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Research Interests

I use computational methods to study issues of mathematical physics. In particular, most of my work has sought to answer questions in the realms of relativity, cosmology, and astrophysics. Below I list particular projects, both current and past:

Computational Astrophysics & Cosmology
A major problem in astrophysics is understanding the process which powers some of the most energetic events observed, namely gamma ray bursts (GRBs) and active galactic nuclei (AGN). That black holes are involved is well accepted but the details of the processes are still mysterious. A strong magnetic field, plasma pressure, and black hole rotation all play roles in converting energy into highly collimated jets.

Black holes and extremely dense stars called neutron stars are abundant and involve very strong gravity. So much so that their motion disturbs spacetime similar to the way a tossed rock disturbs a pond's surface and produces waves. Binaries composed of black holes and neutron stars (so-called compact object binaries) produce gravitational waves. We have not detected such waves yet, but the continued advancement of gravitational wave detectors such as LIGO and Virgo promise an entirely new view of the universe. What will these gravitational signals tell us about the far reaches of the cosmos? Will concurrent observations of both gravitational and electromagnetic (light) radiation reveal more than the sum of their parts?
Also see this magazine article in Physics World (PDF)
and this short movie on LIGO

Cosmology has made tremendous strides in the past two decades measuring the properties of our Universe. The problem is now to explain how the universe came to be this way. Did inflation smooth out things, and if so, how did inflation itself begin? Is the universe that we observe part of some collection of regions ("bubbles") with different properties? Were cosmic strings created in the early universe, and, if so, how might we observe them?

High Performance Computing
Studying such interesting phenomena numerically involves the solution of sets of complicated, nonlinear differential equations, and for many of the problems the computations are extremely demanding. For example, to calculate what happens as two neutron stars orbit each other, radiate gravitational waves, and ultimately merge requires a supercomputer with hundreds of processing cores running for more than a month.

Various techniques and technologies are exploited to shorten processing times. Two examples are adaptive mesh refinement (AMR) and distributed computing. With AMR, a code is programmed to determine where numerical precision is most needed, and finer grained grids are added to such regions dynamically. With a binary neutron star system, AMR would automatically determine that the regions occupied by the neutron stars require fine precision whereas regions far from the stars may have very little precision. As the stars move, the refined regions track the stars.

Distributed computing entails partitioning the numerical work one needs to accomplish over many computer processors or cores. Consider the machine Ranger which has more than 60,000 cores. This partitioning is highly nontrivial because generally the computations in one region depend on the numerical work in another region. Therefore, information has to be passed among the differing processing elements. One widely used example of a tool to enable such communication is Message Passing Interface (MPI). The advent of relegating computational work to one's video card, so-called GPU computing is adding new complexity and power to distributed computing.

Strong gravity is described by Einstein's general theory of relativity, and is a fascinating theory well beyond its relevance to high energy astrophysics. Perhaps most fascinating of all are issues related to the formation of a black hole. What's the smallest black hole one can form? Can the singularity that forms inside black holes ever be visible to those outside any black hole?

Recent developments related to string theory has resulted in an interesting correspondence between solutions of general relativity in a particular type of space with that of quantum field theory lacking gravity. This so-called AdS/CFT correspondence is very exciting for a number of reasons, but most relevant here is that computational solutions of gravity in AdS can be used to better understand quantum field theory. This correspondence also is related to the holographic principle which asserts that all that we normally observe to be occurring in the usual three spatial dimensions can be encoded on the boundary just as holograms encode information about 3D into a 2D film.

Last updated October 10, 2019.
Copyright© 2001--2019 S.L. Liebling
(home) Research Supported by NSF