On the convergence of Regge calculus to general relativity

Motivated by a recent study casting doubt on the correspondence between Regge calculus and general relativity in the continuum limit, we explore a mechanism by which the simplicial solutions can converge whilst the residual of the Regge equations evaluated on the continuum solutions does not. By directly constructing simplicial solutions for the Kasner cosmology we show that the oscillatory behaviour of the discrepancy between the Einstein and Regge solutions reconciles the apparent conflict between the results of Brewin and those of previous studies. We conclude that solutions of Regge calculus are, in general, expected to be second order accurate approximations to the corresponding continuum solutions.Comment: Updated to match published version. Details of numerical calculations added, several sections rewritten. 9 pages, 4 EPS figure

Plasma fluctuations as Markovian noise

Noise theory is used to study the correlations of stationary Markovian fluctuations that are homogeneous and isotropic in space. The relaxation of the fluctuations is modeled by the diffusion equation. The spatial correlations of random fluctuations are modeled by the exponential decay. Based on these models, the temporal correlations of random fluctuations, such as the correlation function and the power spectrum, are calculated. We find that the diffusion process can give rise to the decay of the correlation function and a broad frequency spectrum of random fluctuations. We also find that the transport coefficients may be estimated by the correlation length and the correlation time. The theoretical results are compared with the observed plasma density fluctuations from the tokamak and helimak experiments.Physic

A Kirchhoff-like conservation law in Regge calculus

Simplicial lattices provide an elegant framework for discrete spacetimes. The inherent orthogonality between a simplicial lattice and its circumcentric dual yields an austere representation of spacetime which provides a conceptually simple form of Einstein's geometric theory of gravitation. A sufficient understanding of simplicial spacetimes has been demonstrated in the literature for spacetimes devoid of all non-gravitational sources. However, this understanding has not been adequately extended to non-vacuum spacetime models. Consequently, a deep understanding of the diffeomorphic structure of the discrete theory is lacking. Conservation laws and symmetry properties are attractive starting points for coupling matter with the lattice. We present a simplicial form of the contracted Bianchi identity which is based on the E. Cartan moment of rotation operator. This identity manifests itself in the conceptually-simple form of a Kirchhoff-like conservation law. This conservation law enables one to extend Regge Calculus to non-vacuum spacetimes and provides a deeper understanding of the simplicial diffeomorphism group.Comment: 13 pages, 4 figure

Apparent horizons in simplicial Brill wave initial data

We construct initial data for a particular class of Brill wave metrics using Regge calculus, and compare the results to a corresponding continuum solution, finding excellent agreement. We then search for trapped surfaces in both sets of initial data, and provide an independent verification of the existence of an apparent horizon once a critical gravitational wave amplitude is passed. Our estimate of this critical value, using both the Regge and continuum solutions, supports other recent findings.Comment: 7 pages, 6 EPS figures, LaTeX 2e. Submitted to Class. Quant. Gra

THE USE OF PRIVATE LANDS IN THE U.S. FOR OUTDOOR RECREATION: RESULTS OF A NATIONWIDE SURVEY

Land Economics/Use, Resource /Energy Economics and Policy,

Fast algorithms for computing defects and their derivatives in the Regge calculus

Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such cases it is essential that efficient algorithms be used when computing the defect angles and their derivatives with respect to the leg-lengths. The purpose of this paper is to present details of such an algorithm.Comment: 38 pages, 10 figure

Effectiveness of commercial harvesting in controlling feral-pig populations

Context. The feral pig (Sus scrofa) is a widespread pest species in Australia and its populations are commonly controlled to reduce damage to agriculture and the environment. Feral pigs are also a resource and harvested for commercial export as game meat. Although many other control techniques are used, commercial harvesting of feral pigs is often encouraged by land managers, because it carries little or no cost and is widely perceived to control populations. Aims. To use feral-pig harvesting records, density data and simple harvest models to examine the effectiveness of commercial harvesting to reduce feral-pig populations. Methods. The present study examined commercial harvest off-take on six sites (246-657 km2) in southern Queensland, and 20 large blocks (~2-6000 km2) throughout Queensland. The harvest off-take for each site was divided by monthly or average annual population size, determined by aerial survey, to calculate monthly and annual harvest rates.Asimple harvest model assuming logistic population growth was used to determine the likely effectiveness of harvesting. Key results. Commercial harvest rates were generally low (50%) in long-term population size were isolated occurrences and not maintained across sites and years. High harvest rates were observed only at low densities. Although these harvest rates may be sufficiently high to hold populations at low densities, the population is likely to escape this entrapment following a flush in food supply or a reduction in harvest effort. Implications. Our results demonstrated that, at current harvest rates, commercial harvesting is ineffective for the landscape-scale control of feral-pig populations. Unless harvest rates can be significantly increased, commercial harvesting should be used as a supplement to, rather than as a substitute for, other damage-control techniques

A fully (3+1)-D Regge calculus model of the Kasner cosmology

We describe the first discrete-time 4-dimensional numerical application of Regge calculus. The spacetime is represented as a complex of 4-dimensional simplices, and the geometry interior to each 4-simplex is flat Minkowski spacetime. This simplicial spacetime is constructed so as to be foliated with a one parameter family of spacelike hypersurfaces built of tetrahedra. We implement a novel two-surface initial-data prescription for Regge calculus, and provide the first fully 4-dimensional application of an implicit decoupled evolution scheme (the ``Sorkin evolution scheme''). We benchmark this code on the Kasner cosmology --- a cosmology which embodies generic features of the collapse of many cosmological models. We (1) reproduce the continuum solution with a fractional error in the 3-volume of 10^{-5} after 10000 evolution steps, (2) demonstrate stable evolution, (3) preserve the standard deviation of spatial homogeneity to less than 10^{-10} and (4) explicitly display the existence of diffeomorphism freedom in Regge calculus. We also present the second-order convergence properties of the solution to the continuum.Comment: 22 pages, 5 eps figures, LaTeX. Updated and expanded versio

Impacts on nontarget avian species from aerial meat baiting for feral pigs

Bait containing sodium fluoroacetate (1080) is widely used for the routine control of feral pigs in Australia. In Queensland, meat baits are popular in western and northern pastoral areas where they are readily accepted by feral pigs and can be distributed aerially. Field studies have indicated some levels of interference and consumption of baits by nontarget species and, based on toxicity data and the 1080 content of baits, many nontarget species (particularly birds and varanids) are potentially at risk through primary poisoning. While occasional deaths of species have been recorded, it remains unclear whether the level of mortality is sufficient to threaten the viability or ecological function of species. A series of field trials at Culgoa National Park in south-western Queensland was conducted to determine the effect of broadscale aerial baiting (1.7 baits per km2) on the density of nontarget avian species that may consume baits. Counts of susceptible bird species were conducted prior to and following aerial baiting, and on three nearby unbaited properties, in May and November 2011, and May 2012. A sample of baits was monitored with remote cameras in the November 2011 and May 2012 trials. Over the three baiting campaigns, there was no evidence of a population-level decline among the seven avian nontarget species that were monitored. Thirty per cent and 15% of baits monitored by remote cameras in the November 2011 and May 2012 trials were sampled by birds, varanids or other reptiles. These results support the continued use of 1080 meat baits for feral pig management in western Queensland and similar environs

A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates

We propose a new formulation for 3+1 numerical relativity, based on a constrained scheme and a generalization of Dirac gauge to spherical coordinates. This is made possible thanks to the introduction of a flat 3-metric on the spatial hypersurfaces t=const, which corresponds to the asymptotic structure of the physical 3-metric induced by the spacetime metric. Thanks to the joint use of Dirac gauge, maximal slicing and spherical components of tensor fields, the ten Einstein equations are reduced to a system of five quasi-linear elliptic equations (including the Hamiltonian and momentum constraints) coupled to two quasi-linear scalar wave equations. The remaining three degrees of freedom are fixed by the Dirac gauge. Indeed this gauge allows a direct computation of the spherical components of the conformal metric from the two scalar potentials which obey the wave equations. We present some numerical evolution of 3-D gravitational wave spacetimes which demonstrates the stability of the proposed scheme.Comment: Difference w.r.t. v1: Major revision: improved presentation of the tensor wave equation and addition of the first results from a numerical implementation; w.r.t. v2: Minor changes: improved conclusion and figures; w.r.t. v3: Minors changes, 1 figure added; 25 pages, 13 figures, REVTeX, accepted for publication in Phys. Rev.