A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening

We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is flat on average, so that there is no bias due to gravity. We find anomalous scaling: the expected logarithmic smoothing at short length and time scales gives way to roughening in the asymptotic limit, where novel and non-trivial exponents are found.Comment: 7 Pages, 6 Figures; Granular Matter, 2012 (Online

Pharmacokinetic/pharmacodynamic modelling approaches in paediatric infectious diseases and immunology.

Pharmacokinetic/pharmacodynamic (PKPD) modelling is used to describe and quantify dose-concentration-effect relationships. Within paediatric studies in infectious diseases and immunology these methods are often applied to developing guidance on appropriate dosing. In this paper, an introduction to the field of PKPD modelling is given, followed by a review of the PKPD studies that have been undertaken in paediatric infectious diseases and immunology. The main focus is on identifying the methodological approaches used to define the PKPD relationship in these studies. The major findings were that most studies of infectious diseases have developed a PK model and then used simulations to define a dose recommendation based on a pre-defined PD target, which may have been defined in adults or in vitro. For immunological studies much of the modelling has focused on either PK or PD, and since multiple drugs are usually used, delineating the relative contributions of each is challenging. The use of dynamical modelling of in vitro antibacterial studies, and paediatric HIV mechanistic PD models linked with the PK of all drugs, are emerging methods that should enhance PKPD-based recommendations in the future