Second cohomology groups and finite covers

For D an infinite set, k>1 and W the set of k-sets from D, there is a natural closed permutation group G_k which is a non-split extension of \mathbb{Z}_2^W by \Sym(D). We classify the closed subgroups of G_k which project onto \Sym(D)$. The question arises in model theory as a problem about finite covers, but here we formulate and solve it in algebraic terms.Comment: Typos corrected; change of title to 'Second cohomology groups and finite covers of infinite symmetric groups' in published versio

Crossover between mean-field and Ising critical behavior in a lattice-gas reaction-diffusion model

Lattice-gas models for CO oxidation can exhibit a discontinuous nonequilibrium transition between reactive and inactive states, which disappears above a critical CO-desorption rate. Using finite-size-scaling analysis, we demonstrate a crossover from Ising to mean-field behavior at the critical point, with increasing surface mobility of adsorbed CO or with decreasing system size. This behavior is elucidated by analogy with that of equilibrium Ising-type systems with long-range interactions.Comment: 6 pages, 3 figure

Systems issues in airborne Doppler radar/LIDAR certification

This report outlines: (1) thesis; (2) ground clutter challenge; (3) moving scatters (birds, bugs); (4) range ambiguities; and rain attenuation

The Federal Aviation Administration/Massachusetts Institute of Technology (FAA/MIT) Lincoln Laboratory Doppler weather radar program

The program focuses on providing real-time information on hazardous aviation weather to end users such as air traffic control and pilots. Existing systems will soon be replaced by a Next Generation Weather Radar (NEXRAD), which will be concerned with detecting such hazards as heavy rain and hail, turbulence, low-altitude wind shear, and mesocyclones and tornadoes. Other systems in process are the Central Weather Processor (CWP), and the terminal Doppler weather radar (TDWR). Weather measurements near Memphis are central to ongoing work, especially in the area of microbursts and wind shear

Using styles for more effective learning in multicultural and e-learning environments

Purpose – This Special Issue contains selected papers from the thirteenth annual European Learning Styles Information Network (ELSIN) conference held in Ghent, Belgium in June 2008. One of the key aims of ELSIN is to promote understanding of individual learning and cognitive differences through the dissemination of international multidisciplinary research about learning and cognitive styles and strategies of learning and thinking. Design/methodology/approach – Three papers within this special issue consider how style differences can inform the development of e-learning opportunities to enhance the learning of all (Vigentini; Kyprianidou, Demetriadis, Pombortsis and Karatasios; Zhu, Valcke and Schellens). The influence of culture on learning is also raised in the paper of Zhu and colleagues and those of Sulimma and Eaves which both focus more directly on cultural influences on style, learning and teaching. Findings – A number of key themes permeate the studies included in this Special Edition such as: the nature of styles; the intrinsic difficulty of isolating style variables from other variables impacting on performance; inherent difficulties in choosing the most appropriate style measures; the potential of e-learning to attend to individual learning differences; the role of culture in informing attitudes and access to learning; the development of constructivist learning environments to support learning through an understanding of individual differences; and most importantly how one can apply such insights about individual differences to inform and enhance instruction. Originality/value – The papers in this Special Issue contribute to enhanced knowledge about the value of style differences to design constructive learning environments in multicultural and e-learning contexts

Kinetic phase diagrams for the monomer–dimer surface reaction: Unification of mean‐field and lattice–gas behavior

We provide a unified discussion of kinetic phase transitions for mean‐field and lattice–gas treatments of the monomer–dimer surface reaction. For high surfacemobilities, kinetics is typically well described by mean‐field rate equations. These reveal bistability over a range of monomer adsorption rates which diminishes with increasing nonreactive monomer desorption rate d, and vanishes at some critical d=dc. Relative stability in the bistable region is determined from the behavior of chemical waves corresponding to the displacement of one stable state by the other. Their evolution is determined via appropriate reaction–diffusion equations. Conventional diffusion terms are modified here to reflect the influence of the presence of one species on diffusion of the other. We determine equistability (i.e., discontinuous transition) points for d≤dc, and thus construct a kinetic phase diagram including a spinodal line. For lower surface mobilities, analysis of lattice–gas models reveals qualitatively analogous behavior. The key difference is that for lower mobilities, spontaneous fluctuations are effective in automatically selecting the most stable state, i.e., in reducing metastability, and thus producing discontinuous transitions

Exactly solvable irreversible processes on Bethe lattices

We consider the kinetics of processes where the sites of a Bethe lattice are filled irreversibly and, in general, cooperatively by monomers, dimers, or polyatomics. For nearest neighbor and sometimes more general cooperative effects (including random filling as a special case), we show that the infinite hierarchy of rate equations for probabilities of empty subconfigurations can be exacty truncated and solved using a shielding property of empty sites. We indicate, in certain cases, a connection between these Bethe lattice solutions and certain approximate truncation solutions for corresponding processes on ‘‘physical’’ 2‐D and 3‐D lattices with the same coordination number

Existence and uniqueness of bound‐state eigenvectors for some channel coupling Hamiltonians

For the three‐particle, two‐cluster, 2×2 channel coupling Hamiltonians used, e.g., in H+2 and He bound‐state calculations, we demonstrate that typically there exist unique eigenvectors for all bound states. This result also holds, with some technical assumptions on the potentials, for the corresponding 3×3 case provided there are no spurious eigenvectors with bound‐state eigenvalues. The proofs use the analogous results for the corresponding Faddeev‐type Hamiltonians together with spurious multiplier relationships

Kinetic Phase Transitions in Catalytic Reaction Models

We review and augment recent developments in the understanding of microscopic lattice gas models for irreversible surface reactions where diffusion does not play a dominant role. Monomer-monomer reactions exhibit domain coarsening much slower than equilibrium Lifschitz-Cahn-Allen coarsening and instead reflect Voter model behavior. The monomer-dimer reaction is of particular interest as a model for CO oxidation. We provide a sophisticated characterization of the associated first- and second-order kinetic phase transitions (corresponding to poisoning) via \u27epidemic analyses . Here one considers the evolution of reaction starting from an empty patch embedded on an otherwise poisoned surface

Analysis of a diffusion-limited island growth mechanism for chemisorption and epitaxy

We consider an island growth mechanism wherein species adsorbed on top of two-dimensional islands diffuse to the edge and are then incorporated. A simple matrix formulation is developed for this random-walk problem which allows exact calculation of the growth probability distribution, neglecting island rearrangement. Furthermore, we also show how related trapping probabilities can be calculated recursively for various stages of island growth. The case of imperfect trapping at island edges is also considered, and reduction to Eden-model–type growth in the low-trapping-probability regime is demonstrated. In general, the growing islands are rounder and have fewer defects and narrower active zones than Eden clusters