Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

A randomised interventional trial of ω-3-polyunsaturated fatty acids on endothelial function and disease activity in systemic lupus erythematosus

Objective: To determine the clinical effect of dietary supplementation with low-dose ?-3-polyunsaturated fatty acids on disease activity and endothelial function in patients with systemic lupus erythematosus. Methods: A 24-week randomised double-blind placebo-controlled parallel trial of the effect of 3 g of ?-3-polyunsaturated fatty acids on 60 patients with systemic lupus erythematosus was performed. Serial measurements of disease activity using the revised Systemic Lupus Activity Measure (SLAM-R) and British Isles Lupus Assessment Group index of disease activity for systemic lupus erythematosus (BILAG), endothelial function using flow-mediated dilation (FMD) of the brachial artery, oxidative stress using platelet 8-isoprostanes and analysis of platelet membrane fatty acids were taken at baseline, 12 and 24 weeks. Results: In the fish oil group there was a significant improvement at 24 weeks in SLAM-R (from 9.4 (SD 3.0) to 6.3 (2.5), p

A Planetary Nebula around Nova V458 Vulpeculae Undergoing Flash Ionization

Nova V458 Vul erupted on 2007 August 8 and reached a visual magnitude of 8.1 a few days later. Ha images obtained 6 weeks before the outburst as part of the IPHAS Galactic plane survey reveal an 18th magnitude progenitor surrounded by an extended nebula. Subsequent images and spectroscopy of the nebula reveal an inner nebular knot increasing rapidly in brightness due to flash ionization by the nova event. We derive a distance of 13 kpc based on light travel time considerations, which is supported by two other distance estimation methods. The nebula has an ionized mass of 0.2 Msolar and a low expansion velocity: this rules it out as ejecta from a previous nova eruption, and is consistent with it being a ~14,000 year old planetary nebula, probably the product of a prior common envelope (CE) phase of evolution of the binary system. The large derived distance means that the mass of the erupting WD component of the binary is high. We identify two possible evolutionary scenarios, in at least one of which the system is massive enough to produce a Type Ia supernova upon merging.

Geometric bonding effects in the X2A1, A2∑+u, and B2IIg states of Li2F

Published ab-initio and pseudopotential calculations for the dialkali halide systems suggest that the preferred co-linear geometry is for the metal to approach the metal end of the alkali halide. Here, ab-initio calculations on the Li2F system reveal that the well depth on the halide side in this radical is much deeper and is a local saddle-point associated with the ionic non-linear global minima. Although many features of the pseudopotential surfaces are confirmed, significant differences are apparent including the existence of a linear excited state instead of a triangular one, a considerably deeper global minimum some 50% lower in energy and a close approach between the X2A1 and the states, with the minimum 87 kJ mol-1 below the ground state asymptote. All the results can be rationalised as the avoided crossings between a long range, covalent potential dominant within the LiLiF geometry and an ionic state that forms the global minimum. Calculations on the 3rd 2A' potential indicate that even for Li + LiF collisions at ultracold temperatures the collision dynamics could involve as many as three electronic states.

Lowest energy potentials of Li2 + F accessible at ultracold temperatures

Ab initio calculations for the strongly exoergic Li2+F harpoon reaction are presented using density-functional theory, complete active space self-consistent field, and multireference configuration interaction methods to argue that this reaction would be an ideal candidate for investigation with ultracold molecules. The lowest six states are calculated with the aug-correlation-consistent polarized valence triple-zeta basis set and at least two can be accessed by a ground rovibronic Li2 molecule with zero collision energy at all reaction geometries. The large reactive cross section (characteristic of harpoon reactions) and chemiluminescent products are additional attractive features of these reactions.