Multiple boundary peak solutions for some singularly perturbed Neumann problems

We consider the problem \left \{ \begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega, \end{array} \right. where \Omega is a bounded smooth domain in R^N, \varepsilon>$is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses boundary spike solutions such that the spike concentrates, as \varepsilon approaches zero, at a critical point of the mean curvature function H(P), P \in \partial \Omega . It is also known that this equation has multiple boundary spike solutions at multiple nondegenerate critical points of H(P) or multiple local maximum points of H(P). In this paper, we prove that for any fixed positive integer$K$there exist boundary$K-peak$solutions at a local minimum point of$H(P)$. This implies that for any smooth and bounded domain there always exist boundary$K-peak$ solutions. We first use the Liapunov-Schmidt method to reduce the problem to finite dimensions. Then we use a maximizing procedure to obtain multiple boundary spikes

High Efficiency Large Area Polysilicon Solar Cells

Large area (100 sq cm) polysilicon solar cells having efficiencies of up to 14.1% (100 mW/sq cm, 25 C) were fabricated and a detailed analysis was performed to identify the efficiency loss mechanisms. The 1-5 characteristics of the best cell were dominated by recombination in the quasi-neutral base due to the combination of minority carrier diffusion length and base resistivity. An analysis of the microstructural defects present in the material and their effect on the electrical properties is presented

Experimental performance of the regenerator for the Chrysler upgraded automotive gas turbine engine

Automobile gas turbine engine regenerator performance was studied in a regenerator test facility that provided a satisfactory simulation of the actual engine operating environment but with independent control of airflow and gas flow. Velocity and temperature distributions were measured immediately downstream of both the core high-pressure-side outlet and the core low-pressure-side outlet. For the original engine housing, the regenerator temperature effectiveness was 1 to 2 percent higher than the design value, and the heat transfer effectiveness was 2 to 4 percent lower than the design value over the range of test conditions simulating 50 to 100 percent of gas generator speed. Recalculating the design values to account for seal leakage decreased the design heat transfer effectiveness to values consistent with those measured herein. A baffle installed in the engine housing high-pressure-side inlet provided more uniform velocities out of the regenerator but did not improve the effectiveness. A housing designed to provide more uniform axial flow to the regenerator was also tested. Although temperature uniformity was improved, the effectiveness values were not improved. Neither did 50-percent flow blockage (90 degree segment) applied to the high-pressure-side inlet change the effectiveness significantly

Terrestrial Planet Formation in a protoplanetary disk with a local mass depletion: A successful scenario for the formation of Mars

Models of terrestrial planet formation for our solar system have been successful in producing planets with masses and orbits similar to those of Venus and Earth. However, these models have generally failed to produce Mars-sized objects around 1.5 AU. The body that is usually formed around Mars' semimajor axis is, in general, much more massive than Mars. Only when Jupiter and Saturn are assumed to have initially very eccentric orbits (e $\sim$ 0.1), which seems fairly unlikely for the solar system, or alternately, if the protoplanetary disk is truncated at 1.0 AU, simulations have been able to produce Mars-like bodies in the correct location. In this paper, we examine an alternative scenario for the formation of Mars in which a local depletion in the density of the protosolar nebula results in a non-uniform formation of planetary embryos and ultimately the formation of Mars-sized planets around 1.5 AU. We have carried out extensive numerical simulations of the formation of terrestrial planets in such a disk for different scales of the local density depletion, and for different orbital configurations of the giant planets. Our simulations point to the possibility of the formation of Mars-sized bodies around 1.5 AU, specifically when the scale of the disk local mass-depletion is moderately high (50-75%) and Jupiter and Saturn are initially in their current orbits. In these systems, Mars-analogs are formed from the protoplanetary materials that originate in the regions of disk interior or exterior to the local mass-depletion. Results also indicate that Earth-sized planets can form around 1 AU with a substantial amount of water accreted via primitive water-rich planetesimals and planetary embryos. We present the results of our study and discuss their implications for the formation of terrestrial planets in our solar system.Comment: Accepted for publication in The Astrophysical Journa

XMM Follow-Up Observations of Three Swift BAT-Selected Active Galactic Nuclei

We present XMM-Newton observations of three AGN taken as part of a hunt to find very heavily obscured Compton-thick AGN. For obscuring columns greater than 10^25 cm^-2, AGN are only visible at energies below 10 keV via reflected/scattered radiation, characterized by a flat power-law. We therefore selected three objects (ESO 417-G006, IRAS 05218-1212, and MCG -01-05-047) from the Swift BAT hard X-ray survey catalog with Swift X-ray Telescope XRT 0.5-10 keV spectra with flat power-law indices as candidate Compton-thick sources for follow-up observations with the more sensitive instruments on XMM-Newton. The XMM spectra, however, rule out reflection-dominated models based on the weakness of the observed Fe K-alpha lines. Instead, the spectra are well-fit by a model of a power-law continuum obscured by a Compton-thin absorber, plus a soft excess. This result is consistent with previous follow-up observations of two other flat-spectrum BAT-detected AGN. Thus, out of the six AGN in the 22-month BAT catalog with apparently flat Swift XRT spectra, all five that have had follow-up observations are not likely Compton-thick. We also present new optical spectra of two of these objects, IRAS 05218-1212 and MCG -01-05-047. Interestingly, though both these AGN have similar X-ray spectra, their optical spectra are completely different, adding evidence against the simplest form of the geometric unified model of AGN. IRAS 05218-1212 appears in the optical as a Seyfert 1, despite the ~8.5x10^22 cm^-2 line-of-sight absorbing column indicated by its X-ray spectrum. MCG -01-05-047's optical spectrum shows no sign of AGN activity; it appears as a normal galaxy.Comment: 18 pages including 4 figures, accepted by Ap

Coorbital Satellites of Saturn: Congenital Formation

Saturn is the only known planet to have coorbital satellite systems. In the present work we studied the process of mass accretion as a possible mechanism for coorbital satellites formation. The system considered is composed of Saturn, a proto-satellite and a cloud of planetesimals distributed in the coorbital region around a triangular Lagrangian point. The adopted relative mass for the proto-satellite was 10^-6 of Saturn's mass and for each planetesimal of the cloud three cases of relative mass were considered, 10^-14, 10^-13 and 10^-12 masses of Saturn. In the simulations each cloud of planetesimal was composed of 10^3, 5 x 10^3 or 10^4 planetesimals. The results of the simulations show the formation of coorbital satellites with relative masses of the same order of those found in the saturnian system (10^-13 - 10^-9). Most of them present horseshoe type orbits, but a significant part is in tadpole orbit around L_4 or L_5. Therefore, the results indicate that this is a plausible mechanism for the formation of coorbital satellites.Comment: 10 pages, 9 figures, 4 table

Production and fate of the G ring arc particles due to Aegaeon (Saturn LIII)

The G ring arc hosts the smallest satellite of Saturn, Aegaeon, observed with a set of images sent by Cassini spacecraft. Along with Aegaeon, the arc particles are trapped in a 7:6 corotation eccentric resonance with the satellite Mimas. Due to this resonance, both Aegaeon and the arc material are confined to within sixty degrees of corotating longitudes. The arc particles are dust grains which can have their orbital motions severely disturbed by the solar radiation force. Our numerical simulations showed that Aegaeon is responsible for depleting the arc dust population by removing them through collisions. The solar radiation force hastens these collisions by removing most of the 10$~\mu$m sized grains in less than 40 years. Some debris released from Aegaeon's surface by meteoroid impacts can populate the arc. However, it would take 30,000 years for Aegaeon to supply the observed amount of arc material, and so it is unlikely that Aegaeon alone is the source of dust in the arc

Diversity in parasitic nematode genomes: the microRNAs of Brugia pahangi and Haemonchus contortus are largely novel

<b>BACKGROUND:</b> MicroRNAs (miRNAs) play key roles in regulating post-transcriptional gene expression and are essential for development in the free-living nematode Caenorhabditis elegans and in higher organisms. Whether microRNAs are involved in regulating developmental programs of parasitic nematodes is currently unknown. Here we describe the the miRNA repertoire of two important parasitic nematodes as an essential first step in addressing this question. <b>RESULTS:</b> The small RNAs from larval and adult stages of two parasitic species, Brugia pahangi and Haemonchus contortus, were identified using deep-sequencing and bioinformatic approaches. Comparative analysis to known miRNA sequences reveals that the majority of these miRNAs are novel. Some novel miRNAs are abundantly expressed and display developmental regulation, suggesting important functional roles. Despite the lack of conservation in the miRNA repertoire, genomic positioning of certain miRNAs within or close to specific coding genes is remarkably conserved across diverse species, indicating selection for these associations. Endogenous small-interfering RNAs and Piwi-interacting (pi)RNAs, which regulate gene and transposon expression, were also identified. piRNAs are expressed in adult stage H. contortus, supporting a conserved role in germline maintenance in some parasitic nematodes. <b>CONCLUSIONS:</b> This in-depth comparative analysis of nematode miRNAs reveals the high level of divergence across species and identifies novel sequences potentially involved in development. Expression of novel miRNAs may reflect adaptations to different environments and lifestyles. Our findings provide a detailed foundation for further study of the evolution and function of miRNAs within nematodes and for identifying potential targets for intervention

Three AGN Close To The Effective Eddington Limit

The Effective Eddington Limit for dusty gas surrounding AGN is lower than the canonical Eddington limit for hydrogen gas. Previous results from the Swift/BAT 9-month catalogue suggested that in the overwhelming majority of local AGN, the dusty absorbing gas is below this Effective Eddington limit, implying that radiation pressure is insufficient to blow away the absorbing clouds. We present an analysis of three objects from that sample which were found to be close to the Effective Eddington limit (NGC454, 2MASX J03565655-4041453 and XSS J05054-2348), using newly obtained XMM-Newton data. We use the X-ray data to better constrain the absorbing column density, and supplement them with XMM optical monitor (OM) data, infrared Spitzer and Herschel data where available to construct a broad-band spectral energy distribution to estimate refined bolometric luminosities and Eddington ratios for these three objects. The new XMM-Newton observations show all three objects moving away from the region expected for short-lived absorption in the N_H-\lambda_{Edd} plane into the `long-lived absorption' region. We find our conclusions robust to different methods for estimating the bolometric luminosity and Eddington ratio. Interestingly, 2MASX J03565655-4041453 and XSS J05054-2348 now exhibit complex X-ray spectra, at variance with previous analyses of their Swift/XRT data. We find evidence for absorption variability in NGC 454 and 2MASX J03565655-4041453, perhaps implying that although the radiation pressure from the central engine is insufficient to cause clearly detectable outflows, it may cause absorption variations over longer timescales. However, more robust black hole mass estimates would improve the accuracy of the Eddington ratio estimates for these objects.Comment: 13 pages, 10 figures, 3 tables, accepted for publication in MNRA