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

Corrections to scaling for percolative conduction: anomalous behavior at small L

Recently Grassberger has shown that the correction to scaling for the conductance of a bond percolation network on a square lattice is a nonmonotonic function of the linear lattice dimension with a minimum at $L = 10$, while this anomalous behavior is not present in the site percolation networks. We perform a high precision numerical study of the bond percolation random resistor networks on the square, triangular and honeycomb lattices to further examine this result. We use the arithmetic, geometric and harmonic means to obtain the conductance and find that the qualitative behavior does not change: it is not related to the shape of the conductance distribution for small system sizes. We show that the anomaly at small L is absent on the triangular and honeycomb networks. We suggest that the nonmonotonic behavior is an artifact of approximating the continuous system for which the theory is formulated by a discrete one which can be simulated on a computer. We show that by slightly changing the definition of the linear lattice size we can eliminate the minimum at small L without significantly affecting the large L limit.Comment: 3 pages, 4 figures;slightly expanded, 2 figures added. Accepted for publishing in Phys. Rev.

On the rate of convergence of the Hamiltonian particle-mesh method

The Hamiltonian Particle-Mesh (HPM) method is a particle-in-cell method for compressible fluid flow with Hamiltonian structure. We present a numer- ical short-time study of the rate of convergence of HPM in terms of its three main governing parameters. We find that the rate of convergence is much better than the best available theoretical estimates. Our results indicate that HPM performs best when the number of particles is on the order of the number of grid cells, the HPM global smoothing kernel has fast decay in Fourier space, and the HPM local interpolation kernel is a cubic spline

Low density expansion for Lyapunov exponents

In some quasi-one-dimensional weakly disordered media, impurities are large and rare rather than small and dense. For an Anderson model with a low density of strong impurities, a perturbation theory in the impurity density is developed for the Lyapunov exponent and the density of states. The Lyapunov exponent grows linearly with the density. Anomalies of the Kappus-Wegner type appear for all rational quasi-momenta even in lowest order perturbation theory

The role of smoking in social networks on smoking cessation and relapse among adults: A longitudinal study

Understanding the spread of smoking cessation and relapse within social networks may offer new approaches to further curb the smoking epidemic. Whether smoking behavior among social network members determines smoking cessation and relapse of adults however, is less known. For this study, longitudinal data of 4623 adults participating in the Dutch Longitudinal Internet Studies for the Social sciences (LISS) panel were collected in March 2013 with a follow-up in 2014. Logistic regression was used to examine the association between the proportion of smokers in social networks, and (1) smoking cessation (n = 762) and (2) smoking relapse (n = 1905). Analyses were adjusted for the size of the network, age, sex, and education. Respondents with the largest proportion of smokers in their social network were less likely to quit smoking (OR = 0.25; 95% CI = 0.11–0.66) and more likely to experience a relapse (6.08; 3.01–12.00). Smoking cessation and relapse were most strongly associated with the proportion of smokers among household members and friends. The proportion of smokers in family outside the household was not related to smoking cessation and smoking relapse. In conclusion, smoking behavior in social networks, especially among household members and friends, is strongly associated with smoking cessation and relapse. These findings further support the spread of smoking within social networks, and provide evidence for network-based interventions, particularly including household members and friends

How big is too big? Critical Shocks for Systemic Failure Cascades

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold \theta_i determining their capacity to handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P(\theta), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.Comment: 23 pages, 7 Figure

Smallest small-world network

Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show that among all networks with the small-world structure, the most efficient ones have a single ``center'', from which all shortcuts are connected to uniformly distributed nodes over the network. The networks with several centers and a connected subnetwork of shortcuts are shown to be ``almost'' as efficient. Genetic-algorithm simulations further support our results.Comment: 5 pages, 6 figures, REVTeX

Bias reduction in traceroute sampling: towards a more accurate map of the Internet

Traceroute sampling is an important technique in exploring the internet router graph and the autonomous system graph. Although it is one of the primary techniques used in calculating statistics about the internet, it can introduce bias that corrupts these estimates. This paper reports on a theoretical and experimental investigation of a new technique to reduce the bias of traceroute sampling when estimating the degree distribution. We develop a new estimator for the degree of a node in a traceroute-sampled graph; validate the estimator theoretically in Erdos-Renyi graphs and, through computer experiments, for a wider range of graphs; and apply it to produce a new picture of the degree distribution of the autonomous system graph.Comment: 12 pages, 3 figure

Long-term treatment with the dopamine agonist quinagolide of patients with clinically non-functioning pituitary adenoma

OBJECTIVE: This study was performed to evaluate the effect of prolonged treatment with the dopamine agonist quinagolide on serum gonadotropin and alpha-subunit concentrations and tumor volume in patients with clinically non-functioning pituitary adenomas (CNPA). DESIGN: Ten patients with CNPA were treated with quinagolide (0.3 mg daily). The median duration of treatment was 57 months (range 36-93 months). Blood samples for measurement of serum gonadotropin and alpha-subunit concentrations were drawn before treatment, after 5 days, and at each outpatient visit. Computerized tomography or magnetic resonance imaging of the pituitary region and Goldmann perimetry were done before and at regular intervals during treatment. RESULTS: A significant decrease of serum FSH, LH or alpha-subunit concentrations was found in nine patients. The levels remained low during the entire treatment period. In two out of three patients with pre-existing visual field defects a slight improvement was shown during the first months of treatment, but eventually deterioration occurred in all three patients. A fourth patient developed unilateral ophthalmoplegia dur