Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.Comment: 15 pages, LaTe

Influence of local surface albedo variability and ice crystal shape on passive remote sensing of thin cirrus

Airborne measurements of solar spectral radiance reflected by cirrus are performed with the HALO-Solar Radiation (HALO-SR) instrument onboard the High Altitude and Long Range Research Aircraft (HALO) in November 2010. The data are used to quantify the influence of surface albedo variability on the retrieval of cirrus optical thickness and crystal effective radius. The applied retrieval of cirrus optical properties is based on a standard two-wavelength approach utilizing measured and simulated reflected radiance in the visible and near-infrared spectral region. Frequency distributions of the surface albedos from Moderate resolution Imaging Spectroradiometer (MODIS) satellite observations are used to compile surface-albedo-dependent lookup tables of reflected radiance. For each assumed surface albedo the cirrus optical thickness and effective crystal radius are retrieved as a function of the assumed surface albedo. The results for the cirrus optical thickness are compared to measurements from the High Spectral Resolution Lidar (HSRL). The uncertainty in cirrus optical thickness due to local variability of surface albedo in the specific case study investigated here is below 0.1 and thus less than that caused by the measurement uncertainty of both instruments. It is concluded that for the retrieval of cirrus optical thickness the surface albedo variability is negligible. However, for the retrieval of crystal effective radius, the surface albedo variability is of major importance, introducing uncertainties up to 50%. Furthermore, the influence of the bidirectional reflectance distribution function (BRDF) on the retrieval of crystal effective radius was investigated and quantified with uncertainties below 10%, which ranges below the uncertainty caused by the surface albedo variability. The comparison with the independent lidar data allowed for investigation of the role of the crystal shape in the retrieval. It is found that if assuming aggregate ice crystals, the HSRL observations fit best with the retrieved optical thickness from HALO-SR

Characterization of Rotating Cavitation in a Four Bladed Inducer

This work aims to characterize the dynamic behavior of a four bladed inducer and clarify the physical mechanism that leads to the onset of rotating cavitation. The inducer under consideration is representative of a low-pressure liquid oxygen pump (LPOP) inducer of modern design and incorporates several standard design features used in rocket turbopumps to suppress rotating cavitation. The mechanism is characterized based on a combination of two-phase numerical simulations and inducer experiments. Experimental measurements demonstrate a supersynchronous rotating cavity in the periphery of the inducer inlet at frequencies between 1.2 and 1.6 times rotor frequency and a synchronous 2nd spatial harmonic pattern associated with alternate blade cavitation. The analysis indicates a causal link between alternate blade cavitation and rotating cavitation, with a distinct cut-on cut-off behavior. Numerical calculations and high-speed videos elucidate the mechanism of breakdown of alternate blade cavitation and the formation of rotating cavitation. The present work suggests that rotating cavitation is caused by the coupling of the cavities on adjacent blades during alternate blade cavitation. Due to the nearly tangential flow, the vortex lines from one of the non-cavitating blades wrap around the blade leading edge of the adjacent blade, which yields a drop in static pressure and cavity formation. The tip vortex cavity interaction with the leading edge of the blade leads to sheet cavity breakdown with periodic growth and collapse of cavities, creating the apparent super-synchronous rotation of the cavitating region.United States. National Aeronautics and Space Administration (NASA Marshall Space Flight Center

Numerical test of the damping time of layer-by-layer growth on stochastic models

We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.Comment: 4 pages, source LaTeX file and 5 PS figure

Pediatric Phantom Dosimetry of Kodak 9000 Cone-beam Computed Tomography

Purpose: The purpose of the study was to evaluate the radiation dose of the Kodak 9000 cone-beam computed tomography (CBCT) device for different anatomical areas using a pediatric phantom. Methods: Absorbed doses resulting from maxillary and mandibular region three by five cm CBCT volumes of an anthropomorphic 10-year-old child phantom were acquired using optical stimulated dosimetry. Equivalent doses were calculated for radiosensitive tissues in the head and neck area, and effective dose for maxillary and mandibular examinations were calculated following the 2007 recommendations of the International Commission on Radiological Protection (ICRP). Results: Of the mandibular scans, the salivary glands had the highest equivalent dose (1,598 microsieverts [μSv]), followed by oral mucosa (1,263 μSv), extrathoracic airway (pharynx, larynx, and trachea; 859 μSv), and thyroid gland (578 μSv). For the maxilla, the salivary glands had the highest equivalent dose (1,847 μSv), followed closely by oral mucosa (1,673 μSv), followed by the extrathoracic airway (pharynx, larynx, and trachea; 1,011 μSv) and lens of the eye (202 μSv). Conclusion: Compared to previous research of the Kodak 9000, completed with the adult phantom, a child receives one to three times more radiation for mandibular scans and two to 10 times more radiation for maxillary scans

Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

Cilia at the node of mouse embryos sense fluid flow for left-right determination via Pkd2

Unidirectional fluid flow plays an essential role in the breaking of left-right (L-R) symmetry in mouse embryos, but it has remained unclear how the flow is sensed by the embryo. We report that the Ca2+ channel Polycystin-2 (Pkd2) is required specifically in the perinodal crown cells for sensing the nodal flow. Examination of mutant forms of Pkd2 shows that the ciliary localization of Pkd2 is essential for correct L-R patterning. Whereas Kif3a mutant embryos, which lack all cilia, failed to respond to an artificial flow, restoration of primary cilia in crown cells rescued the response to the flow. Our results thus suggest that nodal flow is sensed in a manner dependent on Pkd2 by the cilia of crown cells located at the edge of the node.CREST of the Japan Science and Technology Corporation; NIH [P30 DK090744]; Human Frontier Science Program [ST00246/2003C]; Deutsche Forschungsgemeinschaft [PE 853/2]; Japan Society for the Promotion of Science; American Heart Association [R10682]info:eu-repo/semantics/publishedVersio

In vivo cell-autonomous transcriptional abnormalities revealed in mice expressing mutant huntingtin in striatal but not cortical neurons

Huntington's disease (HD), caused by a CAG repeat expansion in the huntingtin (HTT) gene, is characterized by abnormal protein aggregates and motor and cognitive dysfunction. Htt protein is ubiquitously expressed, but the striatal medium spiny neuron (MSN) is most susceptible to dysfunction and death. Abnormal gene expression represents a core pathogenic feature of HD, but the relative roles of cell-autonomous and non-cell-autonomous effects on transcription remain unclear. To determine the extent of cell-autonomous dysregulation in the striatum in vivo, we examined genome-wide RNA expression in symptomatic D9-N171-98Q (a.k.a. DE5) transgenic mice in which the forebrain expression of the first 171 amino acids of human Htt with a 98Q repeat expansion is limited to MSNs. Microarray data generated from these mice were compared with those generated on the identical array platform from a pan-neuronal HD mouse model, R6/2, carrying two different CAG repeat lengths, and a relatively high degree of overlap of changes in gene expression was revealed. We further focused on known canonical pathways associated with excitotoxicity, oxidative stress, mitochondrial dysfunction, dopamine signaling and trophic support. While genes related to excitotoxicity, dopamine signaling and trophic support were altered in both DE5 and R6/2 mice, which may be either cell autonomous or non-cell autonomous, genes related to mitochondrial dysfunction, oxidative stress and the peroxisome proliferator-activated receptor are primarily affected in DE5 transgenic mice, indicating cell-autonomous mechanisms. Overall, HD-induced dysregulation of the striatal transcriptome can be largely attributed to intrinsic effects of mutant Htt, in the absence of expression in cortical neuron

Random Walks for Spike-Timing Dependent Plasticity

Random walk methods are used to calculate the moments of negative image equilibrium distributions in synaptic weight dynamics governed by spike-timing dependent plasticity (STDP). The neural architecture of the model is based on the electrosensory lateral line lobe (ELL) of mormyrid electric fish, which forms a negative image of the reafferent signal from the fish's own electric discharge to optimize detection of sensory electric fields. Of particular behavioral importance to the fish is the variance of the equilibrium postsynaptic potential in the presence of noise, which is determined by the variance of the equilibrium weight distribution. Recurrence relations are derived for the moments of the equilibrium weight distribution, for arbitrary postsynaptic potential functions and arbitrary learning rules. For the case of homogeneous network parameters, explicit closed form solutions are developed for the covariances of the synaptic weight and postsynaptic potential distributions.Comment: 18 pages, 8 figures, 15 subfigures; uses revtex4, subfigure, amsmat