Space Agency for LISA, a space based gravitational wave detector scheduled for launch in 2011. We are at the beginning of a new era in astrophysics research, as these detectors allow us to observe directly the bulk motions of matter in violent cosmological events such as black hole/black hole collisions. The success of both ground and space based detectors will require accurate numerical modeling, although for different reasons. Because the target signals for ground based detectors are very weak, a clear theoretical understanding of the expected signals will be needed to help separate signal from instrument noise. For the space based LISA detector collisions between supermassive black holes, each with a billion times the mass of our sun, are expected to generate very strong gravitational waves that can be detected easily. Accurate theoretical modeling will be used to filter these large signals from the data stream, and in the process uncover weaker signals from other physically interesting gravitational wave sources.
I am currently working with NCSU graduate students and with the theoretical relativity group at NASA Goddard Space Flight Center to develop an accurate, stable numerical relativity code for solving the Einstein equations of general relativity. While there are several numerical relativity groups around the world pursuing this goal, the Goddard group is leading the way in developing a code with adaptive mesh refinement. With adaptive mesh refinement, our code can automatically increase the resolution of the computational grid in the regions that are most difficult to simulate. Ultimately, this feature will be essential for any numerical relativity code in order to resolve the details of the source and at the same time track the gravitational radiation that spreads into space. My work with the Goddard group is primarily in support of the space based gravitational wave detector LISA. As such, our main focus is the numerical simulation of supermassive black hole collisions. These results will apply as well to collisions of ``ordinary'' (a few solar masses) black holes, events that should be visible to the ground based gravitational wave detectors LIGO and VIRGO.
One of the main challenges facing the numerical relativity community is to find a stable numerical integration algorithm for the Einstein equations. Current algorithms tend to suffer from the problem of unphysical, exponentially growing modes which quickly cause the code to crash. I am currently working to develop a new integration scheme based on variational integrators. Variational integrators are obtained from a discretization of the action principlefor the system, rather than the equations of motion. For mechanical systems variational integrators are farsuperior in their ability to keep the energy of the system conserved. The analog of energy conservation for general relativity is the preservation of a set of constraint equations. There is currently good evidence to suggest that the unphysical modes in general relativity are constraint violating modes. The hope is that a variational integrator will suppress these unphysical modes and yield a stable numerical evolution.
Recent Publications
"Midpoint Rule as a Variational-Symplectic Integrator: Hamiltonian Systems,"
Phys. Rev. D.
J.D. Brown.
"Conformal Invariance and the Conformal-Traceless Decompsition of the Gravitational Field,"
Phys. Rev. D
71.
J.D. Brown.
(2005). p. 104011.
"Multigrid Elliptic Equation Solver with Adaptive Mesh Refinement,"
J. Comp. Phys.
209.
J.D. Brown and L.L. Lowe.
(2005). p. 582-598.
"Distorted Black Hole Initial Data using the Puncture Method,"
Phys. Rev. D
70.
J.D. Brown and L.L. Lowe.
(2004). p. 124014.
"Evolving a puncture black hole with fixed mesh refinement,"
Phys. Rev. D
70.
B. Imbiriba, J. Baker, D.-I. Choi, J. Centrella, D.R. Fiske, J.D. Brown, J.R. van Meter, and K. Olson.
(2004). p. 124025.
Click here to view a larger list of publications.
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