We propose a class of mean-field models for the isostatic transition of systems of soft spheres, in which the contact network is modeled as a random graph and each contact is associated to d degrees of freedom. We study such models in the hypostatic, isostatic, and hyperstatic regimes. The density of states is evaluated by both the cavity method and exact diagonalization of the dynamical matrix. We show that the model correctly reproduces the main features of the density of states of real packings and, moreover, it predicts the presence of localized modes near the lower band edge. Finally, the behavior of the density of states D(ω)∼ωα for ω→0 in the hyperstatic regime is studied. We find that the model predicts a nontrivial dependence of α on the details of the coordination distribution.

Benetti F.P.C., Parisi G., Pietracaprina F., Sicuro G. (2018). Mean-field model for the density of states of jammed soft spheres. PHYSICAL REVIEW. E, 97(6), 062157-1-062157-14 [10.1103/PhysRevE.97.062157].

Mean-field model for the density of states of jammed soft spheres

Sicuro G.
2018

Abstract

We propose a class of mean-field models for the isostatic transition of systems of soft spheres, in which the contact network is modeled as a random graph and each contact is associated to d degrees of freedom. We study such models in the hypostatic, isostatic, and hyperstatic regimes. The density of states is evaluated by both the cavity method and exact diagonalization of the dynamical matrix. We show that the model correctly reproduces the main features of the density of states of real packings and, moreover, it predicts the presence of localized modes near the lower band edge. Finally, the behavior of the density of states D(ω)∼ωα for ω→0 in the hyperstatic regime is studied. We find that the model predicts a nontrivial dependence of α on the details of the coordination distribution.
2018
Benetti F.P.C., Parisi G., Pietracaprina F., Sicuro G. (2018). Mean-field model for the density of states of jammed soft spheres. PHYSICAL REVIEW. E, 97(6), 062157-1-062157-14 [10.1103/PhysRevE.97.062157].
Benetti F.P.C.; Parisi G.; Pietracaprina F.; Sicuro G.
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/958330
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? 2
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 23
social impact