Correction-to-scaling exponent for two-dimensional percolation

We show that the correction-to-scaling exponents in two-dimensional percolation are bounded by Omega <= 72/91, omega = D Omega <= 3/2, and Delta_1 = nu omega <= 2, based upon Cardy's result for the critical crossing probability on an annulus. The upper bounds are consistent with many previous measurements of site percolation on square and triangular lattices, and new measurements for bond percolation presented here, suggesting this result is exact. A scaling form evidently applicable to site percolation is also found

Number of spanning clusters at the high-dimensional percolation thresholds

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions for d>6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review

Automated biowaste sampling system, solids subsystem operating model, part 2

The detail design and fabrication of the Solids Subsystem were implemented. The system's capacity for the collection, storage or sampling of feces and vomitus from six subjects was tested and verified

Circumstellar Disks in the Outer Galaxy: the Star-Forming Region NGC 1893

It is still debated whether star formation process depends on environment. In particular it is yet unclear whether star formation in the outer Galaxy, where the environmental conditions are, theoretically, less conducive, occurs in the same way as in the inner Galaxy. We investigate the population of NGC1893, a young cluster ~3-4 Myr in the outer part of the Galaxy (galactic radius >11 Kpc), to explore the effects of environmental conditions on star forming regions. We present infrared observations acquired using the IRAC camera onboard the Spitzer Space Telescope and analyze the color-color diagrams to establish the membership of stars with excesses. We also merge this information with that obtained from Chandra ACIS-I observations, to identify the Class III population. We find that the cluster is very rich, with 242 PMS Classical T-Tauri stars and 7 Class 0/I stars. We identify 110 Class III candidate cluster members in the ACIS-I field of view. We estimate a disk fraction for NGC1893 of about 67%, similar to fractions calculated for nearby star forming regions of the same age. Although environmental conditions are unfavorable, star formation can clearly be very successful in the outer Galaxy, allowing creation of a very rich cluster like NGC1893.Comment: 10 pages,7 figures,4 table

Ages, Distances, and the Initial Mass Functions of Stellar Clusters

We provide a review of the current status of several topics on the ages, distances, and mass functions of open clusters, with a particular emphasis on illuminating the areas of uncertainty. Hipparcos has obtained parallaxes for nearby open clusters that have expected accuracies much better than has been previously achievable. By using the lithium depletion boundary method and isochrone fitting based on much improved new theoretical evolutionary models for low mass stars, it is arguable that we will soon have have much better age scales for clusters and star-forming regions. With improved optical and near-IR cameras, we are just now beginning to extend the mass function of open clusters like the Pleiades into the regime below the hydrogen burning mass limit. Meanwhile, observations in star-forming regions are in principle capable of identifying objects down to of order 10 Jupiter masses.Comment: 13 pages, including 3 embedded figures (4 EPS files). To appear in "11th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun," ed. R. J. Garcia Lopez, R. Rebolo, and M. R. Zapatero Osori

SPITZER observations of the λ Orionis cluster. II. Disks around solar-type and low-mass stars

We present IRAC/MIPS Spitzer Space Telescope observations of the solar-type and the low-mass stellar population of the young (~5Myr) λ Orionis cluster. Combining optical and Two Micron All Sky Survey photometry, we identify 436 stars as probable members of the cluster. Given the distance (450 pc) and the age of the cluster, our sample ranges in mass from 2 M_⊙ to objects below the substellar limit. With the addition of the Spitzer mid-infrared data, we have identified 49 stars bearing disks in the stellar cluster. Using spectral energy distribution slopes, we place objects in several classes: non-excess stars (diskless), stars with optically thick disks, stars with “evolved disks” (with smaller excesses than optically thick disk systems), and “transitional disk” candidates (in which the inner disk is partially or fully cleared). The disk fraction depends on the stellar mass, ranging from ~6% for K-type stars (R_C − J 4). We confirm the dependence of disk fraction on stellar mass in this age range found in other studies. Regarding clustering levels, the overall fraction of disks in the λ Orionis cluster is similar to those reported in other stellar groups with ages normally quoted as ~5Myr

Rotation of Low-mass Stars in Taurus with K2

We present an analysis of K2 light curves (LCs) from Campaigns 4 and 13 for members of the young (~3 Myr) Taurus association, in addition to an older (~30 Myr) population of stars that is largely in the foreground of the Taurus molecular clouds. Out of 156 of the highest-confidence Taurus members, we find that 81% are periodic. Our sample of young foreground stars is biased and incomplete, but nearly all stars (37/38) are periodic. The overall distribution of rotation rates as a function of color (a proxy for mass) is similar to that found in other clusters: the slowest rotators are among the early M spectral types, with faster rotation toward both earlier FGK and later M types. The relationship between period and color/mass exhibited by older clusters such as the Pleiades is already in place by Taurus age. The foreground population has very few stars but is consistent with the USco and Pleiades period distributions. As found in other young clusters, stars with disks rotate on average slower, and few with disks are found rotating faster than ~2 days. The overall amplitude of the LCs decreases with age, and higher-mass stars have generally lower amplitudes than lower-mass stars. Stars with disks have on average larger amplitudes than stars without disks, though the physical mechanisms driving the variability and the resulting LC morphologies are also different between these two classes

Model for Cumulative Solar Heavy Ion Energy and Linear Energy Transfer Spectra

A probabilistic model of cumulative solar heavy ion energy and LET spectra is developed for spacecraft design applications. Spectra are given as a function of confidence level, mission time period during solar maximum and shielding thickness. It is shown that long-term solar heavy ion fluxes exceed galactic cosmic ray fluxes during solar maximum for shielding levels of interest. Cumulative solar heavy ion fluences should therefore be accounted for in single event effects rate calculations and in the planning of space missions

Rotation of Late-Type Stars in Praesepe with K2

We have Fourier analyzed 941 K2 light curves of likely members of Praesepe, measuring periods for 86% and increasing the number of rotation periods (P) by nearly a factor of four. The distribution of P vs. (V-K), a mass proxy, has three different regimes: (V-K)<1.3, where the rotation rate rapidly slows as mass decreases; 1.3<(V-K)<4.5, where the rotation rate slows more gradually as mass decreases; and (V-K)>4.5, where the rotation rate rapidly increases as mass decreases. In this last regime, there is a bimodal distribution of periods, with few between $\sim$2 and $\sim$10 days. We interpret this to mean that once M stars start to slow down, they do so rapidly. The K2 period-color distribution in Praesepe ($\sim$790 Myr) is much different than in the Pleiades ($\sim$125 Myr) for late F, G, K, and early-M stars; the overall distribution moves to longer periods, and is better described by 2 line segments. For mid-M stars, the relationship has similarly broad scatter, and is steeper in Praesepe. The diversity of lightcurves and of periodogram types is similar in the two clusters; about a quarter of the periodic stars in both clusters have multiple significant periods. Multi-periodic stars dominate among the higher masses, starting at a bluer color in Praesepe ((V-K)$\sim$1.5) than in the Pleiades ((V-K)$\sim$2.6). In Praesepe, there are relatively more light curves that have two widely separated periods, $\Delta P >$6 days. Some of these could be examples of M star binaries where one star has spun down but the other has not.Comment: Accepted by Ap