Long Range Hops and the Pair Annihilation Reaction A+A->0: Renormalization Group and Simulation

A simple example of a non-equilibrium system for which fluctuations are important is a system of particles which diffuse and may annihilate in pairs on contact. The renormalization group can be used to calculate the time dependence of the density of particles, and provides both an exact value for the exponent governing the decay of particles and an epsilon-expansion for the amplitude of this power law. When the diffusion is anomalous, as when the particles perform Levy flights, the critical dimension depends continuously on the control parameter for the Levy distribution. The epsilon-expansion can then become an expansion in a small parameter. We present a renormalization group calculation and compare these results with those of a simulation.Comment: As-published version; two significant errors fixed, two references adde

Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.Comment: 20 pages. Some changes, the most important being on Conjecture 3.2, three references added ([Mas75], [MB90] and [Yu94]) and one reference updated [BS12]. Accepted in Bull. Brazil. Mat. So

Aquatic weed management: Herbicides

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A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0

We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A -> 0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the following cases: (a) annihilation in the infinite line and in infinite (discrete) chains; (b) annihilation with input of single particles, adjacent particle pairs, and particle pairs separated by a given distance; (c) annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings, with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some other minor changes, to conform with final for

Lattice Kinetics of Diffusion-Limited Coalescence and Annihilation with Sources

We study the 1D kinetics of diffusion-limited coalescence and annihilation with back reactions and different kinds of particle input. By considering the changes in occupation and parity of a given interval, we derive sets of hierarchical equations from which exact expressions for the lattice coverage and the particle concentration can be obtained. We compare the mean-field approximation and the continuum approximation to the exact solutions and we discuss their regime of validity.Comment: 24 pages and 3 eps figures, Revtex, accepted for publication in J. Phys.

Beyond Prejudice as Simple Antipathy: Hostile and Benevolent Sexism Across Cultures

The authors argue that complementary hostile and benevolent componen:s of sexism exist ac ro.ss cultures. Male dominance creates hostile sexism (HS). but men's dependence on women fosters benevolent sexism (BS)-subjectively positive attitudes that put women on a pedestal but reinforce their subordination. Research with 15,000 men and women in 19 nations showed that (a) HS and BS are coherenl constructs th at correlate positively across nations, but (b) HS predicts the ascription of negative and BS the ascription of positive traits to women, (c) relative to men, women are more likely to reject HS than BS. especially when overall levels of sexism in a culture are high, and (d) national averages on BS and HS predict gender inequal ity across nations. These results challenge prevailing notions of prejudice as an antipathy in that BS (an affectionate, patronizing ideology) reflects inequality and is a cross-culturally pervasive complement to HS

Water Quality at Caddo Lake, Center for Invasive Species Eradication: Final Report

Giant salvinia, a highly invasive aquatic fern native to South America, poses a serious threat to Texas’ waters and has done so since its discovery in the state in the 1990s. If left unmanaged, giant salvinia can cause a multitude of impacts including loss of recreational use, reductions in biodiversity, decreases in water quality, and monetary losses due to control costs and lost revenues. To counter this threat, the Center for Invasive Species Eradication (CISE) was created in 2010 with funding support from then U.S. Senator Kay Bailey Hutchison and the USDA Natural Resource Conservation Service (NRCS) to advance the knowledge about this species and treatment options and hopefully enable eradication of this noxious non-native plant species in Texas. Special focus of the Center’s efforts was placed on Caddo Lake. It is Texas’ only natural lake and has been plagued by giant salvinia since 2006. Levels of the invader present have risen and fallen with changes in weather and lake levels yet the threat it poses remains despite considerable treatment efforts

Reaction Front in an A+B -> C Reaction-Subdiffusion Process

We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone

Discovery and integration of Web 2.0 content into geospatial information infrastructures: a use case in wild fire monitoring

Efficient environment monitoring has become a major concern for society to guarantee sustainable development. For instance, forest fire detection and analysis is important to provide early warning systems and identify impact. In this environmental context, availability of up-to-date information is very important for reducing damages caused. Environmental applications are deployed on top of GeospatialInformation Infrastructures (GIIs) to manage information pertaining to our environment. Suchinfrastructures are traditionally top-down infrastructures that do not consider user participation. This provokes a bottleneck in content publication and therefore a lack of content availability. On the contrary mainstream IT systems and in particular the emerging Web 2.0 Services allow active user participation that is becoming a massive source of dynamic geospatial resources. In this paper, we present a webservice, that implements a standard interface, offers a unique entry point for spatial data discovery, both in GII services and web 2.0 services. We introduce a prototype as proof of concept in a forest fire scenario, where we illustrate how to leverage scientific data and web 2.0 conten