A Variational Principle for Dissipative Fluid Dynamics

In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.Comment: 15 page

Clebsch Potentials in the Variational Principle for a Perfect Fluid

Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in the latter description. We give a simple explanation for these fields; they are introduced to fix both ends of a pathline in the variational calculus. This restriction is imposed in the former description, and should be imposed in the latter description. It is also shown that we can derive a canonical Hamiltonian formulation for a perfect fluid by regarding the velocity field as the input in the framework of control theory.Comment: 15 page

Failure Mechanism of True 2D Granular Flows

Most previous experimental investigations of two-dimensional (2D) granular column collapses have been conducted using three-dimensional (3D) granular materials in narrow horizontal channels (i.e., quasi-2D condition). Our recent research on 2D granular column collapses by using 2D granular materials (i.e., aluminum rods) has revealed results that differ markedly from those reported in the literature. We assume a 2D column with an initial height of h0 and initial width of d0, a defined as their ratio (a =h0/d0), a final height of h , and maximum run-out distance of d . The experimental data suggest that for the low a regime (a <0.65) the ratio of the final height to initial height is 1. However, for the high a regime (a >0.65), the ratio of a to (d-d0)/d0, h0/h , or d/d0 is expressed by power-law relations. In particular, the following power-function ratios (h0/h=1.42a^2/3 and d/d0=4.30a^0.72) are proposed for every a >0.65. In contrast, the ratio (d-d0)/d0=3.25a^0.96 only holds for 0.65< a1.5. In addition, the influence of ground contact surfaces (hard or soft beds) on the final run-out distance and destruction zone of the granular column under true 2D conditions is investigated.Comment: 8 page

Earthquake Induced Slope Failure Simulation by SPH

Majority of slope stability, slope displacement and soil liquefaction analyses subjected to earthquake loading condition employed the finite element method (FEM) as the standard numerical tool. However, mechanism of soil failure in such condition often involved extremely large deformation and failure behaviors, which were unable to be modeled by FEM since this method was suffered from the grid distortion. In an attempt to overcome this limitation, we present herein our first attempt to extend the smoothed particle hydrodynamics (SPH) method to analyze slope failure behavior due to seismic shaking. For the sake of simplicity, effect of pore-water pressure was not taken into consideration. The numerical framework was then applied to simulate the failure behavior of a slope subjected to a seismic loading. Experimental model was also conducted to verify the numerical performance. It is shown that SPH can simulate fairly well the slope failure behavior in the model test, especially in prediction of the failure surface. The paper suggests that SPH should be considered as a powerful alternative for computation of geomaterials subjected to earthquake loading conditions

A New Galactic Extinction Map of the Cygnus Region

We have made a Galactic extinction map of the Cygnus region with 5' spatial resolution. The selected area is 80^\circ to 90^\circ in the Galactic longitude and -4^\circ to 8^\circ in the Galactic latitude. The intensity at 140 \mum is derived from the intensities at 60 and 100 \mum of the IRAS data using the tight correlation between 60, 100, and 140 \mum found in the Galactic plane. The dust temperature and optical depth are calculated with 5' resolution from the 140 and 100 \mum intensity, and Av is calculated from the optical depth. In the selected area, the mean dust temperature is 17 K, the minimum is 16 K, and the maximum is 30 K. The mean Av is 6.5 mag, the minimum is 0.5 mag, and the maximum is 11 mag. The dust temperature distribution shows significant spatial variation on smaller scales down to 5'. Because the present study can trace the 5'-scale spatial variation of the extinction, it has an advantage over the previous studies, such as the one by Schlegel, Finkbeiner, & Davis, who used the COBE/DIRBE data to derive the dust temperature distribution with a spatial resolution of 1^\circ. The difference of Av between our map and Schlegel et al.'s is \pm 3 mag. A new extinction map of the entire sky can be produced by applying the present method.Comment: 27 pages, 14 figures, accepted for publication in Ap

Mevastatin reduces cartilage degradation in rabbit experimental osteoarthritis through inhibition of synovial inflammation

SummaryObjectiveTo examine the therapeutic efficacy of an HMG-CoA reductase inhibitor (statin) in rabbit osteoarthritis (OA) in vitro and in vivo.MethodsIn the presence or absence of mevastatin, rabbit chondrocytes and synoviocytes were incubated with Interleukin-1β (IL-1β), and analyzed by biochemical methods. Thirty-two mature rabbits that underwent bilateral anterior cruciate ligament transaction (ACLT) received six consecutive weekly intra-articular injections of mevastatin at three different concentrations or a control solution. All animals were sacrificed 6 weeks after ACLT, and the knee joints were assessed by morphological, histological, immunohistochemical, and biochemical methods.ResultsMevastatin inhibited IL-1β stimulation of gene expression of monocyte chemoattractant protein-1 (MCP-1) and matrix-metalloproteinases 3 (MMP-3), in synoviocytes but not chondrocytes. The levels of MCP-1 and MMP-3 productions in synoviocytes were significantly reduced by statin-treatment. In rabbit with OA, intra-articular injection of mevastatin significantly reduced cartilage degradation, as assessed by morphological and histological examinations. Synovial tissues of knees treated with mevastatin showed less severe inflammatory responses with reduced thickness of synovial cell lining and less infiltration of subsynovial CD68+monocyte lineage cells compared to untreated control knees. Relative mRNA expressions of MCP-1, IL-1β, MMP-3, and MMP-13 were reduced in synovial tissues, but not articular cartilage, of knees treated with mevastatin compared with untreated control knees.ConclusionDuring the development of experimental OA, intra-articular administration of HMG-CoA reductase inhibitor (statin) reduces inflammatory cell infiltration and matrix-degrading enzyme expression, thus limiting cartilage degradation

Deep Thermal Infrared Imaging of HR 8799 bcde: New Atmospheric Constraints and Limits on a Fifth Planet

We present new $L^\prime$ (3.8 $\mu m$) and Br-$\alpha$ (4.05 $\mu m$) data and reprocessed archival $L^\prime$ data for the young, planet-hosting star HR 8799 obtained with Keck/NIRC2, VLT/NaCo and Subaru/IRCS. We detect all four HR 8799 planets in each dataset at a moderate to high signal-to-noise (SNR $\gtrsim$ 6-15). We fail to identify a fifth planet, "HR 8799 f", at $r$ $<$ 15 $AU$ at a 5-$\sigma$ confidence level: one suggestive, marginally significant residual at 0.2" is most likely a PSF artifact. Assuming companion ages of 30 $Myr$ and the Baraffe (Spiegel \& Burrows) planet cooling models, we rule out an HR 8799 f with mass of 5 $M_{J}$ (7 $M_{J}$), 7 $M_{J}$ (10 $M_{J}$), and 12 $M_{J}$ (13 $M_{J}$) at $r_{proj}$ $\sim$ 12 $AU$, 9 $AU$, and 5 $AU$, respectively. All four HR 8799 planets have red early T dwarf-like $L^\prime$ - [4.05] colors, suggesting that their SEDs peak in between the $L^\prime$ and $M^\prime$ broadband filters. We find no statistically significant difference in HR 8799 cde's colors. Atmosphere models assuming thick, patchy clouds appear to better match HR 8799 bcde's photometry than models assuming a uniform cloud layer. While non-equilibrium carbon chemistry is required to explain HR 8799 bc's photometry/spectra, evidence for it from HR 8799 de's photometry is weaker. Future, deep IR spectroscopy/spectrophotometry with the Gemini Planet Imager, SCExAO/CHARIS, and other facilities may clarify whether the planets are chemically similar or heterogeneous.Comment: 18 pages, 6 Tables, and 9 Figures. Fig. 1a is the key figure. Accepted for publication in Ap