Eternity and the cosmological constant

The purpose of this paper is to analyze the stability of interacting matter in the presence of a cosmological constant. Using an approach based on the heat equation, no imaginary part is found for the effective potential in the presence of a fixed background, which is the n-dimensional sphere or else an analytical continuation thereof, which is explored in some detail.Comment: 45 pages, 6 figure

Lif, the lysostaphin immunity factor, complements FemB in staphylococcal peptidoglycan interpeptide bridge formation

The formation of the Staphylococcus aureus peptidoglycan pentaglycine interpeptide chain needs FemA and FemB for the incorporation of glycines Gly2-Gly3, and Gly4-Gly5, respectively. The lysostaphin immunity factor Lif was able to complement FemB, as could be shown by serine incorporation and by an increase in lysostaphin resistance in the wild-type as well as in a femB mutant. However, Lif could not substitute for FemA in femA or in femAB-null mutants. Methicillin resistance, which is dependent on functional FemA and FemB, was not complemented by Lif, suggesting that serine-substituted side chains are a lesser substrate for penicillin-binding protein PBP2′ in methicillin resistanc

The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement

Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1 Minkowski space to S^3, are computed in three spatial dimensions (3D) using adaptive mesh refinement (AMR). For initial data with compact support the model is known to have two regimes, one in which regular initial data forms a singularity and another in which the energy is dispersed to infinity. The transition between these regimes has been shown in spherical symmetry to demonstrate threshold behavior similar to that between black hole formation and dispersal in gravitating theories. Here, I generalize the result by removing the assumption of spherical symmetry. The evolutions suggest that the spherically symmetric critical solution remains an intermediate attractor separating the two end states.Comment: 5 pages, 5 figures, 1 table; To be published in Phys. Rev. D.; Added discussion of initial data; Added figure and reference

Data compression in the presence of observational error correlations

Numerical weather prediction (NWP) models are moving towards km-scale (and smaller) resolutions in order to forecast high-impact weather. As the resolution of NWP models increase the need for high-resolution observations to constrain these models also increases. A major hurdle to the assimilation of dense observations in NWP is the presence of non-negligible observation error correlations (OECs). Despite the difficulty in estimating these error correlations, progress is being made, with centres around the world now explicitly accounting for OECs in a variety of observation types. This paper explores how to make efficient use of this potentially dramatic increase in the amount of data available for assimilation. In an idealised framework it is illustrated that as the length-scales of the OECs increase the scales that the analysis is most sensitive to the observations become smaller. This implies that a denser network of observations is more beneficial with increasing OEC length-scales. However, the computational and storage burden associated with such a dense network may not be feasible. To reduce the amount of data, a compression technique based on retaining the maximum information content of the observations can be used. When the OEC length-scales are large (in comparison to the prior error correlations), the data compression will select observations of the smaller scales for assimilation whilst throwing out the larger scale information. In this case it is shown that there is a discrepancy between the observations with the maximum information and those that minimise the analysis error variances. Experiments are performed using the Ensemble Kalman Filter and the Lorenz-1996 model, comparing different forms of data reduction. It is found that as the OEC length-scales increase the assimilation becomes more sensitive to the choice of data reduction technique