The Planetary Nebulae Luminosity Function and distances to Virgo, Hydra I and Coma clusters

The luminosity function of planetary nebulae populations in galaxies within 10-15 Mpc distance has a cut-off at bright magnitudes and a functional form that is observed to be invariant in different galaxy morphological types. Thus it is used as a secondary distance indicator in both early and late-type galaxies. Recent deep surveys of planetary nebulae populations in brightest cluster galaxies (BCGs) seem to indicate that their luminosity functions deviate from those observed in the nearby galaxies. We discuss the evidence for such deviations in Virgo, and indicate which physical mechanisms may alter the evolution of a planetary nebula envelope and its central star in the halo of BCGs. We then discuss preliminary results for distances for the Virgo, Hydra I and Coma clusters based on the observed planetary nebulae luminosity functions.Comment: 5 pages, one figure. To appear on the Proceedings of the IAU Symp. 289 "Advancing the physics of cosmic distances

Atomistic study of electronic structure of PbSe nanowires

Lead Selenide (PbSe) is an attractive `IV-VI' semiconductor material to design optical sensors, lasers and thermoelectric devices. Improved fabrication of PbSe nanowires (NWs) enables the utilization of low dimensional quantum effects. The effect of cross-section size (W) and channel orientation on the bandstructure of PbSe NWs is studied using an 18 band $sp^3d^5$ tight-binding theory. The bandgap increases almost with the inverse of the W for all the orientations indicating a weak symmetry dependence. [111] and [110] NWs show higher ballistic conductance for the conduction and valence band compared to [100] NWs due to the significant splitting of the projected L-valleys in [100] NWs.Comment: 4 figures, Prepared for AP

Fluctuations of a long, semiflexible polymer in a narrow channel

We consider an inextensible, semiflexible polymer or worm-like chain, with persistence length $P$ and contour length $L$, fluctuating in a cylindrical channel of diameter $D$. In the regime $D\ll P\ll L$, corresponding to a long, tightly confined polymer, the average length of the channel $$ occupied by the polymer and the mean square deviation from the average vary as $=[1-\alpha_\circ(D/P)^{2/3}]L$ and $<\Delta R_\parallel^{\thinspace 2}\thinspace>=\beta_\circ(D^2/P)L$, respectively, where $\alpha_\circ$ and $\beta_\circ$ are dimensionless amplitudes. In earlier work we determined $\alpha_\circ$ and the analogous amplitude $\alpha_\Box$ for a channel with a rectangular cross section from simulations of very long chains. In this paper we estimate $\beta_\circ$ and $\beta_\Box$ from the simulations. The estimates are compared with exact analytical results for a semiflexible polymer confined in the transverse direction by a parabolic potential instead of a channel and with a recent experiment. For the parabolic confining potential we also obtain a simple analytic result for the distribution of $R_\parallel$ or radial distribution function, which is asymptotically exact for large $L$ and has the skewed shape seen experimentally.Comment: 21 pages, including 4 figure