Small-scale behaviour in deterministic reaction models (Articolo in rivista)

Type
Label
  • Small-scale behaviour in deterministic reaction models (Articolo in rivista) (literal)
Anno
  • 2010-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1088/1751-8113/43/40/405002 (literal)
Alternative label
  • Paolo Politi (1); Daniel ben-Avraham (2,3) (2010)
    Small-scale behaviour in deterministic reaction models
    in Journal of physics. A, Mathematical and theoretical (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Paolo Politi (1); Daniel ben-Avraham (2,3) (literal)
Pagina inizio
  • 405002 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://iopscience.iop.org/1751-8121/43/40/405002 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 43 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#note
  • fasc. (40). IOP Publishing. (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 40 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • (1) Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy (2) Physics Department, Clarkson University, Potsdam, NY 13699-5820, USA (3) Department of Mathematics, Clarkson University, Potsdam, NY 13699-5815, USA (literal)
Titolo
  • Small-scale behaviour in deterministic reaction models (literal)
Abstract
  • In a recent paper published in this journal (2009 J. Phys. A: Math. Theor. 42 495004) we studied a one-dimensional particles system where nearest particles attract with a force inversely proportional to a power ? of their distance and coalesce upon encounter. Numerics yielded a distribution function h(z) for the gap between neighbouring particles, with h(z) ~ z?(?) for small z and ?(?) ?. We can now prove analytically that in the strict limit of z ? 0, ? = ? for ? 0, corresponding to the mean-field result, and we compute the length scale where the mean field breaks down. More generally, in that same limit correlations are negligible for any similar reaction model where attractive forces diverge with vanishing distance. The actual meaning of the measured exponent ?(?) remains an open question. (literal)
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