Patterns and long range correlations in idealized granular flows
An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the dow field u(r, t) (vortices) and in the density held n(r, t) (clusters), driven by unstable fluctuations, delta a = {delta n, delta u}. Their spatial correlations, (delta a(r, t)delta a(r', t)], as measured in molecular dynamics simulations, exhibit long range correlations; the mean vortex diameter grows as xi(t) proportional to root ln t; there occur transitions to macroscopic shearing states, etc. The Cahn-Hilliard theory of spinodal decomposition offers a qualitative understanding and quantitative estimates of the observed phenomena. When intrinsic length scales are of the order of the system size, effects of physical boundaries and periodic boundaries (finite size effects in simulations) are important.
long range correlations granular matter pattern formulation