Digital program for dynamics of non-rigid gravity gradient satellites

Digital program for dynamics of nonrigid gravity gradient satellite

Surveying the solar system by measuring angles and times: from the solar density to the gravitational constant

A surprisingly large amount of information on our solar system can be gained from simple measurements of the apparent angular diameters of the sun and the moon. This information includes the average density of the sun, the distance between earth and moon, the radius of the moon, and the gravitational constant. In this note it is described how these and other quantities can be obtained by simple earthbound measurements of angles and times only, without using any explicit information on distances between celestial bodies. The pedagogical and historical aspects of these results are also discussed briefly.Comment: 12 pges, one figur

Viscous evolution of point vortex equilibria: The collinear state

When point vortex equilibria of the 2D Euler equations are used as initial conditions for the corre- sponding Navier-Stokes equations (viscous), typically an interesting dynamical process unfolds at short and intermediate time scales, before the long time single peaked, self-similar Oseen vortex state dom- inates. In this paper, we describe the viscous evolution of a collinear three vortex structure that cor- responds to an inviscid point vortex fixed equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that the system immediately begins to rotate unsteadily, a mechanism we attribute to a 'viscously induced' instability. We then examine in detail the qualitative and quantitative evolution of the system as it evolves toward the long-time asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations that occur both in a fixed reference frame, and in an appropriately chosen rotating reference frame. The evolution of passive particles in this viscously evolving flow is shown and interpreted in relation to these evolving streamline patterns.Comment: 17 pages, 15 figure

Remarkable symmetries in the Milky Way disk's magnetic field

Using a new, expanded compilation of extragalactic source Faraday rotation measures (RM) we investigate the broad underlying magnetic structure of the Galactic disk at latitudes $|b|$ $\lesssim 15^{\circ}$ over all longitudes $l$, where our total number of RM's in this low-latitude range of the Galactic sky is comparable to those in the combined Canadian Galactic Plane Survey(CGPS) at $|b| < 4^{\circ}$ and the Southern Galactic Plane (SGPS) $|b| < 1.5^{\circ}$ survey. We report newly revealed, remarkably coherent patterns of RM at $|b|$ $\lesssim 15^{\circ}$ from $l \sim 270^{\circ}$ to $\sim 90^\circ$ and RM($l$) features of unprecedented clarity that replicate in $l$ with opposite sign on opposite sides of the Galactic center. They confirm a highly patterned bisymmetric field structure toward the inner disc, an axisymmetic pattern toward the outer disc, and a very close coupling between the CGPS/SGPS RM's at $|b| \lesssim 3^{\circ}$ ("mid-plane") and our new RM's up to $|b| \sim 15^{\circ}$ ("near-plane"). Our analysis also shows the approximate $z$-height -- the vertical height of the coherent component of the disc field above the Galactic disc's mid-plane -- to be $\sim 1.5$kpc out to $\sim 6$ kpc from the Sun. This identifies the approximate height of the transition layer to the halo field structure. We find no RM sign change across the plane within $|b| \sim 15^{\circ}$ in any longitude range. The prevailing {\it disc} field pattern, and its striking degree of large scale ordering confirm that our side of the Milky Way has a very organized underlying magnetic structure, for which the inward spiral pitch angle is $5.5^{\circ}\, \pm 1^{\circ}$ at all $|b|$ up to $\sim 12^{\circ}$ in the inner semicircle of Galactic longitudes. It decreases to $\sim 0^{\circ}$ toward the anticentre.Comment: 7 pages, 5 figures, Version 3. Accepted 2011 for publication in Publications of the Astronomical Society of Australia(PASA

Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics

Starting from a system of $N$ radial Schr\"odinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N \times N$ exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on $N (N+1)/2$ unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\times 2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has 0, 1 or 2 bound states, and 0 or 1 resonance; the potential parameters are explicitly expressed in terms of its bound-state energies, of its resonance energy and width, or of the open-channel scattering length, which solves schematic inverse problems. As a first physical application, exactly-solvable $2\times 2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interplays with a bound or virtual state close to threshold, which results in a large background scattering length.Comment: 19 pages, 15 figure

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

High Resolution X-Ray Imaging of the Center of IC342

We presented the result of a high resolution (FWHM~0.5'') 12 ks Chandra HRC-I observation of the starburst galaxy IC342 taken on 2 April 2006. We identified 23 X-ray sources within the central 30' x 30' region of IC342. Our HRC-I observation resolved the historical Ultraluminous X-ray sources (ULX), X3, near the nucleus into 2 sources, namely C12 and C13, for the first time. The brighter source C12, with L(0.08-10keV)=(6.66\pm0.45)\times10^{38}ergs^-1, was spatially extended (~82 pc x 127 pc). From the astrometric registration of the X-ray image, C12 was at R.A.=03h:46m:48.43s, decl.=+68d05m47.45s, and was closer to the nucleus than C13. Thus we concluded that source was not an ULX and must instead be associated with the nucleus. The fainter source C13, with L(0.08-10keV)=(5.1\pm1.4) x 10^{37}ergs^-1 was consistent with a point source and located $6.51'' at P.A. 240 degree of C12. We also analyzed astrometrically corrected optical Hubble Space Telescope and radio Very Large Array images, a comparison with the X-ray image showed similarities in their morphologies. Regions of star formation within the central region of IC342 were clearly visible in HST H alpha image and this was the region where 3 optical star clusters and correspondingly our detected X-ray source C12 were observed. We found that a predicted X-ray emission from starburst was very close to the observed X-ray luminosity of C12, suggesting that nuclear X-ray emission in IC342 was dominated by starburst. Furthermore, we discussed the possibility of AGN in the nucleus of IC342. Although our data was not enough to give a firm existence of an AGN, it could not be discarded.Comment: 29 page, 8 figures, accepted by Ap