(1) Institut für Mathematik, Universität Greifswald, Jahnstrasse 15a, 17487 Greifswald, Germany;(2) Applied Mathematics Department, Faculty of Mathematics and Computing, The Open University, Walton Hall, Milton Keynes, MK7 6AA, England
Abstract:
The radial distribution function is a characteristic geometric
quantity of a point set in Euclidean space that reflects itself in the
corresponding diffraction spectrum and related objects of physical
interest. The underlying combinatorial and algebraic structure is
well understood for crystals, but less so for non-periodic
arrangements such as mathematical quasicrystals or model sets. In
this note we summarise several aspects of central versus averaged
shelling, illustrate the difference with explicit examples and
discuss the obstacles that emerge with aperiodic order.