Bond percolation of polymers

We study bond percolation of $N$ non-interacting Gaussian polymers of $\ell$ segments on a 2D square lattice of size $L$ with reflecting boundaries. Through simulations, we find the fraction of configurations displaying {\em no} connected cluster which span from one edge to the opposite edge. From this fraction, we define a critical segment density $\rho_{c}^L(\ell)$ and the associated critical fraction of occupied bonds $p_{c}^L(\ell)$, so that they can be identified as the percolation threshold in the $L \to \infty$ limit. Whereas $p_{c}^L(\ell)$ is found to decrease monotonically with $\ell$ for a wide range of polymer lengths, $\rho_{c}^L(\ell)$ is non-monotonic. We give physical arguments for this intriguing behavior in terms of the competing effects of multiple bond occupancies and polymerization.Comment: 4 pages with 6 figure

Are Light Sterile Neutrinos Preferred or Disfavored by Cosmology?

We find that the viability of a cosmological model that incorporates 2 sterile neutrinos with masses around 1 eV each, as favored by global neutrino oscillation analyses including short baseline results, is significantly dependent on the choice of datasets included in the analysis and the ability to control the systematic uncertainties associated with these datasets. Our analysis includes a variety of cosmological probes including the cosmic microwave background (WMAP7+SPT), Hubble constant (HST), galaxy power spectrum (SDSS-DR7), and supernova distances (SDSS and Union2 compilations). In the joint observational analysis, our sterile neutrino model is equally favored as a LCDM model when using the MLCS light curve fitter for the supernova measurements, and strongly disfavored by the data at \Delta\chi^2 ~ 18 when using the SALT2 fitter. When excluding the supernova measurements, the sterile neutrino model is disfavored by the other datasets at \Delta\chi^2 ~ 12, and at best becomes mildly disfavored at \Delta\chi^2 ~ 3 when allowing for curvature, evolving dark energy, additional relativistic species, running of the spectral index, and freedom in the primordial helium abundance. No single additional parameter accounts for most of this effect. Therefore, if laboratory experiments continue to favor a scenario with roughly eV mass sterile neutrinos, and if this becomes decisively disfavored by cosmology, then a more exotic cosmological model than explored here may become necessary.Comment: 10 pages, 3 figures. Minor refinements, reflects version accepted for publication in PR