Polarization of the Crab Nebula with disordered magnetic components

In this paper, we present an expanding disc model to derive polarization properties of the Crab nebula. The distribution function of the plasma and the energy density of the magnetic field are prescribed as function of the distance from the pulsar by using the model by Kennel and Coroniti (1984) with $\sigma = 0.003$, where $\sigma$ is the ratio of Poynting flux to the kinetic energy flux in the bulk motion just before the termination shock. Unlike previous models, we introduce disordered magnetic field, which is parameterized by the fractional energy density of the disordered component. Flow dynamics is not solved. The mean field is toroidal. Averaged polarization degree over the disc is obtained as a function of inclination angle and fractional energy density of the disordered magnetic field. It is found for the Crab that the disordered component has about 60 percent of the magnetic field energy. This value is also supported by the facts that the disc appears not `lip-shape' but as `rings' in the intensity map as was observed, and that the highest polarization degree of $\sim 40$ percent is reproduced for rings, being consistent with the observation. We suggest that because the disordered field contributes rather pressure than tension, the pinch force may be over-estimated in previous relativistic magnetohydrodynamic simulations. Disruption of the toroidal magnetic field with alternating direction, which is proposed by Lyubarski (2003), may actually takes place. The relativistic flow speed, which is indicated by the front-back contrast, can be detected in asymmetry in distributions of the position angle and depolarization.Comment: 7 pages, 8 figures, accepted for publication in MNRA

Toda Hierarchy with Indefinite Metric

We consider a generalization of the full symmetric Toda hierarchy where the matrix $\tilde {L}$ of the Lax pair is given by $\tilde {L}=LS$, with a full symmetric matrix $L$ and a nondegenerate diagonal matrix $S$. The key feature of the hierarchy is that the inverse scattering data includes a class of noncompact groups of matrices, such as $O(p,q)$. We give an explicit formula for the solution to the initial value problem of this hierarchy. The formula is obtained by generalizing the orthogonalization procedure of Szeg\"{o}, or the QR factorization method of Symes. The behaviors of the solutions are also studied. Generically, there are two types of solutions, having either sorting property or blowing up to infinity in finite time. The $\tau$-function structure for the tridiagonal hierarchy is also studied.Comment: 26 pages, LaTe

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Thesis--University of Tsukuba, D.Sc.(A), no. 238, 1984. 3. 2

Protogenin mediates cell adhesion for ingression and re-epithelialization of paraxial mesodermal cells

AbstractIn the avian embryo, precursor cells of the paraxial mesoderm that reside in the epiblast ingress through the primitive streak and migrate bilaterally in an anterolateral direction. Herein, we report on the roles of Protogenin (PRTG), an immunoglobulin superfamily protein expressed on the surface of the ingressing and migrating cells that give rise to the paraxial mesoderm, in paraxial mesoderm development. An aggregation assay using L-cells showed that PRTG mediates homophilic cell adhesion. Overexpression of PRTG in the presumptive paraxial mesoderm delayed mesodermal cell migration due to augmented adhesiveness. In contrast, siRNA knockdown of PRTG impaired successive ingression of epiblast cells and disorganized the epithelial structure of the somites. These results suggest that PRTG mediates cell adhesion to regulate continuous ingression of cells giving rise to the paraxial mesodermal lineage, as well as tissue integrity

A strategy to predict the global warming gas from stock farming —Potential scaling law of the released methane from livestock—

This work examines a scaling approach to predict the amount of methane released from the daily activity of livestock on farms. The subject animals are ruminants, i.e. having rumen or a ruminant stomach, that generates methane through digestion processes via several microbial fermentation steps. The produced methane is mixed into their breathing and released into the atmosphere. Existing data on methane released from various kinds of ruminant livestock were correlated as a power function of an animal’s weight, with an exponent near 0.92. This value is larger than a value of 0.75 which was related to the general metabolism rates for various animals. These differences may be explained by structure differences of the digestive organs or, more precisely, the difference in the relative length of the small intestine against animal size. Smaller animals have relatively longer small intestines, suggesting that the digestive activity in their stomachs is relatively less-active with less methane production as compared to larger animals. Validity of these structurally-dependent hypothesis was examined and a scaling law is proposed. The derived scaling law can then be used to estimate the release of global warming gas from various kinds of livestock and help to consider reduction strategies to decrease this emitted methane

Scale model test to estimate thermal damage by fire in aircraft cargo

The Federal Aviation Administration (FAA) requires fire detectors to alarm within one minute of the start of a fire in cargo compartments of airplanes. To determine whether such alarm timing works, investigations of the thermal damage to ceilings and other structures during the early stage of a fire were accomplished to demonstrate compliance with these FAA regulations. The objective was to test the feasibility of predicting convective heat transfer in early stage of a cargo compartment fire by conducting reduced scale (lab scale) experiments. First, the scaling laws was derived and validated. Then, full-scale and half-scale experiments were performed with attention to the heat fluxes from the fires. Similarity between the scaled tests were verified by matching dimensionless fire power profiles. Comparisons between the two-scale results showed good agreement in dimensionless heat fluxes to the ceiling and the rear bulkhead, thereby pointing to the capability of scale modeling as an effective tool for the present purpose