Damage Due to Spot Cavitation on Hemisperical Cylindrical Body (Comparison Between Isolated Cavity and Parallel Cavities)

When the Reynolds number is larger than the critical value or laminar separation is eliminated by a trip installed on a hemispherical cylindrical body, attached spot cavitation is observed occasionally. It occurs at fixed place in the vicinity of the minimum mean pressure and grows into a triangular wedge. In the present investigation, isolated and parallel spot cavitation is artificially generated on the hemispherical body adn the behavior of the cavitation is observed by instantaneous photographs. The frequency of damaging blows in the range of the flow speed of 25 to 50 m/s is obtained by counting the number of damaged pits on an aluminum specimen. When spot cavitation occurs adjacently, the cavity become rather stable. The pitting rate at the maximum damage zone by the parallel spot cavitation is much smaller than that by the isolated spot cavitation. The total pitting rates at the maximum damage zone by the isolated and parallel spot cavitation vary roughly 5th power of the flow speed for the both cases

Physical Properties of UDF12 Galaxies in Cosmological simulations

We have performed a large cosmological hydrodynamics simulation tailored to the deep survey with the Hubble Space Telescope made in 2012, the so-called UDF12 campaign. After making a light-cone output, we have applied the same color selection criteria as the UDF12 campaign to select galaxies from our simulation, and then, have examined the physical properties of them as a proxy of the real observed UDF12 galaxies at $z > 7$. As a result, we find that the halo mass is almost linearly proportional to the observed ultraviolet (UV) luminosity ($4 \times 10^{11}~{\rm M_{\odot}}$ at $M_{\rm UV} = -21$). The dust attenuation and UV slope $\beta$ well correlates with the observed UV luminosity, which is consistent with observations quantitatively. The star formation rate (SFR) is also linearly proportional to the stellar mass and the specific SFR shows only a weak dependency on the mass. We also find an increasing star formation history with a time-scale of $\sim100$ Myr in the high-$z$ galaxies. An average metallicity weighted by the Lyman continuum luminosity reaches up to $>0.1$ Solar even at $z \sim 10$, suggesting a rapid metal enrichment. We also expect $\geq 0.1$ mJy at 350 GHz of the dust thermal emission from the galaxies with $H_{160} \leq 27$, which can be detectable with the Atacama Large Milimetre-submilimetre Array. The galaxies selected by the UDF12 survey contribute to only $52--12\%$ of the cosmic SFR density from $z \sim 7$ to $z \sim 10$, respectively. The James Webb Space Telescope will push the detection fraction up to $77--72\%$.Comment: re-Submitted to MNRAS; 16 pages; 14 figures; 1 tables

Quantization of the crossing number of a knot diagram

We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected plane curve, we consider oriented knot diagrams obtained from the plane curve as states to take the sum of the warping crossing polynomials for all the states for the plane curve. As an application, we show that every closed transversely intersected plane curve with even crossing points has two independent canonical orientations and every based closed transversely intersected plane curve with odd crossing points has two independent canonical orientations.Comment: 14 pages, 14 figure

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