Exact results at the 2-D percolation point

We derive exact expressions for the excess number of clusters b and the excess cumulants b_n of a related quantity at the 2-D percolation point. High-accuracy computer simulations are in accord with our predictions. b is a finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula for the number of clusters per site n_c in the infinite system limit; the bn correct bulk cumulants. b and b_n are universal, and thus depend only on the system's shape. Higher-order corrections show no apparent dependence on fractional powers of the system size.Comment: 12 pages, 2 figures, LaTeX, submitted to Physical Review Letter

Transport on percolation clusters with power-law distributed bond strengths: when do blobs matter?

The simplest transport problem, namely maxflow, is investigated on critical percolation clusters in two and three dimensions, using a combination of extremal statistics arguments and exact numerical computations, for power-law distributed bond strengths of the type $P(\sigma) \sim \sigma^{-\alpha}$. Assuming that only cutting bonds determine the flow, the maxflow critical exponent \ve is found to be \ve(\alpha)=(d-1) \nu + 1/(1-\alpha). This prediction is confirmed with excellent accuracy using large-scale numerical simulation in two and three dimensions. However, in the region of anomalous bond capacity distributions ($0\leq \alpha \leq 1$) we demonstrate that, due to cluster-structure fluctuations, it is not the cutting bonds but the blobs that set the transport properties of the backbone. This ``blob-dominance'' avoids a cross-over to a regime where structural details, the distribution of the number of red or cutting bonds, would set the scaling. The restored scaling exponents however still follow the simplistic red bond estimate. This is argued to be due to the existence of a hierarchy of so-called minimum cut-configurations, for which cutting bonds form the lowest level, and whose transport properties scale all in the same way. We point out the relevance of our findings to other scalar transport problems (i.e. conductivity).Comment: 9 pages + Postscript figures. Revtex4+psfig. Submitted to PR

Magnetoresistance of Three-Constituent Composites: Percolation Near a Critical Line

Scaling theory, duality symmetry, and numerical simulations of a random network model are used to study the magnetoresistance of a metal/insulator/perfect conductor composite with a disordered columnar microstructure. The phase diagram is found to have a critical line which separates regions of saturating and non-saturating magnetoresistance. The percolation problem which describes this line is a generalization of anisotropic percolation. We locate the percolation threshold and determine the t = s = 1.30 +- 0.02, nu = 4/3 +- 0.02, which are the same as in two-constituent 2D isotropic percolation. We also determine the exponents which characterize the critical dependence on magnetic field, and confirm numerically that nu is independent of anisotropy. We propose and test a complete scaling description of the magnetoresistance in the vicinity of the critical line.Comment: Substantially revised version; description of behavior in finite magnetic fields added. 7 pages, 7 figures, submitted to PR

The Largest Cluster in Subcritical Percolation

The statistical behavior of the size (or mass) of the largest cluster in subcritical percolation on a finite lattice of size $N$ is investigated (below the upper critical dimension, presumably $d_c=6$). It is argued that as $N \to \infty$ the cumulative distribution function converges to the Fisher-Tippett (or Gumbel) distribution $e^{-e^{-z}}$ in a certain weak sense (when suitably normalized). The mean grows like $s_\xi^* \log N$, where $s_\xi^*(p)$ is a ``crossover size''. The standard deviation is bounded near $s_\xi^* \pi/\sqrt{6}$ with persistent fluctuations due to discreteness. These predictions are verified by Monte Carlo simulations on $d=2$ square lattices of up to 30 million sites, which also reveal finite-size scaling. The results are explained in terms of a flow in the space of probability distributions as $N \to \infty$. The subcritical segment of the physical manifold ($0 < p < p_c$) approaches a line of limit cycles where the flow is approximately described by a ``renormalization group'' from the classical theory of extreme order statistics.Comment: 16 pages, 5 figs, expanded version to appear in Phys Rev

Universality of the Crossing Probability for the Potts Model for q=1,2,3,4

The universality of the crossing probability $\pi_{hs}$ of a system to percolate only in the horizontal direction, was investigated numerically by using a cluster Monte-Carlo algorithm for the $q$-state Potts model for $q=2,3,4$ and for percolation $q=1$. We check the percolation through Fortuin-Kasteleyn clusters near the critical point on the square lattice by using representation of the Potts model as the correlated site-bond percolation model. It was shown that probability of a system to percolate only in the horizontal direction $\pi_{hs}$ has universal form $\pi_{hs}=A(q) Q(z)$ for $q=1,2,3,4$ as a function of the scaling variable $z= [ b(q)L^{\frac{1}{\nu(q)}}(p-p_{c}(q,L)) ]^{\zeta(q)}$. Here, $p=1-\exp(-\beta)$ is the probability of a bond to be closed, $A(q)$ is the nonuniversal crossing amplitude, $b(q)$ is the nonuniversal metric factor, $\zeta(q)$ is the nonuniversal scaling index, $\nu(q)$ is the correlation length index. The universal function $Q(x) \simeq \exp(-z)$. Nonuniversal scaling factors were found numerically.Comment: 15 pages, 3 figures, revtex4b, (minor errors in text fixed, journal-ref added

Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters

Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random lattices, and square lattices with free and periodic boundary conditions, in vertical and horizontal directions, respectively, and with various aspect ratio $L_{1}/L_{2}$. We calculate the probability for the appearance of $n$ percolating clusters, $W_{n},$ the percolating probabilities, $P$, the average fraction of lattice bonds (sites) in the percolating clusters, $_{n}$ ($_{n}$), and the probability distribution function for the fraction $c$ of lattice bonds (sites), in percolating clusters of subgraphs with $n$ percolating clusters, $f_{n}(c^{b})$ ($f_{n}(c^{s})$). Using a small number of nonuniversal metric factors, we find that $W_{n}$, $P$, $_{n}$ ($_{n}$), and $f_{n}(c^{b})$ ($f_{n}(c^{s})$) for random lattices, duals of random lattices, and square lattices have the same universal finite-size scaling functions. We also find that nonuniversal metric factors are independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure

Decreased Bone Mineral Density in Adults Born with Very Low Birth Weight: A Cohort Study

Petteri Hovi and colleagues evaluate skeletal health in 144 adults born preterm with very low birth weight and show that as adults these individuals have significantly lower bone mineral density than do their term-born peers

Hand washing with soap and water together with behavioural recommendations prevents infections in common work environment: an open cluster-randomized trial

<p>Abstract</p> <p>Background</p> <p>Hand hygiene is considered as an important means of infection control. We explored whether guided hand hygiene together with transmission-limiting behaviour reduces infection episodes and lost days of work in a common work environment in an open cluster-randomized 3-arm intervention trial.</p> <p>Methods</p> <p>A total of 21 clusters (683 persons) were randomized to implement hand hygiene with soap and water (257 persons), with alcohol-based hand rub (202 persons), or to serve as a control (224 persons). Participants in both intervention arms also received standardized instructions on how to limit the transmission of infections. The intervention period (16 months) included the emergence of the 2009 influenza pandemic and the subsequent national hand hygiene campaign influencing also the control arm.</p> <p>Results</p> <p>In the total follow-up period there was a 6.7% reduction of infection episodes in the soap-and water arm (p = 0.04). Before the onset of the anti-pandemic campaign, a statistically significant (p = 0.002) difference in the mean occurrence of infection episodes was observed between the control (6.0 per year) and the soap-and-water arm (5.0 per year) but not between the control and the alcohol-rub arm (5.6 per year). Neither intervention had a decreasing effect on absence from work.</p> <p>Conclusions</p> <p>We conclude that intensified hand hygiene using water and soap together with behavioural recommendations can reduce the occurrence of self-reported acute illnesses in common work environment. Surprisingly, the occurrence of reported sick leaves also increased in the soap-and water-arm.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov: <a href="http://www.clinicaltrials.gov/ct2/show/NCT00981877">NCT00981877</a></p> <p>Source of funding</p> <p>The Finnish Work Environment Fund and the National Institute for Health and Welfare.</p

Decreased Fetal Size Is Associated With β-Cell Hyperfunction in Early Life and Failure With Age

OBJECTIVE—Low birth weight is associated with diabetes in adult life. Accelerated or “catch-up” postnatal growth in response to small birth size is thought to presage disease years later. Whether adult disease is caused by intrauterine β-cell–specific programming or by altered metabolism associated with catch-up growth is unknown