1,395 research outputs found
Pegs and Ropes: Geometry at Stonehenge
A recent computer-aided-design investigation of the Neolithic 56 Aubrey Hole circuit at Stonehenge has led to the discovery of an astonishingly simple geometrical construction for drawing an approximately regular 56-sided polygon, feasible with a compass and straightedge. In the present work, we prove analytically that the aforementioned construction yields as a byproduct, an extremely accurate method for approximating a regular heptagon, and we quantify the accuracy that prehistoric surveyors may have ideally attained using simple pegs and ropes. We compare this method with previous approximations, and argue that it is likely to be at the same time the simplest and most accurate. Implications of our findings are discussed
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
The disordered flat phase of a crystal surface - critical and dynamic properties
We analyze a restricted SOS model on a square lattice with nearest and
next-nearest neighbor interactions, using Monte Carlo techniques. In
particular, the critical exponents at the preroughening transition between the
flat and disordered flat (DOF) phases are confirmed to be non-universal.
Moreover, in the DOF phase, the equilibration of various profiles imprinted on
the crystal surface is simulated, applying evaporation kinetics and surface
diffusion. Similarities to and deviations from related findings in the flat and
rough phases are discussed.Comment: 4 pages, 4 figures, submitted to Phys. Rev.
Island Density in Homoepitaxial Growth:Improved Monte Carlo Results
We reexamine the density of two dimensional islands in the submonolayer
regime of a homoepitaxially growing surface using the coarse grained Monte
Carlo simulation with random sequential updating rather than parallel updating.
It turns out that the power law dependence of the density of islands on the
deposition rate agrees much better with the theoretical prediction than
previous data obtained by other methods if random sequential instead of
parallel updating is used.Comment: Latex with 2 PS figure file
Capture-zone scaling in island nucleation: phenomenological theory of an example of universal fluctuation behavior
In studies of island nucleation and growth, the distribution of capture
zones, essentially proximity cells, can give more insight than island-size
distributions. In contrast to the complicated expressions, ad hoc or derived
from rate equations, usually used, we find the capture-zone distribution can be
described by a simple expression generalizing the Wigner surmise from random
matrix theory that accounts for the distribution of spacings in a host of
fluctuation phenomena. Furthermore, its single adjustable parameter can be
simply related to the critical nucleus of growth models and the substrate
dimensionality. We compare with extensive published kinetic Monte Carlo data
and limited experimental data. A phenomenological theory sheds light on the
result.Comment: 5 pages, 4 figures, originally submitted to Phys. Rev. Lett. on Dec.
15, 2006; revised version v2 tightens and focuses the presentation,
emphasizes the importance of universal features of fluctuations, corrects an
error for d=1, replaces 2 of the figure
Scaling and Universality in Models of Step Bunching: The "C+-C-" Model
We study further the recently introduced [Ranguelov et al., Comptes Rendus de
l'Acad. Bulg. des Sci. 60, 4 (2007) 389] "C+-C-" model of step flow crystal
growth over wide range of model parameters. The basic assumption of the model
is that the reference ("equilibrium") densities used to compute the
supersaturation might be different on either side of a step. We obtain the
condition for linear stability of the whole step train in the form CL/CR>1 (L/R
stands for left/right in a descending from left to right step train). Further
we integrate numerically the equations of step motion to monitor the bunching
process in the long times limit. Thus we obtain the exact size- and time-
scaling of the step bunches including the numerical prefactors. We show that in
a broad range of parameters the morphology is characterized with appearance of
the minimal interstep distance in the bunch in the beginning of the bunches (at
the trailing edge of the bunch) and may be described by a single universality
class, different from those already generated by continuum theories [Krug et
al., PRB 71, 045412].Comment: 18 pages, 9 figure
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