Finite-size scaling study of the ballistic deposition model in (1+1)-dimensions

We performed extensive Monte Carlo simulations of the ballistic deposition model in (1 + 1)-dimensions for several system sizes up to 1280 lattice constants, on the square lattice. Though the ballistic deposition model is generally accepted to belong to the Kardar Parisi-Zhang (KPZ) universality class, strong corrections to scaling prevent numerical estimates of the exponents close to the asymptotic values. We obtained a ³ 0.40, b ³ 0.30, and z ³ 1.16, which are consistent with the expected KPZ values of a = 1/2, b = 1/3, and z = 3/2. We found a slow, and even non monotonic, convergence of the exponents towards the asymptotic values, which corroborates previous claims in the literature of strong corrections to scaling

Evolution of far-from-equilibrium nanostructures on Ag(100) surfaces: Protrusions and indentations at extended step edges

Scanning tunneling microscopy is used to monitor the formation and relaxation of nanoprotrusions and nanoindentations at extended step edges following submonolayer deposition of Ag on Ag(100). Deposition of up to about 1/4 ML Ag produces isolated two-dimensional (2D) Ag clusters, which subsequently diffuse, collide, and coalesce with extended step edges, thus forming protrusions. Deposition of larger submonolayer amounts of Ag causes existing step edges to advance across terraces, incorporating 2D islands. The resulting irregular step structure rapidly straightens after terminating deposition, except for a few larger indentations. Relaxation of these far-from-equilibrium step-edge nanoconfigurations is monitored to determine rates for restructuring versus local geometry and feature size. This behavior is analyzed utilizing kinetic Monte Carlo simulations of an atomistic lattice-gas model for relaxation of step-edge nanostructures. In this model, mass transport is mediated by diffusion along the step edge (i.e., “periphery diffusion”). The model consistently fits observed behavior, and allows a detailed characterization of the relaxation process, including assessment of key activation energies

Smoluchowski ripening of Ag islands on Ag(100)

Using scanning tunneling microscopy, we study the post-deposition coarsening of distributions of large, two-dimensional Ag islands on a perfect Ag(100) surface at 295 K. The coarsening process is dominated by diffusion, and subsequent collision and coalescence of these islands. To obtain a comprehensive characterization of the coarsening kinetics, we perform tailored families of experiments, systematically varying the initial value of the average island size by adjusting the amount of Ag deposited (up to 0.25 ML). Results unambiguously indicate a strong decrease in island diffusivity with increasing island size. An estimate of the size scaling exponent follows from a mean-field Smoluchowski rate equation analysis of experimental data. These rate equations also predict a rapid depletion in the initial population of smaller islands. This leads to narrowing of the size distribution scaling function from its initial form, which is determined by the process of island nucleation and growth during deposition. However, for later times, a steady increase in the width of this scaling function is predicted, consistent with observed behavior. Finally, we examine the evolution of Ag adlayers on a strained Ag(100) surface, and find significantly enhanced rates for island diffusion and coarsening

Parking and the visual perception of space

Using measured data we demonstrate that there is an amazing correspondence among the statistical properties of spacings between parked cars and the distances between birds perching on a power line. We show that this observation is easily explained by the fact that birds and human use the same mechanism of distance estimation. We give a simple mathematical model of this phenomenon and prove its validity using measured data

Exact Solutions of Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation

We report exact results for one-dimensional reaction-diffusion models A+A -> inert, A+A -> A, and A+B -> inert, where in the latter case like particles coagulate on encounters and move as clusters. Our study emphasized anisotropy of hopping rates; no changes in universal properties were found, due to anisotropy, in all three reactions. The method of solution employed mapping onto a model of coagulating positive integer charges. The dynamical rules were synchronous, cellular-automaton type. All the asymptotic large-time results for particle densities were consistent, in the framework of universality, with other model results with different dynamical rules, when available in the literature.Comment: 28 pages in plain TeX + 2 PostScript figure

Anisotropic Diffusion-Limited Reactions with Coagulation and Annihilation

One-dimensional reaction-diffusion models A+A -> 0, A+A -> A, and $A+B -> 0, where in the latter case like particles coagulate on encounters and move as clusters, are solved exactly with anisotropic hopping rates and assuming synchronous dynamics. Asymptotic large-time results for particle densities are derived and discussed in the framework of universality.Comment: 13 pages in plain Te

Anomalous self-diffusion in the ferromagnetic Ising chain with Kawasaki dynamics

We investigate the motion of a tagged spin in a ferromagnetic Ising chain evolving under Kawasaki dynamics. At equilibrium, the displacement is Gaussian, with a variance growing as $A t^{1/2}$. The temperature dependence of the prefactor $A$ is derived exactly. At low temperature, where the static correlation length $\xi$ is large, the mean square displacement grows as $(t/\xi^2)^{2/3}$ in the coarsening regime, i.e., as a finite fraction of the mean square domain length. The case of totally asymmetric dynamics, where $(+)$ (resp. $(-)$) spins move only to the right (resp. to the left), is also considered. In the steady state, the displacement variance grows as $B t^{2/3}$. The temperature dependence of the prefactor $B$ is derived exactly, using the Kardar-Parisi-Zhang theory. At low temperature, the displacement variance grows as $t/\xi^2$ in the coarsening regime, again proportionally to the mean square domain length.Comment: 22 pages, 8 figures. A few minor changes and update