Learn More
We introduce a fast implementation of the pivot algorithm for self-avoiding walks, which we use to obtain large samples of walks on the cubic lattice of up to 33x10{6} steps. Consequently the critical exponent nu for three-dimensional self-avoiding walks is determined to great accuracy; the final estimate is nu=0.587 597(7). The method can be adapted to(More)
We evaluate the virial coefficients B k for k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial(More)
Forecasts of range dynamics now incorporate many of the mechanisms and interactions that drive species distributions. However, connectivity continues to be simulated using overly simple distance-based dispersal models with little consideration of how the individual behaviour of dispersing organisms interacts with landscape structure (functional(More)
We give an introduction to the lace expansion for self-avoiding walks, with emphasis on self-avoiding polygons, and with a focus on combinatorial rather than analytical aspects. We derive the lace expansion for self-avoiding walks, and show that this is equivalent to taking the reciprocal of the self-avoiding walk generating function. We list some of the(More)
The equation of state of hard hyperspheres in nine dimensions is calculated both from the values of the first ten virial coefficients and from a Monte Carlo simulation of the pair correlation function at contact. The results are in excellent agreement. In addition, we find that the virial series appears to be dominated by an unphysical singularity or(More)
Deviance information criterion (DIC) calculation and selection of the negative binomial distribution Giant cuttlefish counts were overdispersed (i.e. Poisson variance exceeded the mean) with an excess of zeros, so we tested the ability of four distributions (Poisson, zero-inflated Poisson, negative binomial and zero-inflated negative binomial) to account(More)
The universal asymptotic amplitude ratio between the gyration radius and the hydrodynamic radius of self-avoiding walks is estimated by high-resolution Monte Carlo simulations. By studying chains of length of up to N=2^{25}≈34×10^{6} monomers, we find that the ratio takes the value R_{G}/R_{H}=1.5803940(45), which is several orders of magnitude more(More)
  • 1