345,902 research outputs found

    Stability at Random Close Packing

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    The requirement that packings of hard particles, arguably the simplest structural glass, cannot be compressed by rearranging their network of contacts is shown to yield a new constraint on their microscopic structure. This constraint takes the form a bound between the distribution of contact forces P(f) and the pair distribution function g(r): if P(f) \sim f^{\theta} and g(r) \sim (r-{\sigma})^(-{\gamma}), where {\sigma} is the particle diameter, one finds that {\gamma} \geq 1/(2+{\theta}). This bound plays a role similar to those found in some glassy materials with long-range interactions, such as the Coulomb gap in Anderson insulators or the distribution of local fields in mean-field spin glasses. There is ground to believe that this bound is saturated, offering an explanation for the presence of avalanches of rearrangements with power-law statistics observed in packings

    Cooperative jump motions of jammed particles in a one-dimensional periodic potential

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    Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated and it is compared with theoretical estimates. We find that the size distribution of the cooperative jump motions obeys an exponential law in a large system.Comment: 5 pages, 4 figure

    Methods of averages expansions for artificial satellite applications

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    Formulas derived for averaged potential in artificial satellite theor

    TT-adic exponential sums of polynomials in one variable

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    The TT-adic exponential sum of a polynomial in one variable is studied. An explicit arithmetic polygon in terms of the highest two exponents of the polynomial is proved to be a lower bound of the Newton polygon of the CC-function of the T-adic exponential sum. This bound gives lower bounds for the Newton polygon of the LL-function of exponential sums of pp-power order
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