Dynamics of curved interfaces

Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance principle has been applied. We examine differences and similarities with the classical planar equations. Some characteristic features are the loss of correlation through time and a particular behaviour of the average fluctuations. Dependence on the metric is also explored. The diffusive model that propagates correlations ballistically in the planar situation is particularly interesting, as this propagation becomes nonuniversal in the new regime.Comment: Published versio

Percolation in deposits for competitive models in (1+1)-dimensions

The percolation behaviour during the deposit formation, when the spanning cluster was formed in the substrate plane, was studied. Two competitive or mixed models of surface layer formation were considered in (1+1)-dimensional geometry. These models are based on the combination of ballistic deposition (BD) and random deposition (RD) models or BD and Family deposition (FD) models. Numerically we find, that for pure RD, FD or BD models the mean height of the percolation deposit $\bar h$ grows with the substrate length $L$ according to the generalized logarithmic law $\bar h\propto (\ln (L))^\gamma$, where $\gamma=1.0$ (RD), $\gamma=0.88\pm 0.020$ (FD) and $\gamma=1.52\pm 0.020$ (BD). For BD model, the scaling law between deposit density $p$ and its mean height $\bar h$ at the point of percolation of type $p-p_\infty \propto \bar h^{-1/\nu_h}$ are observed, where $\nu_h =1.74\pm0.02$ is a scaling coefficient. For competitive models the crossover, %in $h$ versus $L$ corresponding to the RD or FD -like behaviour at small $L$ and the BD-like behaviour at large $L$ are observed.Comment: 8 pages,4 figures, Latex, uses iopart.cl

Percolation in Models of Thin Film Depositions

We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and ballistic (BD) deposition rules. In the mixed one-component models with deposition of only conducting particles, the mean height of the percolation layer (measured in monolayers) grows continuously from 0.89832 for the pure RD model to 2.605 for the pure RD model, but the percolation transition belong to the same universality class, as in the 2- dimensional random percolation problem. In two- component models with deposition of conducting and isolating particles, the percolation layer height approaches infinity as concentration of the isolating particles becomes higher than some critical value. The crossover from 2d to 3d percolation was observed with increase of the percolation layer height.Comment: 4 pages, 5 figure

Effect of Palmitic Acid on the Electrical Conductivity of Carbon Nanotubes−Epoxy Resin Composites

We found that the palmitic acid allows an efficient dispersion of carbon nanotubes in the epoxy matrix. We have set up an experimental protocol in order to enhance the CNTs dispersion in epoxy resin. Electrical conductivity is optimal using a 1:1 CNTs to palmitic acid weight ratio. The associated percolation threshold is found between 0.05 and 0.1 wt % CNTs, i.e., between 0.03 and 0.06 vol %. The SEM image shows essentially individual CNTs which is inagreement with conductivity measurements. In comparison with composites without palmitic acid, the use of palmitic acid improves the electrical properties of CNTs-epoxy resin composites