Michael Baake
Diffraction of stochastic point sets: Explicitly computable examples.
Wed, 11/11/2009 - 16:01 — SomNambulAuthors: Michael Baake, Robert V. Moody, Matthias Birkner
Subjects: Mathematical Physics
AbstractStochastic 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.Surprises in aperiodic diffraction.
Thu, 10/01/2009 - 20:55 — SomNambulAuthors: Michael Baake, Uwe Grimm
Subjects: Mathematical Physics
AbstractMathematical diffraction theory is concerned with the diffraction image of a
given structure and the corresponding inverse problem of structure
determination. In recent years, the understanding of systems with continuous
and mixed spectra has improved considerably. Moreover, the phenomenon of
homometry shows various unexpected new facets. Here, we report on some of the
recent results in an exemplary and informal fashion.Similar sublattices of planar lattices.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: Michael Baake, Rudolf Scharlau, Peter Zeiner
Subjects: Metric Geometry
AbstractThe similar sublattices of a planar lattice can be classified via its
multiplier ring. The latter is the ring of rational integers in the generic
case, and an order in an imaginary quadratic field otherwise. Several classes
of examples are discussed, with special emphasis on concrete results. In
particular, we derive Dirichlet series generating functions for the number of
distinct similar sublattices of a given index, and relate them to various zeta
functions of orders in imaginary quadratic fields.
User login
