Computing spacetime curvature via differential-algebraic equations

The equations that govern the behavior of physical systems can often solved numerically using a method of lines approach and differential-algebraic equation (DAE) solvers. For example, such an approach can be used to solve the Einstein field equations of general relativity, and thereby simulate significant astrophysical events. In this paper, we describe some preliminary work in which two model problems in general relativity are formulated, spatially discretized, and then numerically solved as a DAE. In particular, we seek to reproduce the solution to the spherically symmetric Schwarzschild spacetime. This is an important testbed calculation in numerical relativity since the solution is the steady-state for the collision of two (or more) non-rotating black holes. Moreover, analytic late-time properties of the Schwarzschild spacetime are well known and can be used the accuracy of the simulation

Bond-disordered spin systems: Theory and application to doped high-Tc compounds

We examine the stability of magnetic order in a classical Heisenberg model with quenched random exchange couplings. This system represents the spin degrees of freedom in high-$T_\textrm{c}$ compounds with immobile dopants. Starting from a replica representation of the nonlinear $\sigma$-model, we perform a renormalization-group analysis. The importance of cumulants of the disorder distribution to arbitrarily high orders necessitates a functional renormalization scheme. From the renormalization flow equations we determine the magnetic correlation length numerically as a function of the impurity concentration and of temperature. From our analysis follows that two-dimensional layers can be magnetically ordered for arbitrarily strong but sufficiently diluted defects. We further consider the dimensional crossover in a stack of weakly coupled layers. The resulting phase diagram is compared with experimental data for La$_{2-x}$Sr$_x$CuO$_4$.Comment: 12 pages, 5 figure

Boosted three-dimensional black-hole evolutions with singularity excision

Binary black hole interactions provide potentially the strongest source of gravitational radiation for detectors currently under development. We present some results from the Binary Black Hole Grand Challenge Alliance three- dimensional Cauchy evolution module. These constitute essential steps towards modeling such interactions and predicting gravitational radiation waveforms. We report on single black hole evolutions and the first successful demonstration of a black hole moving freely through a three-dimensional computational grid via a Cauchy evolution: a hole moving ~6M at 0.1c during a total evolution of duration ~60M

Measurement of Unpolarized and Polarized Cross Sections for Deeply Virtual Compton Scattering on the Proton at Jefferson Laboratory with CLAS

This paper reports the measurement of polarized and unpolarized cross sections for the ep → e \u27p\u27 γ reaction, which is composed of deeply virtual Compton scattering (DVCS) and Bethe-Heitler (BH) processes, at an electron beam energy of 5.88 GeV at the Thomas Jefferson National Accelerator Facility using the Large Acceptance Spectrometer CLAS. The unpolarized cross sections and polarized cross section differences have been measured over broad kinematics, 0.10 2 \u3c 4.8 GeV2,and 0.09 \u3c −t\u3c 2.00 GeV2. The results are found to be consistent with previous CLAS data, and these new data are discussed in the framework of the generalized parton distribution approach. Calculations with two widely used phenomenological models are approximately compatible with the experimental results over a large portion of the kinematic range of the data

Stable characteristic evolution of generic 3-dimensional single-black-hole spacetimes

We report new results which establish that the accurate 3-dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results cover a selection of distorted, moving and spinning single black holes, with evolution times up to 60,000M.Comment: 4 pages, 3 figure

Gravitational wave extraction and outer boundary conditions by perturbative matching

We present a method for extracting gravitational radiation from a three-dimensional numerical relativity simulation and, using the extracted data, to provide outer boundary conditions. The method treats dynamical gravitational variables as nonspherical perturbations of Schwarzschild geometry. We discuss a code which implements this method and present results of tests which have been performed with a three dimensional numerical relativity code

A comparison of forward and backward pp pair knockout in 3He(e,e'pp)n

Measuring nucleon-nucleon Short Range Correlations (SRC) has been a goal of the nuclear physics community for many years. They are an important part of the nuclear wavefunction, accounting for almost all of the high-momentum strength. They are closely related to the EMC effect. While their overall probability has been measured, measuring their momentum distributions is more difficult. In order to determine the best configuration for studying SRC momentum distributions, we measured the $^3$He$(e,e'pp)n$ reaction, looking at events with high momentum protons ($p_p > 0.35$ GeV/c) and a low momentum neutron ($p_n< 0.2$ GeV/c). We examined two angular configurations: either both protons emitted forward or one proton emitted forward and one backward (with respect to the momentum transfer, $\vec q$). The measured relative momentum distribution of the events with one forward and one backward proton was much closer to the calculated initial-state $pp$ relative momentum distribution, indicating that this is the preferred configuration for measuring SRC.Comment: 8 pages, 9 figures, submitted to Phys Rev C. Version 2 incorporates minor corrections in response to referee comment