Neutral atomic carbon in the globules of the Helix

We report detection of the 609u line of neutral atomic carbon in globules of the Helix nebula. The measurements were made towards the position of peak CO emission. At the same position, we obtained high-quality CO(2-1) and 13CO(2-1) spectra and a 135" x 135" map in CO(2-1). The velocity distribution of CI shows six narrow (1 -> 2 km/sec) components which are associated with individual globules traced in CO. The CI column densities are 0.5 -> 1.2 x 10^16/cm^2. CI is found to be a factor of ~6 more abundant than CO. Our estimate for the mass of the neutral envelope is an order of magnitude larger than previous estimates. The large abundance of CI in the Helix can be understood as a result of the gradual photoionisation of the molecular envelope by the central star's radiation field.Comment: 5 pages, Latex, AAS macros, 3 EPS figures, to appear in Astrophysical Journal Letter

A search for CO+ in planetary nebulae

We have carried out a systematic search for the molecular ion CO+ in a sample of 8 protoplanetary and planetary nebulae in order to determine the origin of the unexpectedly strong HCO+ emission previously detected in these sources. An understanding of the HCO+ chemistry may provide direct clues to the physical and chemical evolution of planetary nebulae. We find that the integrated intensity of the CO+ line may be correlated with that of HCO+, suggesting that the reaction of CO+ with molecular hydrogen may be an important formation route for HCO+ in these planetary nebulae.Comment: 6 pages, 4 figures, accepted for publication in MNRA

Optimal Blackjack Strategy with Lucky Bucks

In the casino game blackjack or 21, mathematically determined best plays have been calculated by various mathematicians and gambling experts. These optimal playing strategies all assume that the casino pays even money on bets (excluding when the player has a blackjack ). However, many casinos offer the player lucky bucks that pay the player either 3-to-2 or 2-to-1. In the usual game, the player\u27s expected loss is under 1¢ per dollar bet. in this paper, we derive optimal strategies under luck-buck conditions, giving the player an expected gain of 26¢ or 55¢ per dollar bet

Redox reactions with empirical potentials: Atomistic battery discharge simulations

Batteries are pivotal components in overcoming some of today's greatest technological challenges. Yet to date there is no self-consistent atomistic description of a complete battery. We take first steps toward modeling of a battery as a whole microscopically. Our focus lies on phenomena occurring at the electrode-electrolyte interface which are not easily studied with other methods. We use the redox split-charge equilibration (redoxSQE) method that assigns a discrete ionization state to each atom. Along with exchanging partial charges across bonds, atoms can swap integer charges. With redoxSQE we study the discharge behavior of a nano-battery, and demonstrate that this reproduces the generic properties of a macroscopic battery qualitatively. Examples are the dependence of the battery's capacity on temperature and discharge rate, as well as performance degradation upon recharge.Comment: 14 pages, 10 figure

Filaments as Possible Signatures of Magnetic Field Structure in Planetary Nebulae

We draw attention to the extreme filamentary structures seen in high-resolution optical images of certain planetary nebulae. We determine the physical properties of the filaments in the nebulae IC 418, NGC 3132, and NGC 6537, and based on their large length-to-width ratios, longitudinal coherence, and morphology, we suggest that they may be signatures of the underlying magnetic field. The fields needed for the coherence of the filaments are probably consistent with those measured in the precursor circumstellar envelopes. The filaments suggest that magnetic fields in planetary nebulae may have a localized and thread-like geometry.Comment: 26 pages with 7 figures. To be published in PASP. For full resolution images see http://physics.nyu.edu/~pjh

A CO Survey of Young Planetary Nebulae

We report the results of a sensitive survey of young planetary nebulae in the CO J=2-1 line that significantly increases the available data on warm, dense, molecular gas in the early phases of planetary nebula formation. The observations were made using the IRAM 30 m telescope with the 3 by 3 pixel Heterodyne Receiver Array (HERA). The array provides an effective means of discriminating the CO emission of planetary nebulae in the galactic plane from contaminating emission of interstellar clouds along the line of sight. 110 planetary nebulae were observed in the survey and 40 were detected. The results increase the number of young planetary nebulae with known CO emission by approximately a factor of two. The CO spectra yield radial velocities for the detected nebulae, about half of which have uncertain or no velocity measurements at optical wavelengths. The CO profiles range from parabolic to double-peaked, tracing the evolution of structure in the molecular gas. The line widths are significantly larger than on the Asymptotic Giant Branch, and many of the lines show extended wings, which probably result from the effects on the envelopes of high velocity jets.Comment: 29 pages, 2 figures (with multiple panels), to be published in Astrophysical Journal Supplement Serie

Solid state television camera system Patent

Solid state television camera system consisting of monolithic semiconductor mosaic sensor and molecular digital readout system

Zeta-Functions for Non-Minimal Operators

We evaluate zeta-functions $\zeta(s)$ at $s=0$ for invariant non-minimal 2nd-order vector and tensor operators defined on maximally symmetric even dimensional spaces. We decompose the operators into their irreducible parts and obtain their corresponding eigenvalues. Using these eigenvalues, we are able to explicitly calculate $\zeta(0)$ for the cases of Euclidean spaces and $N$-spheres. In the $N$-sphere case, we make use of the Euler-Maclaurin formula to develop asymptotic expansions for the required sums. The resulting $\zeta(0)$ values for dimensions 2 to 10 are given in the Appendix.Comment: 26 pages, additional reference

Multiple Molecular H2 Outflows in AFGL 618

We report high spatial (0.5 arcsec) and high spectral (9 km/s) resolution spectro-imaging of the 2.12 micron H2 1-0 S(1) line in the proto-planetary nebula AFGL 618 using BEAR at the CFHT. The observations reveal the presence of multiple, high-velocity, molecular outflows that align with the remarkable optical jets seen in HST images. The structure and kinematics of the outflows show how jets interact with circumstellar gas and shape the environment in which planetary nebulae form.Comment: 14 pages, 5 figures. To appear in The Astrophysical Journal Letter