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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Probability theory and related fields 101 (1995), S. 1-44 
    ISSN: 1432-2064
    Keywords: 60F10 ; 60G57 ; 60K35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider a dynamical interacting particle system whose empirical distribution tends to the solution of a spatially homogeneous Boltzmann type equation, as the number of particles tends to infinity. These laws of large numbers were proved for the Maxwellian molecules by H. Tanaka [Tal] and for the hard spheres by A.S. Sznitman [Szl]. In the present paper we investigate the corresponding large deviations: the large deviation upper bound is obtained and, using convex analysis, a non-variational formulation of the rate function is given. Our results hold for Maxwellian molecules with a cutoff potential and for hard spheres.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Aquatic ecology 26 (1992), S. 347-354 
    ISSN: 1573-5125
    Keywords: habitat preference ; Axarus ; behaviour ; dispersion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract During fall draw-down of a reservoir in northeast Kansas it was observed that larvae ofAxarus festivus were restricted to highly weathered Pennsylvanian Shale outcrops and surrounding coarse sediments with high-clay content derived from erosion of the shale outcroppings. Larvae constructed burrows into the outcrops and eroded coarse sediments, which they used to filter feed by setting up currents through the burrows. Burrows were widely distributed over the outcrops, with average densities ranging from 372–2,351 burrows m−2. However, closer inspection revealed that burrows were more common at apices of individual shale strata, where weathering of the outcrop was most advanced. Here burrows were more uniformly distributed and densities ranged to 4,166 burrows m−2. 73% of burrows contained larvae. Burrows were generally U-shaped, and averaged 1.8 mm in diameter and 42 mm in total length. Laboratory experiments revealed that 4th instar larvae removed from burrows could construct new burrows in weathered shale, but preferentially used old empty burrows if available. When given choices among alternative sediment combinations of sandvs. finely-ground shale, sandvs. coarsely-ground shale, and finely-ground shalevs. coarsely-ground shale, larvae exhibited statistically significant preferences for the finely-ground shales (P〈0.001), coarsely-ground shales (P〈0.001), and coarsely-ground shales (P〈0.01), respectively. It is concluded that larvae (1) actively select shale or high-clay content sediments, (2) can differentiate among sediments with differing physical properties and (3) exhibit behavioral choices for sediment types that guide them toward shale outcrops.
    Type of Medium: Electronic Resource
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