DRIVEN DIFFUSIVE SYSTEMS WITH A MOVING OBSTACLE - A VARIATION ON THE BRAZIL NUTS PROBLEM

The authors present some surprising results of computer simulations on the driven diffusive motion of a 'polymer' in a 'sea of monomers'. The particles move on a lattice subject to a driving field that biases jump rates in a direction perpendicular to the polymer which occupies L sites (monomers occupy one site). This produces a stochastic asymmetric simple exclusion dynamics of the polymer-monomer lattice system. Simulations on a two-dimensional square lattice exhibit unexpected behaviour of the polymer velocity as a function of its length: the velocity V(L) first decreases and then increases. This may have relevance for the size segregation of particulate matter which results from the relative motion of different size particles induced by shaking (the Brazil nuts phenomenon). The location of the minimum of V(L) depends on the nature of the driving fields and on the density.