20 research outputs found
Gaussian Free Field in the background of correlated random clusters, formed by metallic nanoparticles
The effect of metallic nano-particles (MNPs) on the electrostatic potential
of a disordered 2D dielectric media is considered. The disorder in the media is
assumed to be white-noise Coulomb impurities with normal distribution. To
realize the correlations between the MNPs we have used the Ising model with an
artificial temperature that controls the number of MNPs as well as their
correlations. In the limit, one retrieves the Gaussian free
field (GFF), and in the finite temperature the problem is equivalent to a GFF
in iso-potential islands. The problem is argued to be equivalent to a
scale-invariant random surface with some critical exponents which vary with
and correspondingly are correlation-dependent. Two type of observables have
been considered: local and global quantities. We have observed that the MNPs
soften the random potential and reduce its statistical fluctuations. This
softening is observed in the local as well as the geometrical quantities. The
correlation function of the electrostatic and its total variance are observed
to be logarithmic just like the GFF, i.e. the roughness exponent remains zero
for all temperatures, whereas the proportionality constants scale with .
The fractal dimension of iso-potential lines (), the exponent of the
distribution function of the gyration radius (), and the loop lengths
(), and also the exponent of the loop Green function change in
terms of in a power-law fashion, with some critical exponents reported
in the text. Importantly we have observed that
, in which is the spin
correlation length in the Ising model
Statistical analysis of the drying pattern of coffee
In this study, we experimentally study the dried pattern droplets of coffee
with and without sugar. We statistically analyze the rough surface formed after
the stain becomes dried. The amount of sugar is controlled by the mass .
Along with the formation of the coffee ring, we discuss the Marangoni effect,
in the system, and also analyzed the statistics of the cracks. For large enough
values, the exponents approach to the ones for the Gaussian free field
(GFF) (the loop fractal dimension , loop and gyration radius
distribution exponents and respectively). Using
the multifractal analysis (MA) for the mass configuration of the dried pattern,
we numerically show that, the mass-fractal dimension is for the
case without sugar, which decreases increasing the sugar. This is explained by
the fact that the droplet becomes more hydrophilic, resulting in more sparse
spatial patterns, in agreement compatible with the contact angle analysis
Sandpiles Subjected to Sinusoidal Drive
This paper considers a sandpile model subjected to a sinusoidal external
drive with the time period . We develop a theoretical model for the Green
function in a large limit, which predicts that the avalanches are
anisotropic and elongated in the oscillation direction. We track the problem
numerically and show that the system shows additionally a regime where the
avalanches are elongated in the perpendicular direction with respect to the
oscillations. We find a transition point between these two regimes. The power
spectrum of avalanche size and the grains wasted from the parallel and
perpendicular directions are studied. These functions show power-law behaviour
in terms of the frequency with exponents, which run with