Effects of Dust Scattering in Expanding Spherical Nebulae

The mean intensity of planetary nebulae with an expanding atmosphere is modeled by considering dusty and dust-free atmospheres. The bulk matter density is determined from the adopted velocity field through the equation of continuity. The gas is assumed to consist of hydrogen and helium and the gas-to-dust mass ratio is taken to be $3\times10^{-4}$. The Rayleigh phase function is employed for atomic scattering while the full Mie theory of scattering is incorporated for determining the dust scattering and absorption cross-section as well as the phase function for the angular distribution of photons after scattering. It is shown that in a dust free atmosphere, the mean intensity increases with the increase in the expansion velocity that makes the medium diluted. The mean intensity profile changes significantly when dust scattering is incorporated. The increase in forward scattering of photons by the dust particles yields into an increase in the mean intensity as compared to that without dust. The mean intensity increases as the particle size is increased. Thus it is shown that both the expansion of the medium and the presence of dust play important role in determining the mean intensity of a planetary nebulae.Comment: 18 pages, Elseveir style (cls file included), 5 postscript figures, Accepted for publication in New Astronom

Research designs considerations for chronic pain prevention clinical trials: IMMPACT recommendations

Although certain risk factors can identify individuals who aremost likely to develop chronic pain, few interventions to prevent chronic pain have been identified. To facilitate the identification of preventive interventions, an IMMPACTmeeting was convened to discuss research design considerations for clinical trials investigating the prevention of chronic pain. We present general design considerations for prevention trials in populations that are at relatively high risk for developing chronic pain. Specific design considerations included subject identification, timing and duration of treatment, outcomes, timing of assessment, and adjusting for risk factors in the analyses.We provide a detailed examination of 4 models of chronic pain prevention (ie, chronic postsurgical pain, postherpetic neuralgia, chronic low back pain, and painful chemotherapy-induced peripheral neuropathy). The issues discussed can, inmany instances, be extrapolated to other chronic pain conditions. These examples were selected because they are representative models of primary and secondary prevention, reflect persistent pain resulting from multiple insults (ie, surgery, viral infection, injury, and toxic or noxious element exposure), and are chronically painful conditions that are treated with a range of interventions. Improvements in the design of chronic pain prevention trials could improve assay sensitivity and thus accelerate the identification of efficacious interventions. Such interventions would have the potential to reduce the prevalence of chronic pain in the population. Additionally, standardization of outcomes in prevention clinical trials will facilitate meta-analyses and systematic reviews and improve detection of preventive strategies emerging from clinical trials

On the Hyperfine structure of certain Hg I lines in the electrodeless discharge

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