Vanderbilt initiative for gravity, waves, and fluids

VandyGRAF Initiative

VandyGRAF Initiative

The Vanderbilt Initiative for Gravity, Waves, and Fluids is an interdisciplinary research venture providing mathematicians, physicists, and astrophysicists with the resources and space to connect and collaboratively work on problems of outstanding scientific merit, such as:

  • General relativity: theoretical, mathematical, numerical, or experimental, including, but not restricted to, black holes, gravitational radiation, and multimessenger astrophysics.
  • Fluid mechanics: theoretical, mathematical, numerical, or experimental, including, but not restricted to, relativistic fluids far from equilibrium.
  • Evolution of partial differential equations related to fluids and gravity, including, but not restricted to, the geometric analysis of waves and fluids.
  • The physics and mathematics of neutron star mergers and high-energy nuclear collisions.

VandyGRAF Seminar Series

All VandyGRAF talks will take place in SC 6333, unless indicated below.


Jacob Lange, University of Texas Austin

March 29, 12:00 pm - 2:00 pm

On the Importance of Expanding and Improving Numerical Relativity Simulations

Abstract: Since the original breakthrough of the numerical relativity (NR) evolution codes, multiple research groups have been able to solve Einstein’s equations numerically on supercomputers to simulate merging binary black hole gravitational wave sources. While these NR simulations can be directly compared to the data using special configurations parameter estimation codes, these waveforms are mostly used to calibrate and verify the accuracy semi-analytical gravitational wave models. These models are in turn used for production level parameter estimation analyses of gravitational wave detections from the LIGO-Virgo-KAGRA Collaboration. Because of this, it is essential not only to expand our current NR simulation grid into more exotic parts of parameter space (i.e. more unequal mass ratios, more extreme precessing spins, inclusion of eccentricity) but also to improve the accuracy of our current simulations as we prepare for next generation detectors. For the former, I present a novel algorithm that suggests new NR simulation placement based off of the interpolated likelihood as well as the error to that interpolated likelihood when directly comparing the NR waveforms to a real event. This allows the placement of new simulations to be in relevant parts of parameter space (high likelihood) as well as in sparse parts of parameter space for the existing grid (high error in interpolated likelihood). For the latter, I present parameter estimation results investigating the effects of waveform systematics due to NR resolution. With our current expected signal-to-noise ratios (SNR) for signals from our current ground-based detectors, the resolutions used to generate the current catalogs of NR simulations are considered large enough to be indistinguishable from an infinite resolution simulation (i.e. statistical errors dominate). As our current and next generation detectors increase our sensitivity, the systematic errors due to our finite resolution becomes more important. Following up from a previous mismatch study by Ferguson et. al. comparing different resolutions for a given simulation using different detectors, I present preliminary work that quantifies the impact of resolution error by injecting these different resolution simulations at different SNRs based off the criteria investigated in Ferguson et. al.

Leonardo Abbrescia, Vanderbilt University

April 5, 12:00 pm - 2:00 pm

The mathematics of shockwaves

Abstract: Shockwaves are very prevalent in physical phenomena: supernova explosions, high-energy particle collisions, condensed matter under extreme conditions, etc. From these situations, one might intuitively think that there is some violent mechanism driving a shock. In this talk, we will see how the mathematics of shock waves proves that this is not the case. For the PDEs that model many of the physical systems we care about, shock waves can form in finite time even for small and completely smooth initial conditions. Moreover, the state variables are bounded at the initial shock singularity. Most of the talk will focus on Burgers’ equation and 1D compressible isentropic Euler, but we will discuss more recent work if time permits.

David Garfinkle, Oakland University

April 12, 12:00 pm - 2:00 pm

Gravitational wave memory and its electromagnetic analog

Abstract: Gravitational waves stretch and squeeze space, but even when the wave has passed there is a residual stretch and squeeze known as gravitational wave memory. This memory is a consequence of the nonlinear Einstein field equations, but can be most easily understood by using linear perturbation theory. Furthermore this linear perturbative treatment is best understood by using manifestly gauge invariant variables: in this case the Weyl tensor. Gravitational perturbation theory using the Weyl tensor is analogous to Maxwell’s equations for electromagnetism. Correspondingly, there is an electromagnetic analog of gravitational wave memory called electromagnetic memory. I will present a proposal for how to measure electromagnetic memory.

Grisha Tarnopolsky, Carnegie Mellon University

April 19, 12:00 pm - 2:00 pm