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 $p_c=p_0[(d-1)(q-1)]^{-a}d^{\ b}$, where $d$ is the space dimension and $q$ the coordination number. All thresholds up to $d\rightarrow \infty$ are found to belong to only three universality classes. For first two classes $b=0$ for site dilution while $b=a$ for bond dilution. The last one associated to high dimensions is characterized by $b=2a-1$ for both sites and bonds. Classes are defined by a set of value for $\{p_0; \ a\}$. Deviations from available numerical estimates at $d \leq 7$ are within $\pm 0.008$ and $\pm 0.0004$ for high dimensional hypercubic expansions at $d \geq 8$. 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