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An experimental and numerical smoothed particle hydrodynamics (SPH) analysis was performed for the convective flow arising from a horizontal, thin cylindrical heat source enclosed in a glycerin-filled, slender enclosure at low Rayleigh numbers ($1.18\leq {\rm Ra}\leq 242$). Both the experiments and the SPH calculations were performed for positive ($0.1\leq\Delta T\leq 10$ K) and negative ($-10\leq\Delta T\leq -0.1$ K) temperature differences between the source and the surrounding fluid. In all cases a pair of steady, counter-rotating vortices is formed, accompanied by a plume of vertically ascending flow just above the source for $\Delta T>0$ and a vertically descending flow just below the source for $\Delta T<0$. The maximum flow velocities always occur within the ascending/descending plumes. The SPH predictions are found to match the experimental observations acceptably well with root-mean-square errors in the velocity profiles of the order of $\sim 10^{-5}$ m s$^{-1}$. The fact that the SPH method is able to reveal the detailed features of the flow phenomenon demonstrates the correctness of the approach., Comment: 24 pages, 13 figures

We construct smooth finite elements spaces on Powell-Sabin triangulations that form an exact sequence. The first space of the sequence coincides with the classical $C^1$ Powell-Sabin space, while the others form stable and divergence-free yielding pairs for the Stokes problem. We develop degrees of freedom for these spaces that induce projections that commute with the differential operators.

We present experimental evidence of metastable magnetic domains in cylindrical CoNi nanowires. Transverse (perpendicular) domains have been previously observed only in flat nanostrips. Here they are found together with more conventional vortex domains along the same cylindrical nanowire, denoting a bistable system with similar free energies. The surface and the inner magnetization distribution in both types of domains are analyzed by Photo-Emission Electron Microscopy (PEEM) with X-ray magnetic circular dichroism (XMCD) contrast, and hysteresis loop in individual nanowires are measured by Magneto-optical Kerr effect. These experimental data are understood and compared with complementary micromagnetic simulations. The transverse domain states are potentially more important for sensing and recording applications than commonly observed vortex domains since they create larger surface stray fields.

We present a hierarchical basis preconditioning strategy for the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation considering both simply and multiply connected geometries.To this end, we first consider the direct application of hierarchical basis preconditioners, developed for the Electric Field Integral Equation (EFIE), to the PMCHWT. It is notably found that, whereas for the EFIE a diagonal preconditioner can be used for obtaining the hierarchical basis scaling factors, this strategy is catastrophic in the case of the PMCHWT since it leads to a severly ill-conditioned PMCHWT system in the case of multiply connected geometries. We then proceed to a theoretical analysis of the effect of hierarchical bases on the PMCHWT operator for which we obtain the correct scaling factors and a provably effective preconditioner for both low frequencies and mesh refinements. Numerical results will corroborate the theory and show the effectiveness of our approach.

We describe the performance of the Boolardy Engineering Test Array (BETA), the prototype for the Australian Square Kilometre Array Pathfinder telescope ASKAP. BETA is the first aperture synthesis radio telescope to use phased array feed technology, giving it the ability to electronically form up to nine dual-polarization beams. We report the methods developed for forming and measuring the beams, and the adaptations that have been made to the traditional calibration and imaging procedures in order to allow BETA to function as a multi-beam aperture synthesis telescope. We describe the commissioning of the instrument and present details of BETA's performance: sensitivity, beam characteristics, polarimetric properties and image quality. We summarise the astronomical science that it has produced and draw lessons from operating BETA that will be relevant to the commissioning and operation of the final ASKAP telescope., Comment: Accepted for publication in PASA

We report the discovery of a new 21-cm HI absorption system using commissioning data from the Boolardy Engineering Test Array of the Australian Square Kilometre Array Pathfinder (ASKAP). Using the 711.5 - 1015.5 MHz band of ASKAP we were able to conduct a blind search for the 21-cm line in a continuous redshift range between $z = 0.4$ and 1.0, which has, until now, remained largely unexplored. The absorption line is detected at $z = 0.44$ towards the GHz-peaked spectrum radio source PKS B1740$-$517 and demonstrates ASKAP's excellent capability for performing a future wide-field survey for HI absorption at these redshifts. Optical spectroscopy and imaging using the Gemini-South telescope indicates that the HI gas is intrinsic to the host galaxy of the radio source. The narrow OIII emission lines show clear double-peaked structure, indicating either large-scale outflow or rotation of the ionized gas. Archival data from the \emph{XMM-Newton} satellite exhibit an absorbed X-ray spectrum that is consistent with a high column density obscuring medium around the active galactic nucleus. The HI absorption profile is complex, with four distinct components ranging in width from 5 to 300 km s$^{-1}$ and fractional depths from 0.2 to 20 per cent. In addition to systemic HI gas, in a circumnuclear disc or ring structure aligned with the radio jet, we find evidence for a possible broad outflow of neutral gas moving at a radial velocity of $v \sim 300$ km s$^{-1}$. We infer that the expanding young radio source ($t_{\rm age} \approx 2500$ yr) is cocooned within a dense medium and may be driving circumnuclear neutral gas in an outflow of $\sim$ 1 $\mathrm{M}_{\odot}$ yr$^{-1}$., Comment: 18 pages, 11 figures, accepted for publication in MNRAS

We investigate the long-term dynamics of spin textures prepared by cooling unmagnetized spinor gases of F=1 $^{87}$Rb to quantum degeneracy, observing domain coarsening and a strong dependence of the equilibration dynamics on the quadratic Zeeman shift $q$. For small values of $|q|$, the textures arrive at a configuration independent of the initial spin-state composition, characterized by large length-scale spin domains, and the establishment of easy-axis (negative $q$) or easy-plane (positive $q$) magnetic anisotropy. For larger $|q|$, equilibration is delayed as the spin-state composition of the degenerate spinor gas remains close to its initial value. These observations support the mean-field equilibrium phase diagram predicted for a ferromagnetic spinor Bose-Einstein condensate, but also illustrate that equilibration is achieved under a narrow range of experimental settings, making the F=1 $^{87}$Rb gas more suitable for studies of nonequilibrium quantum dynamics.

(abridged) We study the hydrodynamic evolution of a non-spherical core-collapse supernova in two spatial dimensions. We find that our model displays a strong tendency to expand toward the pole. We demonstrate that this expansion is a physical property of the low-mode, SASI instability. The SASI leaves behind a large lateral velocity gradient in the post shock layer which affects the evolution for minutes and hours later. This results in a prolate deformation of the ejecta and a fast advection of Ni-rich material from moderate latitudes to the polar regions. This effect might actually be responsible for the global asymmetry of the nickel lines in SN 1987A. The simulations demonstrate that significant radial and lateral motions in the post-shock region, produced by convective overturn and the SASI during the early explosion phase, contribute to the evolution for minutes and hours after shock revival. They lead to both later clump formation, and a significant prolate deformation of the ejecta which are observed even as late as one week after the explosion. As pointed out recently by Kjaer et al., such an ejecta morphology is in good agreement with the observational data of SN 1987A. Systematic future studies are needed to investigate how the SASI-induced late-time lateral expansion depends on the dominant mode of the SASI, and to which extent it is affected by the dimensionality of the simulations. The impact on and importance of the SASI for the distribution of iron group nuclei and the morphology of the young SNR argues for future three-dimensional explosion and post-explosion studies on singularity-free grids that cover the entire sphere. Given the results of our 2D resolution study, present 3D simulations must be regarded as underresolved, and their conclusions must be verified by a proper numerical convergence analysis in three dimensions., Comment: 16 pages, 20 figures, accepted for publication in Astronomy & Astrophysics

We report on the spin textures produced by cooling unmagnetized $^{87}$Rb F=1 spinor gases into the regime of quantum degeneracy. At low temperatures, magnetized textures form that break translational symmetry and display short-range periodic magnetic order characterized by one- or two-dimensional spatial modulations with wavelengths much smaller than the extent of the quasi-two-dimensional degenerate gas. Spin textures produced upon cooling spin mixtures with a non-zero initial magnetic quadrupole moment also show ferromagnetic order that, at low temperature, coexists with the spatially modulated structure., Comment: 6 pages, revised substantially following reviewer comments and further analysis

Dynamical instabilities due to spin-mixing collisions in a $^{87}$Rb F=1 spinor Bose-Einstein condensate are used as an amplifier of quantum spin fluctuations. We demonstrate the spectrum of this amplifier to be tunable, in quantitative agreement with mean-field calculations. We quantify the microscopic spin fluctuations of the initially paramagnetic condensate by applying this amplifier and measuring the resulting macroscopic magnetization. The magnitude of these fluctuations is consistent with predictions of a beyond-mean-field theory. The spinor-condensate-based spin amplifier is thus shown to be nearly quantum-limited at a gain as high as 30 dB.

Helical spin textures in a $^{87}$Rb F=1 spinor Bose-Einstein condensate are found to decay spontaneously toward a spatially modulated structure of spin domains. This evolution is ascribed to magnetic dipolar interactions that energetically favor the short-wavelength domains over the long-wavelength spin helix. This is confirmed by eliminating the dipolar interactions by a sequence of rf pulses and observing a suppression of the formation of the short-range domains. This study confirms the significance of magnetic dipole interactions in degenerate $^{87}$Rb F=1 spinor gases.

We demonstrate a precision magnetic microscope based on direct imaging of the Larmor precession of a $^{87}$Rb spinor Bose-Einstein condensate. This magnetometer attains a field sensitivity of 8.3 pT/Hz$^{1/2}$ over a measurement area of 120 $\mu$m$^2$, an improvement over the low-frequency field sensitivity of modern SQUID magnetometers. The corresponding atom shot-noise limited sensitivity is estimated to be 0.15 pT/Hz$^{1/2}$ for unity duty cycle measurement. The achieved phase sensitivity is close to the atom shot-noise limit suggesting possibilities of spatially resolved spin-squeezed magnetometry. This magnetometer marks a significant application of degenerate atomic gases to metrology.

Nonlinear magneto-optical Faraday rotation (NMOR) on the potassium D1 and D2 lines was used to study Zeeman relaxation rates in an antirelaxation paraffin-coated 3-cm diameter potassium vapor cell. Intrinsic Zeeman relaxation rates of $\gamma^{NMOR}/2\pi=2.0(6) {\rm Hz}$ were observed. The relatively small hyperfine intervals in potassium lead to significant differences in NMOR in potassium compared to rubidium and cesium. Using laser optical pumping, widths and frequency shifts were also determined for transitions between ground-state hyperfine sublevels of $^{39}$K atoms contained in the same paraffin-coated cell. The intrinsic hyperfine relaxation rate of $\gamma^{hf}_{expt}/2\pi = 10.6(7) $Hz and a shift of $-9.1(2) $Hz were observed. These results show that adiabatic relaxation gives only a small contribution to the overall hyperfine relaxation in the case of potassium, and the relaxation is dominated by other mechanisms similar to those observed in previous studies with rubidium., Comment: 8pages, 10 figures

We report on an experimental and theoretical study of the dynamic (ac) Stark effect on a forbidden transition. A general framework for parameterizing and describing off-resonant ac-Stark shifts is presented. A model is developed to calculate spectral line shapes resulting from resonant excitation of atoms in an intense standing light-wave in the presence of off-resonant ac-Stark shifts. The model is used in the analysis and interpretation of a measurement of the ac-Stark shifts of the static-electric-field-induced \mbox{${\rm 6s^2}~ ^1{\rm S}_0~\to ~{\rm 5d6s}~ ^3{\rm D}_1\:$} transition at 408 nm in atomic Yb. The results are in agreement with estimates of the ac-Stark shift of the transition under the assumption that the shift is dominated by that of the ${\rm 6s^2 \:} ^1{\rm S}_0\:$ ground state. A detailed description of the experiment and analysis is presented. A bi-product of this work is an independent determination (from the saturation behavior of the 408-nm transition) of the Stark transition polarizability, which is found to be in agreement with our earlier measurement. This work is part of the ongoing effort aimed at a precision measurement of atomic parity-violation effects in Yb., Comment: 15 pages, 11 figs

The simple supersymmetric approach recently used by Dutt, Gangopadhyaya, and Sukhatme [Am. J. Phys. 65 400 (1997)] for spherical harmonics is generalized to Jacobi equation, including also the intermediate Gegenbauer case, Comment: 6 pages, LaTex