3,046 research outputs found
Percolation of hard disks
Random arrangements of points in the plane, interacting only through a simple
hard core exclusion, are considered. An intensity parameter controls the
average density of arrangements, in analogy with the Poisson point process. It
is proved that at high intensity, an infinite connected cluster of excluded
volume appears with positive probability.Comment: 16 pages, 6 figure
Connectedness percolation of hard convex polygonal rods and platelets
The properties of polymer composites with nanofiller particles change
drastically above a critical filler density known as the percolation threshold.
Real nanofillers, such as graphene flakes and cellulose nanocrystals, are not
idealized disks and rods but are often modeled as such. Here we investigate the
effect of the shape of the particle cross section on the geometric percolation
threshold. Using connectedness percolation theory and the second-virial
approximation, we analytically calculate the percolation threshold of hard
convex particles in terms of three single-particle measures. We apply this
method to polygonal rods and platelets and find that the universal scaling of
the percolation threshold is lowered by decreasing the number of sides of the
particle cross section. This is caused by the increase of the surface area to
volume ratio with decreasing number of sides.Comment: 7 pages, 3 figures; added references, corrected typo, results
unchange
Granular Collapse as a Percolation Transition
Inelastic collapse is found in a two-dimensional system of inelastic hard
disks confined between two walls which act as an energy source. As the
coefficient of restitution is lowered, there is a transition between a state
containing small collapsed clusters and a state dominated by a large collapsed
cluster. The transition is analogous to that of a percolation transition. At
the transition the number of clusters n_s of size s scales as with .Comment: 10 pages revtex, 5 figures, accepted by Phys Rev E many changes and
corrections from previous submissio
Connectivity percolation in suspensions of hard platelets
We present a study on connectivity percolation in suspensions of hard
platelets by means of Monte Carlo simulation. We interpret our results using a
contact-volume argument based on an effective single--particle cell model. It
is commonly assumed that the percolation threshold of anisotropic objects
scales as their inverse aspect ratio. While this rule has been shown to hold
for rod-like particles, we find that for hard plate-like particles the
percolation threshold is non-monotonic in the aspect ratio. It exhibits a
shallow minimum at intermediate aspect ratios and then saturates to a constant
value. This effect is caused by the isotropic-nematic transition pre-empting
the percolation transition. Hence the common strategy to use highly
anisotropic, conductive particles as fillers in composite materials in order to
produce conduction at low filler concentration is expected to fail for
plate-like fillers such as graphene and graphite nanoplatelets
Transport, Geometrical and Topological Properties of Stealthy Disordered Hyperuniform Two-Phase Systems
Disordered hyperuniform many-particle systems have attracted considerable
recent attention. One important class of such systems is the classical ground
states of "stealthy potentials." The degree of order of such ground states
depends on a tuning parameter. Previous studies have shown that these
ground-state point configurations can be counterintuitively disordered,
infinitely degenerate, and endowed with novel physical properties (e.g.,
negative thermal expansion behavior). In this paper, we focus on the disordered
regime in which there is no long-range order, and control the degree of
short-range order. We map these stealthy disordered hyperuniform point
configurations to two-phase media by circumscribing each point with a possibly
overlapping sphere of a common radius : the "particle" and "void" phases are
taken to be the space interior and exterior to the spheres, respectively. We
study certain transport properties of these systems, including the effective
diffusion coefficient of point particles diffusing in the void phase as well as
static and time-dependent characteristics associated with diffusion-controlled
reactions. Besides these effective transport properties, we also investigate
several related structural properties, including pore-size functions, quantizer
error, an order metric, and percolation threshold. We show that these
transport, geometrical and topological properties of our two-phase media
derived from decorated stealthy ground states are distinctly different from
those of equilibrium hard-sphere systems and spatially uncorrelated overlapping
spheres
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