On the fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media

The fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by $\sigma_{\theta_J}$) decay with the lattice size according to the power-law $\sigma_{\theta_J} \propto L^{-1/ \nu}$. The exponent $\nu$ depends on the dimensionality $D$ of the substrate and the fractal dimension of the set where the RSA process actually takes place ($d_f$) according to $\nu = 2 / (2D - d_f)$.This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers on homogeneous and stochastic fractal substrates. Furthermore, our predictions are in excellent agreement with different previous numerical results. It is also shown that, studying correlated stochastic processes, one can define various fluctuating quantities designed to capture either the underlying physics of individual processes or that of the whole system. So, subtle differences in the definitions may lead to dramatically different physical interpretations of the results. Here, this statement is demonstrated for the case of RSA of dimers on binary alloys.Comment: 20 pages, 8 figure

Targeting Conservation Investments in Heterogeneous Landscapes: A distance function approach and application to watershed management

To achieve a given level of an environmental amenity at least cost, decision-makers must integrate information about spatially variable biophysical and economic conditions. Although the biophysical attributes that contribute to supplying an environmental amenity are often known, the way in which these attributes interact to produce the amenity is often unknown. Given the difficulty in converting multiple attributes into a unidimensional physical measure of an environmental amenity (e.g., habitat quality), analyses in the academic literature tend to use a single biophysical attribute as a proxy for the environmental amenity (e.g., species richness). A narrow focus on a single attribute, however, fails to consider the full range of biophysical attributes that are critical to the supply of an environmental amenity. Drawing on the production efficiency literature, we introduce an alternative conservation targeting approach that relies on distance functions to cost-efficiently allocate conservation funds across a spatially heterogeneous landscape. An approach based on distance functions has the advantage of not requiring a parametric specification of the amenity function (or cost function), but rather only requiring that the decision-maker identify important biophysical and economic attributes. We apply the distance-function approach empirically to an increasingly common, but little studied, conservation initiative: conservation contracting for water quality objectives. The contract portfolios derived from the distance-function application have many desirable properties, including intuitive appeal, robust performance across plausible parametric amenity measures, and the generation of ranking measures that can be easily used by field practitioners in complex decision-making environments that cannot be completely modeled. Working Paper # 2002-01

Gamma-ray burst data from DMSP satellites

A number of gamma-ray bursts have been detected by means of gamma-ray detectors aboard three Air Force Defense Meteorological Satellite Program (DMSP) satellites, in polar orbits at 800 km altitude. The gamma-ray data have a 2-second resolving time, and are usually telemetered in 5 energy bins in the range 50--1000 keV. Although it is not possible to detect gamma-ray bursts when the DMSP satellites are passing through the radiation belt or the South Atlantic Anomaly, or when the source is obscured by the Earth, a number of gamma-ray bursts have been detected by two or even three of the satellites. The DMSP data may be of considerable, assistance in evaluating time histories, locations, and spectra of gamma-ray bursts