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  • 1
    Electronic Resource
    Electronic Resource
    Meromorphic structure of the Mellin transforms and short-distance behavior of correlation integrals (1992)
    Springer
    Journal of statistical physics 66 (1992), S. 515-533 
    Details
    ISSN: 1572-9613
    Keywords: Mixing repellers ; Mellin transform ; potential and energy integrals ; corrections to scaling laws ; singularity spectrum and residues
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The short-distance behavior of the measure of a sphere and of the correlation integral is determined, in the case of disconnected repellers, by scaling laws whose corrections are oscillating functions, periodic or aperiodic, depending on exact or approximate self-similarity of the measure. The Mellin transforms prove to be the correct analytic tool in order to investigate these corrections to scaling. It has been previously proved that they are meromorphic for linear Cantor sets and that the leading pole gives the correlation dimension in agreement with the results of the thermodynamic formalism. Here we show that the residues of these poles can also be computed to any desired accuracy with simple algorithms and that the knowledge of the singularity spectrum of the Mellin transforms provides the Fourier spectrum of the scaling correction for the self-similar measure and that it reproduces the damped oscillations in the generic case. The method applies to the nonlinear repellers such as the disconnected Julia sets by using an approximation theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01060078
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  • 2
    Electronic Resource
    Electronic Resource
    Entanglement complexity of lattice ribbons (1996)
    Springer
    Journal of statistical physics 85 (1996), S. 103-130 
    Details
    ISSN: 1572-9613
    Keywords: Ribbon ; topological entanglement ; knot ; link ; satellite knot ; writhe ; double-stranded polymer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a discrete ribbon model for double-stranded polymers where the ribbon is constrained to lie in a three-dimensional lattice. The ribbon can be open or closed, and closed ribbons can be orientable or nonorientable. We prove some results about the asymptotic behavior of the numbers of ribbons withn plaquettes, and a theorem about the frequency of occurrence of certain patterns in these ribbons. We use this to derive results about the frequency of knots in closed ribbons, the linking of the boundary curves of orientable closed ribbons, and the twist and writhe of ribbons. We show that the centerline and boundary of a closed ribbon are both almost surely knotted in the infinite-n limit. For an orientable ribbon, the expectation of the absolute value of the linking number of the two boundary curves increases at least as fast as √n, and similar results hold for the twist and writhe.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02175557
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