The Lemaitre Model and the Generalisation of the Cosmic Mass

We consider the spherically symmetric metric with a comoving perfect fluid and non-zero pressure -- the Lemaitre metric -- and present it in the form of a calculational algorithm. We use it to review the definition of mass, and to look at the apparent horizon relations on the observer's past null cone. We show that the introduction of pressure makes it difficult to separate the mass from other physical parameters in an invariant way. Under the usual mass definition, the apparent horizon relation, that relates the diameter distance to the cosmic mass, remains the same as in the Lemaitre-Tolman case.Comment: latex, 16 pages, Revision has minor changes due to referee's comments

The Metric of the Cosmos from Luminosity and Age Data

This paper presents the algorithm for determining the Lemaitre-Tolman (LT) model that best fits given datasets for maximum stellar ages, and SNIa luminosities, both as functions of redshift. It then applies it to current cosmological data. Special attention must be given to the handling of the origin, and the region of the maximum diameter distances. As with a previous combination of datasets (galaxy number counts and luminosity distances versus redshift), there are relationships that must hold at the region of the maximum diameter distance, which are unlikely to be obeyed exactly by real data. We show how to make corrections that enable a self-consistent solution to be found. We address the questions of the best way to approximate discrete data with smooth functions, and how to estimate the uncertainties of the output - the 3 free functions that determine a specific LT metric. While current data does not permit any confidence in our results, we show that the method works well, and reasonable LT models do fit with or without a cosmological constant.Comment: 25 pages, 8 figures; matches published versio

Rank deficiency in sparse random GF[2] matrices

Let M be a random m×n matrix with binary entries and i.i.d. rows. The weight (i.e., number of ones) of a row has a specified probability distribution, with the row chosen uniformly at random given its weight. Let N(n,m) denote the number of left null vectors in {0,1}m for M (including the zero vector), where addition is mod 2. We take n,m→∞, with m/n→α>0, while the weight distribution converges weakly to that of a random variable W on {3,4,5,…}. Identifying M with a hypergraph on n vertices, we define the 2-core of M as the terminal state of an iterative algorithm that deletes every row incident to a column of degree 1. We identify two thresholds α∗ and α−, and describe them analytically in terms of the distribution of W. Threshold α∗ marks the infimum of values of α at which n−1logE[N(n,m)] converges to a positive limit, while α− marks the infimum of values of α at which there is a 2-core of non-negligible size compared to n having more rows than non-empty columns. We have 1/2≤α∗≤α−≤1, and typically these inequalities are strict; for example when W=3 almost surely, α∗≈0.8895 and α−≈0.9179. The threshold of values of α for which N(n,m)≥2 in probability lies in [α∗,α−] and is conjectured to equal α−. The random row-weight setting gives rise to interesting new phenomena not present in the case of non-random W that has been the focus of previous work

Mechanisms of particle transport acceleration in porous media

Experimental data show that the groundwater transport of radionuclides in porous media is frequently facilitated when accompanied with colloid particles. This is usually explained by the size exclusion mechanism which implies that the particles move through the largest pores where the flow velocity is higher. We call attention to three other mechanisms which influence the colloid particle motion, while determining both the probable transport facilitation and retardation. First of all, it is shown that the transport facilitation may be significantly reduced and even transformed into a retardation due to the growth of the effective suspension viscosity (a friction-limited facilitation). Secondly, we will show that the transport of particles through the largest pores can be retarded due to a reduced connectivity of the large-pore cluster (a percolation-breakup retardation). Thirdly, we highlight the Fermi mechanism of acceleration known in statistical physics which is based on the elastic collisions between particles. All three effects are analyzed in terms of the velocity enhancement factor, by using statistical models of porous media in the form of a capillary bundle and a 3D capillary network. Optimal and critical regimes of velocity enhancement are quantified. Estimations show that for realistic parameters, the maximal facilitation of colloid transport is close to the experimentally observed data

Police opinions of a proposal for controlled availability of heroin in Australia

The general public, police, service providers, and users/ex-users were asked their views about options for trial design and trial outcomes with regard to a proposal for experimental controlled heroin availability. There was substantial agreement between the samples on issues concerning trial design. In general, the samples from the community, service providers and users/ex-users were more likely to report that a trial would result in positive outcomes, whereas the police sample was more likely to report that a trial would result in negative outcomes. This study illustrates the value of systematic consultation of key groups in exploring the options for change, raising potential difficulties, and highlighting different interest