Variational and accessible soliton approximations to multidimensional solitons in highly nonlocal nonlinear media.

We apply the variational approach to solitons in highly nonlocal nonlinear media in D = 1, 2, 3 dimensions. We compare results obtained by the variational approach with those obtained by the accessible soliton approximation, by considering the same system of equations in the same spatial region and under the same boundary conditions. To assess the accuracy of these approximations, we also compare them with the numerical solution of the equations. We discover that the accessible soliton approximation suffers from systematic errors, when compared to the variational approach and the numerical solution. The errors increase with the dimension of the system. The variational highly nonlocal approximation provides more accurate results in any dimension and as such is more appropriate solution than the accessible soliton approximation.

Kinetics of deposition of oriented superdisks.

We use numerical Monte Carlo simulation to study the kinetics of the deposition of oriented superdisks, bounded by the Lame curves of the form |x|(2p)+|y|(2p)=1 on a regular planar substrate. Recently, it was shown that the maximum packing density as well as jamming density ρ(J) exhibit a discontinuous derivative at p=0.5 when the shape changes from convex to concave form. By careful examination of the late-stage approach to the jamming limit, we find that the leading term in the temporal development is also nonanalytic at p=0.5 and offer heuristic excluded-area arguments for this behavior.