Anisotropic Diffusion Limited Aggregation

Using stochastic conformal mappings we study the effects of anisotropic perturbations on diffusion limited aggregation (DLA) in two dimensions. The harmonic measure of the growth probability for DLA can be conformally mapped onto a constant measure on a unit circle. Here we map $m$ preferred directions for growth of angular width $\sigma$ to a distribution on the unit circle which is a periodic function with $m$ peaks in $[-\pi, \pi)$ such that the width $\sigma$ of each peak scales as $\sigma \sim 1/\sqrt{k}$, where $k$ defines the ``strength'' of anisotropy along any of the $m$ chosen directions. The two parameters $(m,k)$ map out a parameter space of perturbations that allows a continuous transition from DLA (for $m=0$ or $k=0$) to $m$ needle-like fingers as $k \to \infty$. We show that at fixed $m$ the effective fractal dimension of the clusters $D(m,k)$ obtained from mass-radius scaling decreases with increasing $k$ from $D_{DLA} \simeq 1.71$ to a value bounded from below by $D_{min} = 3/2$. Scaling arguments suggest a specific form for the dependence of the fractal dimension $D(m,k)$ on $k$ for large $k$, form which compares favorably with numerical results.Comment: 6 pages, 4 figures, submitted to Phys. Rev.

The Friedheim\u27s of Rock Hill, South Carolina - Accession 715 #67

The Friedheim\u27s of Rock Hill, South Carolina relates the history of the family through narrative, stories, anecdotes and photographs. There is a outline of the family connections at the back of the booklet. The Friedheim Brothers operated a department store in Rock Hill in 1866. The store closed in 1965. The author, C.H. Albright married one of Arnold Friedheim\u27s granddaughters.https://digitalcommons.winthrop.edu/manuscriptcollection_findingaids/2603/thumbnail.jp

Scaling Behavior of Driven Interfaces Above the Depinning Transition

We study the depinning transition for models representative of each of the two universality classes of interface roughening with quenched disorder. For one of the universality classes, the roughness exponent changes value at the transition, while the dynamical exponent remains unchanged. We also find that the prefactor of the width scales with the driving force. We propose several scaling relations connecting the values of the exponents on both sides of the transition, and discuss some experimental results in light of these findings.Comment: Revtex 3.0, 4 pages in PRL format + 5 figures (available at ftp://jhilad.bu.edu/pub/abbhhss/ma-figures.tar.Z ) submitted to Phys Rev Let

New set of measures to analyze non-equilibrium structures

We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface deposition. Patterns growth in the Cahn-Hilliard Equation (used to model spinodal decomposition) are shown to exhibit three distinct stages. Two models of surface growth, namely the continuous Kardar-Parisi-Zhang (KPZ) model and the discrete Restricted-Solid-On-Solid (RSOS) model are shown to have different saturation exponents

Trapping mechanism in overdamped ratchets with quenched noise

A trapping mechanism is observed and proposed as the origin of the anomalous behavior recently discovered in transport properties of overdamped ratchets subject to external oscillatory drive in the presence of quenched noise. In particular, this mechanism is shown to appear whenever the quenched disorder strength is greater than a threshold value. The minimum disorder strength required for the existence of traps is determined by studying the trap structure in a disorder configuration space. An approximation to the trapping probability density function in a disordered region of finite length included in an otherwise perfect ratchet lattice is obtained. The mean velocity of the particles and the diffusion coefficient are found to have a non-monotonic dependence on the quenched noise strength due to the presence of the traps.Comment: 21 pages, 6 figures, to appear in PR

Logarithmic roughening in a growth process with edge evaporation

Roughening transitions are often characterized by unusual scaling properties. As an example we investigate the roughening transition in a solid-on-solid growth process with edge evaporation [Phys. Rev. Lett. 76, 2746 (1996)], where the interface is known to roughen logarithmically with time. Performing high-precision simulations we find appropriate scaling forms for various quantities. Moreover we present a simple approximation explaining why the interface roughens logarithmically.Comment: revtex, 6 pages, 7 eps figure

Stochastic growth equations on growing domains

The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different regimes are clearly identified: for small $\gamma$ the interface becomes correlated, and the dynamics is dominated by diffusion; for large $\gamma$ the interface stays uncorrelated, and the dynamics is dominated by dilution. In this second regime, for short time intervals and spatial scales the critical exponents corresponding to the non-growing substrate situation are recovered. For long time differences or large spatial scales the situation is different. Large spatial scales show the uncorrelated character of the growing interface. Long time intervals are studied by means of the auto-correlation and persistence exponents. It becomes apparent that dilution is the mechanism by which correlations are propagated in this second case.Comment: Published versio

Absence of non-trivial asymptotic scaling in the Kashchiev model of polynuclear growth

In this brief comment we show that, contrary to previous claims [Bartelt M C and Evans J W 1993 {\it J.\ Phys.\ A} ${\bf 26}$ 2743], the asymptotic behaviour of the Kashchiev model of polynuclear growth is trivial in all spatial dimensions, and therefore lies outside the Kardar-Parisi-Zhang universality class.Comment: 3 pages, 4 postscript figures, uses eps

Growth Models And The Question Of Universality Classes

In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different universality classes, i.e. they are described by different differential equations. In the present paper we describe a mapping of ``growth rules'' to differential operators and give plausibility arguments for this mapping. We illustrate the validity of our theory by applying it to published results