Low temperature shape relaxation of 2-d islands by edge diffusion

We present a precise microscopic description of the limiting step for low temperature shape relaxation of two dimensional islands in which activated diffusion of particles along the boundary is the only mechanism of transport allowed. In particular, we are able to explain why the system is driven irreversibly towards equilibrium. Based on this description, we present a scheme for calculating the duration of the limiting step at each stage of the relaxation process. Finally, we calculate numerically the total relaxation time as predicted by our results and compare it with simulations of the relaxation process.Comment: 11 pages, 5 figures, to appear in Phys. Rev.

Self-organized metal nanostructures through laser driven thermocapillary convection

When ultrathin metal films are subjected to multiple cycles of rapid melting and resolidification by a ns pulsed laser, spatially correlated interfacial nanostructures can result from a competition among several possible thin film self-organizing processes. Here we investigate self-organization and the ensuing length scales when Co films (1-8 nm thick) on SiO_{\text{2}} surfaces are repeatedly and rapidly melted by non-uniform (interference) laser irradiation. Pattern evolution produces nanowires, which eventually break-up into nanoparticles exhibiting spatial order in the nearest neighbor spacing, \lambda_{NN2}.The scaling behavior is consistent with pattern formation by thermocapillary flow and a Rayleigh-like instability. For h_{0}\leq2 nm, a hydrodynamic instability of a spinodally unstable film leads to the formation of nanoparticles.Comment: 10 pages, 3 figure

Closed Universes With Black Holes But No Event Horizons As a Solution to the Black Hole Information Problem

We show it is possible for the information paradox in black hole evaporation to be resolved classically. Using standard junction conditions, we attach the general closed spherically symmetric dust metric to a spacetime satisfying all standard energy conditions but with a single point future c-boundary. The resulting Omega Point spacetime, which has NO event horizons, nevertheless has black hole type trapped surfaces and hence black holes. But since there are no event horizons, information eventually escapes from the black holes. We show that a scalar quintessence field with an appropriate exponential potential near the final singularity would give rise to an Omega Point final singularity.Comment: 27 pages in LaTex2e, no figure

Duality between quantum symmetric algebras

Using certain pairings of couples, we obtain a large class of two-sided non-degenerated graded Hopf pairings for quantum symmetric algebras.Comment: 15 pages. Letters in Math. Phy., to appear soo