16,660 research outputs found
Analytical approach to directed sandpile models on the Apollonian network
We investigate a set of directed sandpile models on the Apollonian network,
which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659
(1989)) for Euclidian lattices. They are characterized by a single parameter
, that restricts the number of neighbors receiving grains from a toppling
node. Due to the geometry of the network, two and three point correlation
functions are amenable to exact treatment, leading to analytical results for
the avalanche distributions in the limit of an infinite system, for .
The exact recurrence expressions for the correlation functions are numerically
iterated to obtain results for finite size systems, when larger values of
are considered. Finally, a detailed description of the local flux properties is
provided by a multifractal scaling analysis.Comment: 7 pages in two-column format, 10 illustrations, 5 figure
Non-Local Product Rules for Percolation
Despite original claims of a first-order transition in the product rule model
proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies
indicate that this percolation model, in fact, displays a continuous
transition. The distinctive scaling properties of the model at criticality,
however, strongly suggest that it should belong to a different universality
class than ordinary percolation. Here we introduce a generalization of the
product rule that reveals the effect of non-locality on the critical behavior
of the percolation process. Precisely, pairs of unoccupied bonds are chosen
according to a probability that decays as a power-law of their Manhattan
distance, and only that bond connecting clusters whose product of their sizes
is the smallest, becomes occupied. Interestingly, our results for
two-dimensional lattices at criticality shows that the power-law exponent of
the product rule has a significant influence on the finite-size scaling
exponents for the spanning cluster, the conducting backbone, and the cutting
bonds of the system. In all three cases, we observe a continuous variation from
ordinary to (non-local) explosive percolation exponents.Comment: 5 pages, 4 figure
Preparation and characterization of methacrylate hydrogels for zeta potential control
A technique based on the measurement of streaming potentials has been developed to evaluate the effects of hydrophilic coatings on electroosmotic flow. The apparatus and procedure are described as well as some results concerning the electrokinetic potential of glass capillaries as a function of ionic strength, pH, and temperature. The effect that turbulence and entrance flow conditions have on accurate streaming potential measurements is discussed. Various silane adhesion promoters exhibited only a slight decrease in streaming potential. A coating utilizing a glycidoxy silane base upon which methylcellulose is applied affords a six-fold decrease over uncoated tubes. Hydrophilic methacrylate gels show similar streaming potential behavior, independent of the water content of the gel. By introduction of positive or negative groups into the hydrophilic methacrylate gels, a range of streaming potential values are obtained having absolute positive or negative signs
Qualitative Analysis of Polycycles in Filippov Systems
In this paper, we are concerned about the qualitative behaviour of planar
Filippov systems around some typical minimal sets, namely, polycycles. In the
smooth context, a polycycle is a simple closed curve composed by a collection
of singularities and regular orbits, inducing a first return map. Here, this
concept is extended to Filippov systems by allowing typical singularities lying
on the switching manifold. Our main goal consists in developing a method to
investigate the unfolding of polycycles in Filippov systems. In addition, we
applied this method to describe bifurcation diagrams of Filippov systems around
certain polycycles
How dense can one pack spheres of arbitrary size distribution?
We present the first systematic algorithm to estimate the maximum packing
density of spheres when the grain sizes are drawn from an arbitrary size
distribution. With an Apollonian filling rule, we implement our technique for
disks in 2d and spheres in 3d. As expected, the densest packing is achieved
with power-law size distributions. We also test the method on homogeneous and
on empirical real distributions, and we propose a scheme to obtain
experimentally accessible distributions of grain sizes with low porosity. Our
method should be helpful in the development of ultra-strong ceramics and high
performance concrete.Comment: 5 pages, 5 figure
Memory effects on the statistics of fragmentation
We investigate through extensive molecular dynamics simulations the
fragmentation process of two-dimensional Lennard-Jones systems. After
thermalization, the fragmentation is initiated by a sudden increment to the
radial component of the particles' velocities. We study the effect of
temperature of the thermalized system as well as the influence of the impact
energy of the ``explosion'' event on the statistics of mass fragments. Our
results indicate that the cumulative distribution of fragments follows the
scaling ansatz , where is
the mass, and are cutoff parameters, and is a scaling
exponent that is dependent on the temperature. More precisely, we show clear
evidence that there is a characteristic scaling exponent for each
macroscopic phase of the thermalized system, i.e., that the non-universal
behavior of the fragmentation process is dictated by the state of the system
before it breaks down.Comment: 5 pages, 8 figure
- …