Numerical test of the damping time of layer-by-layer growth on stochastic models

We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.Comment: 4 pages, source LaTeX file and 5 PS figure

Anisotropy of Growth of the Close-Packed Surfaces of Silver

The growth morphology of clean silver exhibits a profound anisotropy: The growing surface of Ag(111) is typically very rough while that of Ag(100) is smooth and flat. This serious and important difference is unexpected, not understood, and hitherto not observed for any other metal. Using density functional theory calculations of self-diffusion on flat and stepped Ag(100) we find, for example, that at flat regions a hopping mechanism is favored, while across step edges diffusion proceeds by an exchange process. The calculated microscopic parameters explain the experimentally reported growth properties.Comment: RevTeX, 4 pages, 3 figures in uufiles form, to appear in Phys. Rev. Let

Lattice Effects in Crystal Evaporation

We study the dynamics of a stepped crystal surface during evaporation, using the classical model of Burton, Cabrera and Frank, in which the dynamics of the surface is represented as a motion of parallel, monoatomic steps. The validity of the continuum approximation treated by Frank is checked against numerical calculations and simple, qualitative arguments. The continuum approximation is found to suffer from limitations related, in particular, to the existence of angular points. These limitations are often related to an adatom detachment rate of adatoms which is higher on the lower side of each step than on the upper side ("Schwoebel effect").Comment: DRFMC/SPSMS/MDN, Centre d'Etudes Nucleaires de Grenoble, 25 pages, LaTex, revtex style. 8 Figures, available upon request, report# UBFF30119

Growth of Patterned Surfaces

During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the quality of reproduction decays exponentially with a characteristic time which is linear in the activation energy of surface diffusion. We argue that this life time of a pattern is optimized, if the characteristic feature size of the pattern is larger than $(D/F)^{1/(d+2)}$, where $D$ is the surface diffusion constant, $F$ the deposition rate and $d$ the surface dimension.Comment: 4 pages, 4 figures, uses psfig; to appear in Phys. Rev. Let

Interleukin-8 levels and activity in delayed-healing human thermal wounds

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72020/1/j.1524-475x.2000.00216.x.pd

Random Walks for Spike-Timing Dependent Plasticity

Random walk methods are used to calculate the moments of negative image equilibrium distributions in synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of sensory electric fields. Of particular behavioral importance to the fish is the variance of the equilibrium postsynaptic potential in the presence of noise, which is determined by the variance of the equilibrium weight distribution. Recurrence relations are derived for the moments of the equilibrium weight distribution, for arbitrary postsynaptic potential functions and arbitrary learning rules. For the case of homogeneous network parameters, explicit closed form solutions are developed for the covariances of the synaptic weight and postsynaptic potential distributions.Comment: 18 pages, 8 figures, 15 subfigures; uses revtex4, subfigure, amsmat

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Mounding Instability and Incoherent Surface Kinetics

Mounding instability in a conserved growth from vapor is analysed within the framework of adatom kinetics on the growing surface. The analysis shows that depending on the local structure on the surface, kinetics of adatoms may vary, leading to disjoint regions in the sense of a continuum description. This is manifested particularly under the conditions of instability. Mounds grow on these disjoint regions and their lateral growth is governed by the flux of adatoms hopping across the steps in the downward direction. Asymptotically ln(t) dependence is expected in 1+1- dimensions. Simulation results confirm the prediction. Growth in 2+1- dimensions is also discussed.Comment: 4 pages, 4 figure

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420