Four-vortex motion around a circular cylinder

The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized experimentally by placing a splitter plate in the center plane---, it is found that there is a family of linearly stable equilibria for same-signed vortex pairs. The nonlinear dynamics in the symmetric subspace is investigated and several types of orbits are presented. The analysis reported here provides new insights and reveals novel features of this four-vortex system, such as the fact that there is no equilibrium for two pairs of vortices of opposite signs on the opposite sides of the cylinder. (It is argued that such equilibria might exist for vortex flows past a cylinder confined in a channel.) In addition, a new family of opposite-signed equilibria on the normal line is reported. The stability analysis for antisymmetric perturbations is also carried out and it shows that all equilibria are unstable in this case.Comment: 27 pages, 13 figures, to be published in Physics of Fluid

Radio Emission from the Composite Supernova Remnant G326.3-1.8 (MSH15-56)

High resolution radio observations of the composite supernova remnant (SNR) G326.3-1.8 or MSH 15-56 with the Australia Telescope Compact Array show details of both the shell and the bright plerion which is offset about 1/3 of the distance from the center of the SNR to the shell. The shell appears to be composed of thin filaments, typical of older shell SNRs. The central part of the elongated plerion is composed of a bundle of parallel ridges which bulge out at the ends and form a distinct ring structure on the northwestern end. The magnetic field with a strength of order 45 microGauss, is directed along the axis of the ridges but circles around the northwestern ring. This plerion is large and bright in the radio but is not detected in x-ray or optical wavelengths. There is, however, a faint hard x-ray feature closer to the shell outside the plerion. Perhaps if the supernova explosion left a rapidly moving magnetar with large energy input but initially rapid decay of both relativistic particles and magnetic field, the observed differences with wavelength could be explained.Comment: 15 pages, 10 figures, accepted by Ap

IC 4406: a radio-infrared view

IC 4406 is a large (about 100'' x 30'') southern bipolar planetary nebula, composed of two elongated lobes extending from a bright central region, where there is evidence for the presence of a large torus of gas and dust. We show new observations of this source performed with IRAC (Spitzer Space Telescope) and the Australia Telescope Compact Array. The radio maps show that the flux from the ionized gas is concentrated in the bright central region and originates in a clumpy structure previously observed in H_alpha, while in the infrared images filaments and clumps can be seen in the extended nebular envelope, the central region showing toroidal emission. Modeling of the infrared emission leads to the conclusion that several dust components are present in the nebula.Comment: 22 pages, 7 figures, accepted for publication in The Astrophysical Journal; v.2 has changes in both figures and content; preprint forma

Fluid Mechanical and Electrical Fluctuation Forces in Colloids

Fluctuations in fluid velocity and fluctuations in electric fields may both give rise to forces acting on small particles in colloidal suspensions. Such forces in part determine the thermodynamic stability of the colloid. At the classical statistical thermodynamic level, the fluid velocity and electric field contributions to the forces are comparable in magnitude. When quantum fluctuation effects are taken into account, the electric fluctuation induced van der Waals forces dominate those induced by purely fluid mechanical motions. The physical principles are applied in detail for the case of colloidal particle attraction to the walls of the suspension container and more briefly for the case of forces between colloidal particles.Comment: ReVTeX format, one *.eps figur

VLA Observations of the "Eye of the Tornado"- the High Velocity \HII Region G357.63-0.06

The unusual supernova remnant candidate G357.7-0.1 and the compact source G357.63-0.06 have been observed with the Very Large Array at 1.4 and 8.3 GHz. The H92$\alpha$ line (8.3 GHz) was detected from the compact source with a surprising velocity of about -210 km/s indicating that this source is an \HII region, is most likely located at the Galactic center, and is unrelated to the SNR. The \HI absorption line (1.4 GHz) data toward these sources supports this picture and suggests that G357.7-0.1 lies farther away than the Galactic center.Comment: Latex, 14 pages including 4 figures. Accepted to A

Nonlinear Band Structure in Bose Einstein Condensates: The Nonlinear Schr\"odinger Equation with a Kronig-Penney Potential

All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one dimensional lattice of impurities are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schr\"odinger, or Gross-Pitaevskii, equation for both repulsive and attractive condensates. The appearance of swallowtails in the bands is examined and interpreted in terms of the condensates superfluid properties. The nonlinear stability properties of the Bloch states are described and the stable regions of the bands and swallowtails are mapped out. We find that the Kronig-Penney potential has the same properties as a sinusoidal potential; Bose-Einstein condensates are trapped in sinusoidal optical lattices. The Kronig-Penney potential has the advantage of being analytically tractable, unlike the sinusoidal potential, and, therefore, serves as a good model for experimental phenomena.Comment: Version 2. Fixed typos, added referenc

Impact of birth weight and gender on early postnatal hypothalamic energy balance regulatory gene expression in the young lamb

Peer reviewedPreprin

The functional integral with unconditional Wiener measure for anharmonic oscillator

In this article we propose the calculation of the unconditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. In such a case we can profit from the representation of the integral in question by the parabolic cylinder functions. We show that in such a case the series expansions are uniformly convergent and we find recurrence relations for the Wiener functional integral in the $N$ - dimensional approximation. In continuum limit we find that the generalized Gelfand - Yaglom differential equation with solution yields the desired functional integral (similarly as the standard Gelfand - Yaglom differential equation yields the functional integral for linear harmonic oscillator).Comment: Source file which we sent to journa