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