No abstract

An approach is presented for the theoretical calculation of self-diffusion coefficients of liquid metals. The basic assumption is that the self-diffusion coefficient of a liquid metal is equal to that of an appropriate hard sphere fluid. The hard sphere diameter is dependent upon temperature, and a method is developed for estimating this temperature dependence by exploring the relationship between the diameter and the interatomic potential energy function of the liquid metal. The theory gives accurate results for the magnitude and temperature dependence of the self-diffusion coefficient for many liquid metals. In addition, the physical basis for the theory is consistent with what has been learned about the liquid state from molecular dynamics calculations.

We revisit the issue of non-parametric gravitational lens reconstruction and present a new method to obtain the cluster mass distribution using strong lensing data without using any prior information on the underlying mass. The method relies on the decomposition of the lens plane into individual cells. We show how the problem in this approximation can be expressed as a system of linear equations for which a solution can be found. Moreover, we propose to include information about the null space. That is, make use of the pixels where we know there are no arcs above the sky noise. The only prior information is an estimation of the physical size of the sources. No priors on the luminosity of the cluster or shape of the halos are needed thus making the results very robust. In order to test the accuracy and bias of the method we make use of simulated strong lensing data. We find that the method reproduces accurately both the lens mass and source positions and provide error estimates.Comment: This is the accepted version in MNRAS. Thsi includes improvements suggested by the referee and one new plot. Additional material can be found in http://darwin.cfa.harvard.edu/SLAP/index.asp

We use the latest Planck constraints, and in particular constraints on the derived parameters (Hubble constant and age of the Universe) for the local universe and compare them with local measurements of the same quantities. We propose a way to quantify whether cosmological parameters constraints from two different experiments are in tension or not. Our statistic, T , is an evidence ratio and therefore can be interpreted with the widely used Jeffrey's scale. We find that in the framework of the ΛCDM model, the Planck inferred two dimensional, joint, posterior distribution for the Hubble constant and age of the Universe is in "strong" tension with the local measurements; the odds being ∼ 1:50. We explore several possibilities for explaining this tension and examine the consequences both in terms of unknown errors and deviations from the ΛCDM model. In some one-parameter ΛCDM model extensions, tension is reduced whereas in other extensions, tension is instead increased. In particular, small total neutrino masses are favored and a total neutrino mass above 0.15 eV makes the tension "highly significant" (odds ∼ 1:150). A consequence of accepting this interpretation of the tension is that the degenerate neutrino hierarchy is highly disfavoured by cosmological data and the direct hierarchy is slightly favored over the inverse.