Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of Levy walks on lattices. By including exponentially distributed waiting times separating the successive jump events of a walker, we are led to a description of such Levy walks in terms of multistate processes whose time-evolution is shown to obey a set of coupled delay differential equations. Using simple arguments, we obtain asymptotic solutions to these equations and rederive the scaling laws for the mean squared displacement of such processes. Our calculation includes the computation of all relevant transport coefficients in terms of the parameters of the models.

Giampaolo Cristadoro, Thomas Gilbert, Marco Lenci, David P. Sanders (2014). Transport properties of Lévy walks: An analysis in terms of multistate processes. EUROPHYSICS LETTERS, 108(5), 50002-p1-50002-p6 [10.1209/0295-5075/108/50002].

Transport properties of Lévy walks: An analysis in terms of multistate processes

CRISTADORO, GIAMPAOLO;LENCI, MARCO;
2014

Abstract

Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of Levy walks on lattices. By including exponentially distributed waiting times separating the successive jump events of a walker, we are led to a description of such Levy walks in terms of multistate processes whose time-evolution is shown to obey a set of coupled delay differential equations. Using simple arguments, we obtain asymptotic solutions to these equations and rederive the scaling laws for the mean squared displacement of such processes. Our calculation includes the computation of all relevant transport coefficients in terms of the parameters of the models.
2014
Giampaolo Cristadoro, Thomas Gilbert, Marco Lenci, David P. Sanders (2014). Transport properties of Lévy walks: An analysis in terms of multistate processes. EUROPHYSICS LETTERS, 108(5), 50002-p1-50002-p6 [10.1209/0295-5075/108/50002].
Giampaolo Cristadoro; Thomas Gilbert; Marco Lenci; David P. Sanders
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/11585/506580
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 10
social impact