Pseudo-High-Order Symplectic Integrators

Symplectic N-body integrators are widely used to study problems in celestial mechanics. The most popular algorithms are of 2nd and 4th order, requiring 2 and 6 substeps per timestep, respectively. The number of substeps increases rapidly with order in timestep, rendering higher-order methods impractical. However, symplectic integrators are often applied to systems in which perturbations between bodies are a small factor of the force due to a dominant central mass. In this case, it is possible to create optimized symplectic algorithms that require fewer substeps per timestep. This is achieved by only considering error terms of order epsilon, and neglecting those of order epsilon^2, epsilon^3 etc. Here we devise symplectic algorithms with 4 and 6 substeps per step which effectively behave as 4th and 6th-order integrators when epsilon is small. These algorithms are more efficient than the usual 2nd and 4th-order methods when applied to planetary systems.Comment: 14 pages, 5 figures. Accepted for publication in the Astronomical Journa

Stochastic Dominance, Entropy and Biodiversity Management

In this paper we develop a model of population dynamics using the Shannon entropy index, a measure of diversity that allows for global and specific population shocks. We model the effects of increasing the number of parcels on biodiversity, varying the number of spatially diverse parcels to capture risk diversification. We discuss the concepts of stochastic dominance as a means of project selection, in order to model biodiversity returns and risks. Using a Monte Carlo simulation we find that stochastic dominance may be a useful theoretical construct for project selections but it is unable to rank every case.

Stochastic Dominance, Entropy and Biodiversity Management

In this paper we develop a model of population dynamics using the Shannon entropy index, a measure of diversity that allows for global and specific population shocks. We model the effects of increasing the number of parcels on biodiversity, varying the number of spatially diverse parcels to capture risk diversification. We discuss the concepts of stochastic dominance as a means of project selection, in order to model biodiversity returns and risks. Using a Monte Carlo simulation we find that stochastic dominance may be a useful theoretical construct for project selections but it is unable to rank every case. Key Words: Stochastic Dominance, Entropy, Biodiversity Management

C^+ distribution around S1 in rho Ophiuchi

We analyze a [C II] 158 micron map obtained with the L2 GREAT receiver on SOFIA of the emission/reflection nebula illuminated by the early B star S1 in the rho-OphA cloud core. This data set has been complemented with maps of CO(3-2), 13CO(3-2) and C18O(3-2), observed as a part of the JCMT Gould Belt Survey, with archival HCO^+(4-3) JCMT data, as well as with [O I] 63 and 145 micron imaging with Herschel/PACS. The [C II] emission is completely dominated by the strong PDR emission from the nebula surrounding S1 expanding into the dense Oph A molecular cloud west and south of S1. The [C II] emission is significantly blue shifted relative to the CO spectra and also relative to the systemic velocity, particularly in the northwestern part of the nebula. The [C II] lines are broader towards the center of the S1 nebula and narrower towards the PDR shell. The [C II] lines are strongly self-absorbed over an extended region in the S1 PDR. Based on the strength of the [13C II] F = 2-1 hyperfine component, [C II] is significantly optically thick over most of the nebula. CO and 13CO(3-2) spectra are strongly self-absorbed, while C18O(3-2) is single peaked and centered in the middle of the self-absorption. We have used a simple two-layer LTE model to characterize the background and foreground cloud contributing to the [C II] emission. From this analysis we estimate the extinction due to the foreground cloud to be ~9.9 mag, which is slightly less than the reddening estimated towards S1. Since some of the hot gas in the PDR is not traced by low J CO emission, this result appears quite plausible. Using a plane parallel PDR model with the observed [OI(145)]/[C II] brightness ratio and an estimated FUV intensity of 3100-5000 G0 suggests that the density of the [C II] emitting gas is ~3-4x10^3 cm^-3.Comment: Accepted for publication in Astronomy & Astrophysic

Opening the Treasure Chest in Carina

We have mapped the G287.84-0.82 cometary globule (with the Treasure Chest cluster embedded in it) in the South Pillars region of Carina (i) in [CII], 63micron [OI], and CO(11-10) using upGREAT on SOFIA and (ii) in J=2-1 transitions of CO, 13CO, C18O and J=3-2 transitions of H2CO using the APEX telescope in Chile. We probe the morphology, kinematics, and physical conditions of the molecular gas and the photon dominated regions (PDRs) in G287.84-0.82. The [CII] and [OI] emission suggest that the overall structure of the pillar (with red-shifted photo evaporating tails) is consistent with the effect of FUV radiation and winds from eta-Car and O stars in Trumpler 16. The gas in the head of the pillar is strongly influenced by the embedded cluster, whose brightest member is an O9.5V star, CPD-59 2661. The emission of the [CII] and [OI] lines peak at a position close to the embedded star, while all other tracers peak at another position lying to the north-east consistent with gas being compressed by the expanding PDR created by the embedded cluster. The molecular gas inside the globule is probed with the J=2-1 transitions of CO and isotopologues as well as H2CO, and analyzed using a non-LTE model (escape-probability approach), while we use PDR models to derive the physical conditions of the PDR. We identify at least two PDR gas components; the diffuse part (~10^4 cm^-3) is traced by [CII], while the dense (n~ 2-8x10^5 cm^-3) part is traced by [CII], [OI], CO(11-10). Using the F=2-1 transition of [13CII] detected at 50 positions in the region, we derive optical depths (0.9-5), excitation temperatures of [CII] (80-255 K), and N(C+) of 0.3-1x10^19 cm^-2. The total mass of the globule is ~1000 Msun, about half of which is traced by [CII]. The dense PDR gas has a thermal pressure of 10^7-10^8 K cm^-3, which is similar to the values observed in other regions.Comment: Accepted for publication in Astronomy and Astrophysics (abstract slightly abridged

A methodology for selective removal of orbital debris

Earth-orbiting objects, large enough to be tracked, were surveyed for possible systematic debris removal. Based upon the statistical collision studies of others, it was determined that objects in orbits approximately 1000 km above the Earth's surface are at greatest collisional risk. Russian C-1B boosters were identified as the most important target of opportunity for debris removal. Currently, more than 100 in tact boosters are orbiting the Earth with apogees between 950 km and 1050 km. Using data provided by Energia USA, specific information on the C-1B booster, in terms of rendezvous and capture strategies, was discussed

Surface effects on nanowire transport: numerical investigation using the Boltzmann equation

A direct numerical solution of the steady-state Boltzmann equation in a cylindrical geometry is reported. Finite-size effects are investigated in large semiconducting nanowires using the relaxation-time approximation. A nanowire is modelled as a combination of an interior with local transport parameters identical to those in the bulk, and a finite surface region across whose width the carrier density decays radially to zero. The roughness of the surface is incorporated by using lower relaxation-times there than in the interior. An argument supported by our numerical results challenges a commonly used zero-width parametrization of the surface layer. In the non-degenerate limit, appropriate for moderately doped semiconductors, a finite surface width model does produce a positive longitudinal magneto-conductance, in agreement with existing theory. However, the effect is seen to be quite small (a few per cent) for realistic values of the wire parameters even at the highest practical magnetic fields. Physical insights emerging from the results are discussed.Comment: 15 pages, 7 figure

Electrochemical Detection of Nanoscale Phase Separation in Binary Self-Assembled Monolayers

Developing methods to probe the nature and structure of nanoscale environments continues to be a challenge in nanoscience. We report a cyclic voltammetry investigation of internal, hydrogen-bond driven phase separation of amide-containing thiols and alkane thiols. Amide-containing thiols with a terminal ferrocene carboxylate functional group were investigated in two binary monolayers, one homogeneously mixed and the other phase separated. The electrochemical response of the ferrocene probe was used to monitor adsorbate coverage, environment and phase separation within each of these monolayers. The results demonstrate that the behavior of ferrocene containing monolayers can be used to probe nanoscale organization