Tilings of space and superhomogeneous point processes (Articolo in rivista)

Type
Label
  • Tilings of space and superhomogeneous point processes (Articolo in rivista) (literal)
Anno
  • 2008-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1103/PhysRevE.77.031125 (literal)
Alternative label
  • A. Gabrielli (1,2); M. Joyce (3); S. Torquato (4,5,6,7) (2008)
    Tilings of space and superhomogeneous point processes
    in Physical review. E, Statistical, nonlinear, and soft matter physics (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • A. Gabrielli (1,2); M. Joyce (3); S. Torquato (4,5,6,7) (literal)
Pagina inizio
  • 031125 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 77 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#note
  • American Physical Society (APS). (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 12 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • 1) SMC-INFM, Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, I-00185, Rome, Italy 2) ISC-CNR, Via dei Taurini 19, I-00185 Rome, Italy 3) Laboratoire de Physique Nucléaire et de Hautes Energies, UMR-7585, Université Pierre et Marie Curie, Paris 6, 75252 Paris Cedex 05, France 4) Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA 5) Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544 6) Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA 7) Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544, USA (literal)
Titolo
  • Tilings of space and superhomogeneous point processes (literal)
Abstract
  • We consider the construction of point processes from tilings, with equal- volume tiles, of d- dimensional Euclidean space R-d. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which are ' superhomogeneous' ( or ' hyperuniform') - i. e., for which the structure factor S ( k ) vanishes when the wave vector k tends to zero. The exponent gamma characterizing the leading smallk behavior, S ( k -> 0)proportional to k(gamma), depends in a simple manner on the nature of the correlation properties of the specific tiling and on the conservation of the mass moments of the tiles. Assigning one point to the center of mass of each tile gives the exponent gamma= 4 for any tiling in which the shapes and orientations of the tiles are short- range correlated. Smaller exponents in the range 4- d < gamma < 4 ( and thus always superhomogeneous for d <= 4 ) may be obtained in the case that the latter quantities have long- range correlations. Assigning more than one point to each tile in an appropriate way, we show that one can obtain arbitrarily higher exponents in both cases. We illustrate our results with explicit constructions using known deterministic tilings, as well as some simple stochastic tilings for which we can calculate S ( k ) exactly. Our results provide an explicit analytical construction of point processes with gamma > 4. Applications to condensed matter physics, and also to cosmology, are briefly discussed. (literal)
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