1,092 research outputs found
Results for a critical threshold, the correction-to-scaling exponent and susceptibility amplitude ratio for 2d percolation
We summarize several decades of work in finding values for the percolation
threshold p_c for site percolation on the square lattice, the universal
correction-to-scaling exponent Omega, and the susceptibility amplitude ratio
C^+/C^-, in two dimensions. Recent studies have yielded the precise values p_c
= 0.59274602(4), Omega = 72/91 = 0.791, and C^+/C^- = 161.5(1.5), resolving
long-standing controversies about the last two quantities and verifying the
widely used value p_c = 0.592746 for the first.Comment: Talk presented at 24th Annual Workshop:"Recent Developments in
Computer Simulational Studies in Condensed Matter Physics," Center for
Computational Physics, University of Georgia, Athens, Georgia Feb. 21-25,
201
Percolation in Networks with Voids and Bottlenecks
A general method is proposed for predicting the asymptotic percolation
threshold of networks with bottlenecks, in the limit that the sub-net mesh size
goes to zero. The validity of this method is tested for bond percolation on
filled checkerboard and "stack-of-triangle" lattices. Thresholds for the
checkerboard lattices of different mesh sizes are estimated using the gradient
percolation method, while for the triangular system they are found exactly
using the triangle-triangle transformation. The values of the thresholds
approach the asymptotic values of 0.64222 and 0.53993 respectively as the mesh
is made finer, consistent with a direct determination based upon the predicted
critical corner-connection probability.Comment: to appear, Physical Review E. Small changes from first versio
Boundary conditions in random sequential adsorption
The influence of different boundary conditions on the density of random
packings of disks is studied. Packings are generated using the random
sequential adsorption algorithm with three different types of boundary
conditions: periodic, open, and wall. It is found that the finite size effects
are smallest for periodic boundary conditions, as expected. On the other hand,
in the case of open and wall boundaries it is possible to introduce an
effective packing size and a constant correction term to significantly improve
the packing densities.Comment: 9 pages, 7 figure
On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice
By means of numerical simulations and epidemic analysis, the transition point
of the stochastic, asynchronous Susceptible-Infected-Recovered (SIR) model on a
square lattice is found to be c_0=0.1765005(10), where c is the probability a
chosen infected site spontaneously recovers rather than tries to infect one
neighbor. This point corresponds to an infection/recovery rate of lambda_c =
(1-c_0)/c_0 = 4.66571(3) and a net transmissibility of (1-c_0)/(1 + 3 c_0) =
0.538410(2), which falls between the rigorous bounds of the site and bond
thresholds. The critical behavior of the model is consistent with the 2-d
percolation universality class, but local growth probabilities differ from
those of dynamic percolation cluster growth, as is demonstrated explicitly.Comment: 9 pages, 5 figures. Accepted for publication, Physical Review
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