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We prove for a large class of tilings that, given a finite tile set, if it is possible to tile Euclideann-space with isometric copies of this set, then there is a tiling with the ‘local isomorphism property’.
Research supported in part by NSF Grant No. DMS-9001475. 相似文献
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In previous work, a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an appropriate definition of those packings to be considered optimally dense. Examples are given to illustrate various aspects of the density problem, in particular the shift in emphasis from the analysis of individual packings to spaces of packings. 相似文献
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The European Physical Journal A - In this paper, we have applied a three-dimensional approach for the calculation of the relativistic nucleon-nucleon potential. The quadratic operator relation... 相似文献
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We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The invariant is a quotient of ech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling spaces. We also introduce a module structure on cohomology which is very convenient as well as of intuitive value. 相似文献
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We consider tiling models of round quasicrystals which would have diffraction patterns which are fully rotation invariant—rings instead of Bragg peaks. They can be distinguished from glasses by self-similarity of the pattern of radii of the rings. 相似文献
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Charles Radin 《Communications in Mathematical Physics》1971,21(4):291-302
Sufficient conditions are given to obtain two levels of ergodic behavior for a wide class of dynamical systems. The notion of substate is emphasized and shown to lead to a natural generalization for noncommutative systems of the mean ergodic theorem onL
1. Applications to the time averaging of certain deviations from thermal equilibrium is mentioned. 相似文献
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We introduce a model of granular matter and use a volume/strain ensemble to analyze infinitesimal shearing. Monte Carlo simulation
suggests the model exhibits a second order phase transition associated with the onset of dilatancy. 相似文献