Rate of Homogeneous Crystal Nucleation in molten NaCl

We report a numerical simulation of the rate of crystal nucleation of sodium chloride from its melt at moderate supercooling. In this regime nucleation is too slow to be studied with "brute-force" Molecular Dynamics simulations. The melting temperature of ("Tosi-Fumi") NaCl is $\sim 1060$K. We studied crystal nucleation at $T$=800K and 825K. We observe that the critical nucleus formed during the nucleation process has the crystal structure of bulk NaCl. Interestingly, the critical nucleus is clearly faceted: the nuclei have a cubical shape. We have computed the crystal-nucleation rate using two completely different approaches, one based on an estimate of the rate of diffusive crossing of the nucleation barrier, the other based on the Forward Flux Sampling and Transition Interface Sampling (FFS-TIS) methods. We find that the two methods yield the same result to within an order of magnitude. However, when we compare the extrapolated simulation data with the only available experimental results for NaCl nucleation, we observe a discrepancy of nearly 5 orders of magnitude. We discuss the possible causes for this discrepancy

Two dimensional black-hole as a topological coset model of c=1 string theory

We show that a special superconformal coset (with $\hat c =3$) is equivalent to $c=1$ matter coupled to two dimensional gravity. This identification allows a direct computation of the correlation functions of the $c=1$ non-critical string to all genus, and at nonzero cosmological constant, directly from the continuum approach. The results agree with those of the matrix model. Moreover we connect our coset with a twisted version of a Euclidean two dimensional black hole, in which the ghost and matter systems are mixed.Comment: 51 pages. Appendix by E. Frenke

The long wavelength limit of hard thermal loop effective actions

We derive a closed form expression for the long wavelength limit of the effective action for hard thermal loops in an external gravitational field. It is a function of the metric, independent of time derivatives. It is compared and contrasted with the static limit, and with the corresponding limits in an external Yang-Mills field.Comment: 5 page

Single-file diffusion and kinetics of template assisted assembly of colloids

We report computer simulation studies of the kinetics of ordering of a two dimensional system of particles on a template with a one dimensional periodic pattern. In equilibrium one obtains a re-entrant liquid-solid-liquid phase transition as the strength of the substrate potential is varied. We show that domains of crystalline order grow as $\sim t^{1/z}$, with $z \sim 4$ with a possible cross-over to $z \sim 2$ at late times. We argue that the $t^{1/4}$ law originates from {\em single-file} motion and annihilation of defect pairs of opposite topological charge along channels created by the template.Comment: 4 pages pdflatex 4 pdf figure