Binary-state dynamics (such as the susceptible-infected-susceptible (SIS) model of disease spread, or Glauber spin dynamics) on random networks are accurately approximated using master equations. Standard mean-field and pairwise theories are shown to result from seeking approximate solutions of the master equations. Applications to the calculation of SIS epidemic thresholds and critical points of nonequilibrium spin models are also demonstrated.
Khoury, Maria; Gleeson, James P.; Sancho, J. M.; Lacasta, A. M.; Lindenberg, Katja(American Physical Society, 2009)
Transport and diffusion of particles on modulated surfaces is a nonequilibrium problem which is receiving a great deal of attention due to its technological applications, but analytical calculations are scarce. In earlier ...
Gleeson, James P.; Melnik, Sergey; Ward, Jonathan A; Porter, Mason A; Murcha, Peter J(American Physical Society, 2012)
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is ...
Gleeson, James P.(American Physical Society, 2002)
Recently Vlad et al. [Phys. Rev. E. 63, 066304 (2001)] applied the method of decorrelation trajectories to
the transport of tracers in stochastic velocity fields with constant drift, and found that the average ...
Gleeson, James P.(American Physical Society, 2002)
A quadrature expression is derived for the probability density function of passive tracers advected from a
point by a one-dimensional, single-scale, Gaussian velocity field. The effect of trapping on the tracer moments
and ...
Gleeson, James P.(American Physical Society, 2008)
The mean size of unordered binary avalanches on infinite directed random networks may be determined using the damage propagation function introduced by [B. Samuelsson and J. E. S. Socolar, Phys. Rev. E 74, 036113 (2006)]. ...
