Biomedical subjects

Robert M Ziff

Publications and source records attributed to Robert M Ziff.

7 recordsLinked to original sources

PubMed2006

Anchored critical percolation clusters and 2D electrostatics.

We consider the densities of clusters, at the percolation point of a two-dimensional system, which are anchored in various ways to an edge. These quantities are calculated by use of conformal field theory and computer simulations. We find that they are given by simple functions of the potentials of 2D electrostatic dipoles and that a kind of superposition cum factorization applies. Our results broaden this connection, already known from previous studies, and we present evidence that it is more generally valid. An exact result similar to the Kirkwood superposition approximation emerges.

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PubMed2006

Universal amplitude ratio Gamma-/Gamma+ for two-dimensional percolation.

The amplitude ratio of the susceptibility (or second size moment) for two-dimensional percolation is calculated by two series methods and also by Monte Carlo simulation. The first series method is an approach based upon integrating approximations to the scaling function. The second series method directly uses low- and high-density series expansions of the susceptibility, going to unprecedented orders for both bond and site percolation on the square lattice. Putting all methods together we find a consistent value Gamma-/Gamma+ = 162.5+/-2 , a significant improvement over previous results that placed the value of this ratio variously in the range of 14 to 220.

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PubMed2006

Predictions of bond percolation thresholds for the kagomé and Archimedean (3, 12(2)) lattices.

Here we show how the recent exact determination of the bond percolation threshold for the martini lattice can be used to provide approximations to the unsolved kagomé and (3, 12(2)) lattices. We present two different methods: one which provides an approximation to the inhomogeneous kagomé and bond problems, and the other which gives estimates of for the homogeneous kagomé (0.524 408 8...) and (3, 12(2)) (0.740 421 2...) problems that, respectively, agree with numerical results to five and six significant figures.

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PubMed2006

Generalized cell-dual-cell transformation and exact thresholds for percolation.

Suggested by Scullard's recent star-triangle relation for correlated bond systems, we propose a general "cell-dual-cell" transformation, which allows in principle an infinite variety of lattices with exact percolation thresholds to be generated. We directly verify Scullard's site percolation thresholds, and derive the bond thresholds for his "martini" lattice (pc = 1/square root 2) and the "A" lattice (pc = 0.625457..., solution to p5 - 4p4 + 3p3 + 2p2 - 1 = 0). We also present a precise Monte Carlo test of the site threshold for the "A" lattice.

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PubMed2005

Simple algorithm to test for linking to Wilson loops in percolation.

A simple burning or epidemic type of algorithm is developed in order to test whether any loops in percolation clusters link a fixed reference loop, a problem considered recently by Gliozzi in the context of gauge theory. We test our algorithm at criticality in both two dimensions, where the behavior agrees with a theoretical prediction, and in three dimensions.

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PubMed2005

Response of a catalytic reaction to periodic variation of the CO pressure: increased CO2 production and dynamic phase transition.

We present a kinetic Monte Carlo study of the dynamical response of a Ziff-Gulari-Barshad model for CO oxidation with CO desorption to periodic variation of the CO pressure. We use a square-wave periodic pressure variation with parameters that can be tuned to enhance the catalytic activity. We produce evidence that, below a critical value of the desorption rate, the driven system undergoes a dynamic phase transition between a CO2 productive phase and a nonproductive one at a critical value of the period and waveform of the pressure oscillation. At the dynamic phase transition the period-averaged CO2 production rate is significantly increased and can be used as a dynamic order parameter. We perform a finite-size scaling analysis that indicates the existence of power-law singularities for the order parameter and its fluctuations, yielding estimated critical exponent ratios beta/nu approximately 0.12 and gamma/nu approximately 1.77. These exponent ratios, together with theoretical symmetry arguments and numerical data for the fourth-order cumulant associated with the transition, give reasonable support for the hypothesis that the observed nonequilibrium dynamic phase transition is in the same universality class as the two-dimensional equilibrium Ising model.

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PubMed2004

Effect of monomer geometry on the fractal structure of colloidal rod aggregates.

The fractal structure of clusters formed by diffusion-limited aggregation of rodlike particles is characterized over three decades of the scattering vector q, and displays an unexpected dependence on the aspect ratio of the constituent monomers. Monte Carlo simulations of aggregating Brownian rods corroborate the experimental finding that the measured fractal dimension is an increasing function of the monomer aspect ratio. Moreover, increasing the rod aspect ratio eliminates the structural distinction between diffusion- and reaction-limited cluster aggregation that is observed for spheres.

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