Incollection,
Clustering of sliding passive scalars driven by fluctuating surfaces
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
A collection of passive particles driven by a fluctuating potential
develops interesting correlations in space and time. We consider a
system of damped particles sliding down a fluctuating surface evolving
through Edwards-Wilkinson or Kardar-Parisi-Zhang dynamics. The
particles are found to reach an interesting steady state with long
range order, but with fluctuations which remain large in the
thermodynamic limit. The density-density correlation function is a
scaling function of separation and system size. Interestingly, the
scaling function is singular at small argument, signalling large-scale
clustering without well-defined interfaces --- a breakdown of the
Porod law. The nature of the singularity depends on whether or not
the particles interact with each other --- it is a divergence for
noninteracting particles, and a cusp singularity for particles with
hard core exclusion. Dynamical correlation functions also show
size-dependent scaling with singular scaling functions. These results
have a bearing on the passive scalar problem in fluid dynamics, as our
problem maps onto particles advected by a noisy Burgers fluid. The
properties of our strongly nonequilibrium system turn out to be
surprisingly similar to those of a system of particles at equilibrium
in a quenched disordered Sinai potential.
