Search results for "Logarithmic growth"
showing 7 items of 7 documents
Breakdown of Burton-Prime-Slichter approach and lateral solute segregation in radially converging flows
2005
A theoretical study is presented of the effect of a radially converging melt flow, which is directed away from the solidification front, on the radial solute segregation in simple solidification models. We show that the classical Burton-Prim-Slichter (BPS) solution describing the effect of a diverging flow on the solute incorporation into the solidifying material breaks down for the flows converging along the solidification front. The breakdown is caused by a divergence of the integral defining the effective boundary layer thickness which is the basic concept of the BPS theory. Although such a divergence can formally be avoided by restricting the axial extension of the melt to a layer of fi…
ORDERING KINETICS IN QUASI-ONE-DIMENSIONAL ISING-LIKE SYSTEMS
1993
We present results of a Monte Carlo simulation of the kinetics of ordering in the two-dimensional nearest-neighbor Ising model in anL xM geometry with two free boundaries of length M≫L. This model can be viewed as representing an adsorbant on a stepped surface with mean terrace widthL. We follow the ordering kinetics after quenches to temperatures 0.25 ⩽ T/Tc ⩽ 1 starting from a random initial configuration at a coverage ofΘ=0.5 in the corresponding lattice gas picture. The systems evolve in time according to a Glauber kinetics with nonconserved order parameter. The equilibrium structure is given by a one-dimensional sequence of ordered domains. The ordering process evolves from a short ini…
A model for planktic foraminiferal shell growth
1993
In this paper we analyze the laws of growth that control planktic foraminiferal shell morphology. We assume that isometry is the key toward the understanding of their ontogeny. Hence, our null hypothesis is that these organisms construct isometric shells. To test this hypothesis, geometric models of their shells have been generated with a personal computer. It is demonstrated that early chambers in log-spirally coiled structures cannot follow a strict isometric arrangement. In the real world, the centers of juvenile chambers deviate from the logarithmic growth curve. Juvenile stages are generally more planispiral and contain more chambers per whorl than adult stages. These traits are shown …
Electrophoresis of model colloidal spheres in low salt aqueous suspension
2004
We report on comprehensive measurements of the electrophoretic mobility μ of a highly charged spherical colloid in deionized or low salt aqueous suspensions, where fluid and crystalline order develops with increased packing fraction Φ. We propose the existence of a 'universal' shape of the μ(Φ) showing three distinct regimes: a logarithmic increase, a plateau and a logarithmic decrease. The position and the height of the plateau are found to be influenced by the particle surface properties and the electrolyte concentration. In particular, it starts once the counter-ion concentration becomes equal to the concentration of background electrolyte. This coincides only loosely with the range of Φ…
Ordering of two-dimensional crystals confined in strips of finite width.
2007
Monte Carlo simulations are used to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential $\ensuremath{\propto}{r}^{\ensuremath{-}12}$ in $d=2$ dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width $D$) depends very sensitively on the precise boundary conditions at the two ``walls'' providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and suc…
Surface effects on kinetics of ordering
1992
We study the effects of surfaces on the kinetics of phase changes in Ising-type systems. If the surface effects can be modelled by a field which couples linearly to the local order parameter, the growth of wetting or drying layers occurs. The numerical solution of the corresponding time-dependent Ginzburg-Landau equation yields a temporally logarithmic growth for the thickness of a wetting (drying) layer growing from an unstable dry (wet) state. On the other hand, if one starts off with a metastable state, the radius of a supercritical plug (wet or dry) grows linearly in time, in accordance with recent experimental results.
Quasihyperbolic boundary conditions and Poincaré domains
2002
We prove that a domain in ${\Bbb R}^n$ whose quasihyperbolic metric satisfies a logarithmic growth condition with coefficient $\beta\le 1$ is a (q,p)-\Poincare domain for all p and q satisfying $p\in[1,\infty)\cap(n-n\beta,n)$ and $q\in[p,\beta p^*)$ , where $p^*=np/(n-p)$ denotes the Sobolev conjugate exponent. An elementary example shows that the given ranges for p and q are sharp. The proof makes use of estimates for a variational capacity. When p=2 we give an application to the solvability of the Neumann problem on domains with irregular boundaries. We also discuss the relationship between this growth condition on the quasihyperbolic metric and the s-John condition.