Correlations in nano-scale step fluctuations: comparison of simulation and experiments

We analyze correlations in step-edge fluctuations using the Bortz-Kalos-Lebowitz kinetic Monte Carlo algorithm, with a 2-parameter expression for energy barriers, and compare with our VT-STM line-scan experiments on spiral steps on Pb(111). The scaling of the correlation times gives a dynamic exponent confirming the expected step-edge-diffusion rate-limiting kinetics both in the MC and in the experiments. We both calculate and measure the temperature dependence of (mass) transport properties via the characteristic hopping times and deduce therefrom the notoriously-elusive effective energy barrier for the edge fluctuations. With a careful analysis we point out the necessity of a more complex model to mimic the kinetics of a Pb(111) surface for certain parameter ranges.Comment: 10 pages, 9 figures, submitted to Physical Review

Tube Width Fluctuations in F-Actin Solutions

We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation (BCA). In this systematic generalization of the standard mean-field approach effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.Comment: Final version, 5 pages, 4 figure

A facet is not an island: step-step interactions and the fluctuations of the boundary of a crystal facet

In a recent paper [Ferrari et al., Phys. Rev. E 69, 035102(R) (2004)], the scaling law of the fluctuations of the step limiting a crystal facet has been computed as a function of the facet size. Ferrari et al. use rigorous, but physically rather obscure, arguments. Approaching the problem from a different perspective, we rederive more transparently the scaling behavior of facet edge fluctuations as a function of time. Such behavior can be scrutinized with STM experiments and with numerical simulations.Comment: 3 page

Direct observation of the tube model in F-actin solutions

Mutual uncrossability of polymers generates topological constraints on their conformations and dynamics, which are generally described using the tube model. We imaged confinement tubes for individual polymers within a F-actin solution by sampling over many successive micrographs of fluorescently labeled probe filaments. The resulting average tube width shows the predicted scaling behavior. Unexpectedly, we found an exponential distribution of tube curvatures which is attributed to transient entropic trapping in network void spaces.Comment: 6 pages, 4 figure

Spiral Evolution in a Confined Geometry

Supported nanoscale lead crystallites with a step emerging from a non-centered screw dislocation on the circular top facet were prepared by rapid cooling from just above the melting temperature. STM observations of the top facet show a nonuniform rotation rate and shape of the spiral step as the crystallite relaxes. These features can be accurately modeled using curvature driven dynamics, as in classical models of spiral growth, with boundary conditions fixing the dislocation core and regions of the step lying along the outer facet edge.Comment: 4 pages, 3 figures, to be published in Physical Review Letter

Growing interfaces uncover universal fluctuations behind scale invariance

Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a line, though it is also scale-invariant and arises in nature as various types of interface growth, is far less understood. The two major missing ingredients are: an experiment that allows a quantitative comparison with theory and an analytic solution of the Kardar-Parisi-Zhang (KPZ) equation, a prototypical equation for describing growing interfaces. Here we solve both problems, showing unprecedented universality beyond the scaling laws. We investigate growing interfaces of liquid-crystal turbulence and find not only universal scaling, but universal distributions of interface positions. They obey the largest-eigenvalue distributions of random matrices and depend on whether the interface is curved or flat, albeit universal in each case. Our exact solution of the KPZ equation provides theoretical explanations.Comment: 5 pages, 3 figures, supplementary information available on Journal pag

Nanoscale Equilibrium Crystal Shapes

The finite size and interface effects on equilibrium crystal shape (ECS) have been investigated for the case of a surface free energy density including step stiffness and inverse-square step-step interactions. Explicitly including the curvature of a crystallite leads to an extra boundary condition in the solution of the crystal shape, yielding a family of crystal shapes, governed by a shape parameter c. The total crystallite free energy, including interface energy, is minimized for c=0, yielding in all cases the traditional PT shape (z x3/2). Solutions of the crystal shape for c≠0 are presented and discussed in the context of meta-stable states due to the energy barrier for nucleation. Explicit scaled relationships for the ECS and meta-stable states in terms of the measurable step parameters and the interfacial energy are presented.Comment: 35 page