2,805 research outputs found
Exact bond percolation thresholds in two dimensions
Recent work in percolation has led to exact solutions for the site and bond
critical thresholds of many new lattices. Here we show how these results can be
extended to other classes of graphs, significantly increasing the number and
variety of solved problems. Any graph that can be decomposed into a certain
arrangement of triangles, which we call self-dual, gives a class of lattices
whose percolation thresholds can be found exactly by a recently introduced
triangle-triangle transformation. We use this method to generalize Wierman's
solution of the bow-tie lattice to yield several new solutions. We also give
another example of a self-dual arrangement of triangles that leads to a further
class of solvable problems. There are certainly many more such classes.Comment: Accepted for publication in J. Phys
Critical surfaces for general bond percolation problems
We present a general method for predicting bond percolation thresholds and
critical surfaces for a broad class of two-dimensional periodic lattices,
reproducing many known exact results and providing excellent approximations for
several unsolved lattices. For the checkerboard and inhomogeneous bow-tie
lattices, the method yields predictions that agree with numerical measurements
to more than six figures, and are possibly exact
Phase variation controls expression of Salmonella lipopolysaccharide modification genes by a DNA methylation-dependent mechanism
The O-antigen of Salmonella lipopolysaccharide is a major antigenic determinant and its chemical composition forms the basis for Salmonella serotyping. Modifications of the O-antigen that can affect the serotype include those carried out by the products of glycosyltransferase operons (gtr), which are present on specific Salmonella and phage genomes. Here we show that expression of the gtr genes encoded by phage P22 that confers the O1 serotype is under the control of phase variation. This phase variation occurs by a novel epigenetic mechanism requiring OxyR in conjunction with the DNA methyltransferase Dam. OxyR is an activator or a repressor of the system depending on which of its two binding sites in the gtr regulatory region is occupied. Binding is decreased by methylation at Dam target sequences in either site, and this confers heritability of the expression state to the system. Most Salmonella gtr operons share the key regulatory elements that are identified here as essential for this epigenetic phase variation
Percolative shunting on electrified surface
The surface discharge of electrified dielectrics at high humidity is
considered. The percolative nature of charge transport in electrets is
established. Particular attention is given to the phenomena of adsorption and
nucleation of electrically conducting phase in the cause of percolation cluster
growth on electrified surface. The critical index of the correlation lenght for
percolation cluster is found, and its value is in good agreement with the known
theoretical estimations.Comment: 4 pages with 1 figure, revtex, published in Tech. Phys. Lett. 25
(1999) 877-879 with one additional figur
Directed Percolation and Generalized Friendly Walkers
We show that the problem of directed percolation on an arbitrary lattice is
equivalent to the problem of m directed random walkers with rather general
attractive interactions, when suitably continued to m=0. In 1+1 dimensions,
this is dual to a model of interacting steps on a vicinal surface. A similar
correspondence with interacting self-avoiding walks is constructed for
isotropic percolation.Comment: 4 pages, 3 figures, to be published in Phys. Rev. Let
Universal Formulae for Percolation Thresholds
A power law is postulated for both site and bond percolation thresholds. The
formula writes , where is the space
dimension and the coordination number. All thresholds up to are found to belong to only three universality classes. For first two
classes for site dilution while for bond dilution. The last one
associated to high dimensions is characterized by for both sites and
bonds. Classes are defined by a set of value for . Deviations
from available numerical estimates at are within and
for high dimensional hypercubic expansions at . The
formula is found to be also valid for Ising critical temperatures.Comment: 11 pages, latex, 3 figures not include
Equivalence of operator-splitting schemes for the integration of the Langevin equation
We investigate the equivalence of different operator-splitting schemes for
the integration of the Langevin equation. We consider a specific problem, so
called the directed percolation process, which can be extended to a wider class
of problems. We first give a compact mathematical description of the
operator-splitting method and introduce two typical splitting schemes that will
be useful in numerical studies. We show that the two schemes are essentially
equivalent through the map that turns out to be an automorphism. An associated
equivalent class of operator-splitting integrations is also defined by
generalizing the specified equivalence.Comment: 4 page
Diffuse continuum gamma rays from the Galaxy
A new study of the diffuse Galactic gamma-ray continuum radiation is
presented, using a cosmic-ray propagation model which includes nucleons,
antiprotons, electrons, positrons, and synchrotron radiation. Our treatment of
the inverse Compton (IC) scattering includes the effect of anisotropic
scattering in the Galactic interstellar radiation field (ISRF) and a new
evaluation of the ISRF itself. Models based on locally measured electron and
nucleon spectra and synchrotron constraints are consistent with gamma-ray
measurements in the 30-500 MeV range, but outside this range excesses are
apparent. A harder nucleon spectrum is considered but fitting to gamma rays
causes it to violate limits from positrons and antiprotons. A harder
interstellar electron spectrum allows the gamma-ray spectrum to be fitted above
1 GeV as well, and this can be further improved when combined with a modified
nucleon spectrum which still respects the limits imposed by antiprotons and
positrons. A large electron/IC halo is proposed which reproduces well the
high-latitude variation of gamma-ray emission. The halo contribution of
Galactic emission to the high-latitude gamma-ray intensity is large, with
implications for the study of the diffuse extragalactic component and
signatures of dark matter. The constraints provided by the radio synchrotron
spectral index do not allow all of the <30 MeV gamma-ray emission to be
explained in terms of a steep electron spectrum unless this takes the form of a
sharp upturn below 200 MeV. This leads us to prefer a source population as the
origin of the excess low-energy gamma rays.Comment: Final version accepted for publication in The Astrophysical Journal
(vol. 537, July 10, 2000 issue); Many Updates; 20 pages including 49
ps-figures, uses emulateapj.sty. More details can be found at
http://www.gamma.mpe-garching.mpg.de/~aws/aws.htm
Percolation with Multiple Giant Clusters
We study the evolution of percolation with freezing. Specifically, we
consider cluster formation via two competing processes: irreversible
aggregation and freezing. We find that when the freezing rate exceeds a certain
threshold, the percolation transition is suppressed. Below this threshold, the
system undergoes a series of percolation transitions with multiple giant
clusters ("gels") formed. Giant clusters are not self-averaging as their total
number and their sizes fluctuate from realization to realization. The size
distribution F_k, of frozen clusters of size k, has a universal tail, F_k ~
k^{-3}. We propose freezing as a practical mechanism for controlling the gel
size.Comment: 4 pages, 3 figure
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