Cauchy-perturbative matching and outer boundary conditions I: Methods and tests

We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a set of one-dimensional linear wave equations on a curved background. We illustrate the mathematical properties of our approach and discuss a numerical module we have constructed for this purpose. This module implements the perturbative matching approach in connection with a generic three-dimensional numerical relativity simulation. Tests of its accuracy and second-order convergence are presented with analytic linear wave data.Comment: 13 pages, 6 figures, RevTe

Cauchy-perturbative matching and outer boundary conditions: computational studies

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the solution of a Cauchy evolution of the nonlinear Einstein field equations to a set of one-dimensional linear equations obtained through perturbation techniques over a curved background. We discuss the validity of this approach in the case of linear and mildly nonlinear gravitational waves and show how a numerical module developed for this purpose is able to provide an accurate and numerically convergent description of the gravitational wave propagation and a stable numerical evolution.Comment: 20 pages, RevTe

Critical behavior at Mott-Anderson transition: a TMT-DMFT perspective

We present a detailed analysis of the critical behavior close to the Mott-Anderson transition. Our findings are based on a combination of numerical and analytical results obtained within the framework of Typical-Medium Theory (TMT-DMFT) - the simplest extension of dynamical mean field theory (DMFT) capable of incorporating Anderson localization effects. By making use of previous scaling studies of Anderson impurity models close to the metal-insulator transition, we solve this problem analytically and reveal the dependence of the critical behavior on the particle-hole symmetry. Our main result is that, for sufficiently strong disorder, the Mott-Anderson transition is characterized by a precisely defined two-fluid behavior, in which only a fraction of the electrons undergo a "site selective" Mott localization; the rest become Anderson-localized quasiparticles.Comment: 4+ pages, 4 figures, v2: minor changes, accepted for publication in Phys. Rev. Let

Nevirapine-Induced Heratotoxicity: Incidence, Risk Factors and Associated Mortality in a Primary Care ART Programme in South Africa

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Guns and gender-based violence in South Africa

Background. The criminal use of firearms in South Africa is widespread and a major factor in the country having the thirdhighest homicide rate in the world. Violence is a common feature of South African society. A firearm in the home is a risk factor in intimate partner violence, but this has not been readily demonstrated in South Africa because of a lack of data. Methods. We drew on several South African studies including national homicide studies, intimate partner studies, studies with male participants and studies from the justice sector, to discuss the role of gun ownership in gender-based violence. Conclusion. Guns play a significant role in violence against women in South Africa, most notably in the killing of intimate partners. Although the overall homicide data suggest that death by shooting is decreasing, data for intimate partner violence are not readily available. We have no idea if the overall decrease in gunshot homicides applies to women in relationships, and therefore gun control should remain high on the legislative agenda

Waveform propagation in black hole spacetimes: evaluating the quality of numerical solutions

We compute the propagation and scattering of linear gravitational waves off a Schwarzschild black hole using a numerical code which solves a generalization of the Zerilli equation to a three dimensional cartesian coordinate system. Since the solution to this problem is well understood it represents a very good testbed for evaluating our ability to perform three dimensional computations of gravitational waves in spacetimes in which a black hole event horizon is present.Comment: 13 pages, RevTeX, to appear in Phys. Rev.

Spin Dynamics of a J1-J2-K Model for the Paramagnetic Phase of Iron Pnictides

We study the finite-temperature spin dynamics of the paramagnetic phase of iron pnictides within an antiferromagnetic J_1-J_2 Heisenberg model on a square lattice with a biquadratic coupling $-K (S_i \cdot S_j)^2$ between the nearest-neighbor spins. Our focus is on the paramagnetic phase in the parameter regime of this J_1-J_2-K model where the ground state is a (\pi,0) collinear antiferromagnet. We treat the biquadratic interaction via a Hubbard-Stratonovich decomposition, and study the resulting effective quadratic-coupling model using both modified spin wave and Schwinger boson mean-field theories; the results for the spin dynamics derived from the two methods are very similar. We show that the spectral weight of dynamical structure factor S(q,\omega) is peaked at ellipses in the momentum space at low excitation energies. With increasing energy, the elliptic features expand towards the zone boundary, and gradually split into two parts, forming a pattern around (\pi,\pi). Finally, the spectral weight is anisotropic, being larger along the major axis of the ellipse than along its minor axis. These characteristics of the dynamical structure factor are consistent with the recent measurements of the inelastic neutron scattering spectra on BaFe_2As_2 and SrFe_2As_2.Comment: 13 pages, 11 figures, to be published in Phys. Rev.

Ill-posedness in the Einstein equations

It is shown that the formulation of the Einstein equations widely in use in numerical relativity, namely, the standard ADM form, as well as some of its variations (including the most recent conformally-decomposed version), suffers from a certain but standard type of ill-posedness. Specifically, the norm of the solution is not bounded by the norm of the initial data irrespective of the data. A long-running numerical experiment is performed as well, showing that the type of ill-posedness observed may not be serious in specific practical applications, as is known from many numerical simulations.Comment: 13 pages, 3 figures, accepted for publication in Journal of Mathematical Physics (to appear August 2000