Malcolm Tobias

Web servers and services for electrostatics calculations with APBS and PDB2PQR

APBS and PDB2PQR are widely utilized free software packages for biomolecular electrostatics calculations. Using the Opal toolkit, we have developed a Web services framework for these software packages that enables the use of APBS and PDB2PQR by users who do not have local access to the necessary amount of computational capabilities. This not only increases accessibility of the software to a wider range of scientists, educators, and students but also increases the availability of electrostatics calculations on portable computing platforms. Users can access this new functionality in two ways. First, an Opal‐enabled version of APBS is provided in current distributions, available freely on the web. Second, we have extended the PDB2PQR web server to provide an interface for the setup, execution, and visualization of electrostatic potentials as calculated by APBS. This web interface also uses the Opal framework which ensures the scalability needed to support the large APBS user community. Both of these resources are available from the APBS/PDB2PQR website: http://www.poissonboltzmann.org/.

Three Dimensional Numerical General Relativistic Hydrodynamics ; 1, Formulations, Methods, and Code Tests

This is the first in a series of papers on the construction and validation of a three-dimensional code for general relativistic hydrodynamics, and its application to general relativistic astrophysics. This paper studies the consistency and convergence of our general relativistic hydrodynamic treatment and its coupling to the spacetime evolutions described by the full set of Einstein equations with a perfect fluid source. The numerical treatment of the general relativistic hydrodynamic equations is based on high resolution shock capturing schemes. These schemes rely on the characteristic information of the system. A spectral decomposition for general relativistic hydrodynamics suitable for a general spacetime metric is presented. Evolutions based on three different approximate Riemann solvers coupled to four different discretizations of the Einstein equations are studied and compared. The coupling between the hydrodynamics and the spacetime (the right and left hand side of the Einstein equations) is carried out in a treatment which is second order accurate in {\it both} space and time. Convergence tests for all twelve combinations with a variety of test beds are studied, showing consistency with the differential equations and correct convergence properties. The test-beds examined include shocktubes, Friedmann-Robertson-Walker cosmology tests, evolutions of self-gravitating compact (TOV) stars, and evolutions of relativistically boosted TOV stars. Special attention is paid to the numerical evolution of strongly gravitating objects, e.g., neutron stars, in the full theory of general relativity, including a simple, yet effective treatment for the surface region of the star (where the rest mass density is abruptly dropping to zero).

Three-dimensional numerical general relativistic hydrodynamics. II. Long-term dynamics of single relativistic stars

This is the second in a series of papers on the construction and validation of a three-dimensional code for the solution of the coupled system of the Einstein equations and of the general relativistic hydrodynamic equations, and on the application of this code to problems in general relativistic astrophysics. In particular, we report on the accuracy of our code in the long-term dynamical evolution of relativistic stars and on some new physics results obtained in the process of code testing. The following aspects of our code have been validated: the generation of initial data representing perturbed general relativistic polytropic models ~both rotating and nonrotating!, the long-term evolution of relativistic stellar models, and the coupling of our evolution code to analysis modules providing, for instance, the detection of apparent horizons or the extraction of gravitational waveforms. The tests involve single nonrotating stars in stable equilibrium, nonrotating stars undergoing radial and quadrupolar oscillations, nonrotating stars on the unstable branch of the equilibrium configurations migrating to the stable branch, nonrotating stars undergoing gravitational collapse to a black hole, and rapidly rotating stars in stable equilibrium and undergoing quasiradial oscillations. We have carried out evolutions in full general relativity and compared the results to those obtained either with perturbation techniques, or with lower dimensional numerical codes, or in the Cowling approximation ~in which all the perturbations of the spacetime are neglected!. In all cases an excellent agreement has been found. The numerical evolutions have been carried out using different types of polytropic equations of state using either the rest-mass density only, or the rest-mass density and the internal energy as independent variables. New variants of the spacetime evolution and new high resolution shock capturing treatments based on Riemann solvers and slope limiters have been implemented and the results compared with those obtained from previous methods. In particular, we have found the ‘‘monotonized central differencing’’ limiter to be particularly effective in evolving the relativistic stellar models considered. Finally, we have obtained the first eigenfrequencies of rotating stars in full general relativity and rapid rotation. A long standing problem, such frequencies have not been obtained by other methods. Overall, and to the best of our knowledge, the results presented in this paper represent the most accurate long-term three-dimensional evolutions of relativistic stars available to date.

The astrophysics simulation collaboratory portal: a framework for effective distributed research

We describe the motivation, architecture, and implementation of the Astrophysics Simulation Collaboratory (ASC) portal. The ASC project provides a web-based problem solving framework for the astrophysics community that harnesses the capabilities of emerging computational grids.

Gravitational collapse of gravitational waves in 3D numerical relativity.

We demonstrate that evolutions of three-dimensional, strongly non-linear gravitational waves can be followed in numerical relativity, hence allowing many interesting studies of both fundamental and observational consequences. We study the evolution of time-symmetric, axisymmetric and non-axisymmetric Brill waves, including waves so strong that they collapse to form black holes under their own self-gravity. An estimate for the critical amplitude for black hole formation in a particular interpolating family of initial data is obtained. The gravitational waves emitted in the black hole formation process are compared to those emitted in the head-on collision of two Misner black holes. PACS number~s!: 04.25.Dm, 04.30.Db, 95.30.Sf, 97.60.Lf

Coordinate conditions in three-dimensional numerical relativity

We put forward a few ideas on coordinate (gauge) conditions in numerical relativity. Coordinate conditions are important for long time scale simulations of relativistic systems. We demonstrate the importance of, and propose methods for, the active enforcement of coordinate properties. In particular, the constancy of the determinant of the spatial 3-metric is investigated as such a property. We propose an exceedingly simple but powerful idea for implementing elliptic coordinate conditions that not only makes possible the use of complicated elliptic conditions, but is also a number of orders of magnitude more efficient than existing methods for large-scale three-dimensional simulations.

Shapiro conjecture: Prompt or delayed collapse in the head-on collision of neutron stars?

We study the question of prompt versus delayed collapse in the head-on collision of two neutron stars. We show that the prompt formation of a black hole is possible, contrary to a conjecture of Shapiro which claims that collapse is delayed until after neutrino cooling. An understanding of the limitation of the conjecture is provided in terms of the many time scales involved in the problem. General relativistic simulations with the full set of Einstein equations coupled to the general relativistic hydrodynamic equations are carried out.

Dynamics of Gravitational Waves in 3D: Formulations, Methods, and Tests

The dynamics of gravitational waves is investigated in full (3+1)-dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from nonlinearities and gauge degrees of freedom. Using gravitational waves with amplitudes low enough that one has a good understanding of the physics involved, but large enough to enable nonlinear effects to emerge, we study the coupling between numerical errors, coordinate effects, and the nonlinearities of the theory. We discuss the various strategies used in identifying specific features of the evolution. We show the importance of the flexibility of being able to use different numerical schemes, different slicing conditions, different formulations of the Einstein equations [standard Arnowitt, Deser, and Misner vs first order hyperbolic], and different sets of equations (linearized vs full Einstein equations). A nonlinear scalar field equation is presented which captures some properties of the full Einstein equations, and has been useful in our understanding of the coupling between finite differencing errors and nonlinearities. We present a set of monitoring devices which have been crucial in our studying of the waves, including Riemann invariants, pseudo-energy-momentum tensor, Hamiltonian constraint violation, and Fourier spectrum analysis.

Near-linear regime of gravitational waves in numerical relativity.

We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the amplitude of the wave is low enough that one expects the geometric deviation from flat spacetime to be negligible, but nevertheless, where nonlinearities can excite unstable modes of the Einstein evolution equations causing the metric functions to evolve out of control. The implications of this for numerical relativity are discussed.