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Robert V. Moody

  1. Diffraction of stochastic point sets: Explicitly computable examples.

    Wed, 11/11/2009 - 16:01 — SomNambul
    Authors: Michael Baake, Robert V. Moody, Matthias Birkner
    Subjects: Mathematical Physics
    Abstract

    Stochastic point processes relevant to the theory of long-range aperiodic
    order are considered that display diffraction spectra of mixed type, with
    special emphasis on explicitly computable cases together with a unified
    approach of reasonable generality. The latter is based on the classical theory
    of point processes and the Palm distribution. Several pairs of autocorrelation
    and diffraction measures are discussed which show a duality structure analogous
    to that of the Poisson summation formula for lattice Dirac combs.

  2. Pure Point Dynamical and Diffraction Spectra.

    Tue, 10/27/2009 - 16:01 — SomNambul
    Authors: Boris Solomyak, Jeong-Yup Lee, Robert V. Moody
    Subjects: Dynamical Systems
    Abstract

    We show that for multi-colored Delone point sets with finite local complexity
    and uniform cluster frequencies the notions of pure point diffraction and pure
    point dynamical spectrum are equivalent.

  3. Consequences of Pure Point Diffraction Spectra for Multiset Substitution Systems.

    Mon, 10/26/2009 - 14:11 — SomNambul
    Authors: Boris Solomyak, Jeong-Yup Lee, Robert V. Moody
    Subjects: Metric Geometry
    Abstract

    There is a growing body of results in the theory of discrete point sets and
    tiling systems giving conditions under which such systems are pure point
    diffractive. Here we look at the opposite direction: what can we infer about a
    discrete point set or tiling, defined through a primitive substitution system,
    given that it is pure point diffractive? Our basic objects are Delone multisets
    and tilings, which are self-replicating under a primitive substitution system
    of affine mappings with a common expansive map $Q$.

  4. Deforming Meyer sets.

    Mon, 10/26/2009 - 14:10 — SomNambul
    Authors: Jeong-Yup Lee, Robert V. Moody
    Subjects: Metric Geometry
    Abstract

    A linear deformation of a Meyer set $M$ in $\RR^d$ is the image of $M$ under
    a group homomorphism of the group $[M]$ generated by $M$ into $\RR^d$. We
    provide a necessary and sufficient condition for such a deformation to be a
    Meyer set. In the case that the deformation is a Meyer set and the deformation
    is injective, the deformation is pure point diffractive if the orginal set $M$
    is pure point diffractive.

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