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Thursday, October 04

The Hull and Tiling Space of an Aperiodic Solid

Jean V. Bellissard, Georgia Institute of Technology, Atlanta
Joint Institute for Neutron Sciences Seminar
10:00 AM — 11:00 AM, Joint Institute for Neutron Sciences (Building 8630),
Room A-202
Contact: Hope Moore-Webb (hmoore2@utk.edu), 865.576.8630

Abstract

A solid can be represented by the set $\mathcal L$ of the positions of its atomic nuclei. This set is "uniformly discrete", namely there is a minimum distance between its points. The Hull can be defined as the set of possible limit configurations obtained after translating $\mathcal L$. The Tiling Space is the set of all atomic configurations sharing with $\mathcal L$ the same local patches (modulo translation). It will be shown that these two concepts are equivalent. The mechanical properties of the solid will be shown to be, at least qualitatively, connected with the topological and geometrical properties of the Hull.

Examples will be discussed. At least it will be shown how to construct a microscopic dissipative dynamics, on the Hull, liable to describe the dynamic of the solid in the large.