Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 + y^2, multiplied by an analytic function P(z) of the single complex variable z= x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate wave function psi(x,y) has the form of a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function P(zeta), where zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of P(zeta) again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.Comment: 13 pages, 1 figur

Hydraulics of floods upstream of horseshoe canyons and waterfalls

Horseshoe waterfalls are ubiquitous in natural streams, bedrock canyons, and engineering structures. Nevertheless, water flow patterns upstream of horseshoe waterfalls are poorly known and likely differ from the better studied case of a one-dimensional linear step because of flow focusing into the horseshoe. This is a significant knowledge gap because the hydraulics at waterfalls controls sediment transport and bedrock incision, which can compromise the integrity of engineered structures and influence the evolution of river canyons on Earth and Mars. Here we develop new semiempirical theory for the spatial acceleration of water upstream of, and the cumulative discharge into, horseshoe canyons and waterfalls. To this end, we performed 110 numerical experiments by solving the 2-D depth-averaged shallow-water equations for a wide range of flood depths, widths and discharges, and canyon lengths, widths and bed gradients. We show that the upstream, normal flow Froude number is the dominant control on lateral flow focusing and acceleration into the canyon head and that focusing is limited when the flood width is small compared to a cross-stream backwater length scale. In addition, for sheet floods much wider than the canyon, flow focusing into the canyon head leads to reduced discharge (and drying in cases) across the canyon sidewalls, which is especially pronounced for canyons that are much longer than they are wide. Our results provide new expectations for morphodynamic feedbacks between floods and topography, and thus canyon formation

Coherent vibrations of submicron spherical gold shells in a photonic crystal

Coherent acoustic radial oscillations of thin spherical gold shells of submicron diameter excited by an ultrashort optical pulse are observed in the form of pronounced modulations of the transient reflectivity on a subnanosecond time scale. Strong acousto-optical coupling in a photonic crystal enhances the modulation of the transient reflectivity up to 4%. The frequency of these oscillations is demonstrated to be in good agreement with Lamb theory of free gold shells.Comment: Error in Eqs.2 and 3 corrected; Tabl. I corrected; Fig.1 revised; a model that explains the dependence of the oscillation amplitude of the transient reflectivity with wavelength adde

Spatiotemporally Localized Multidimensional Solitons in Self-Induced Transparency Media

"Light bullets" are multi-dimensional solitons which are localized in both space and time. We show that such solitons exist in two- and three-dimensional self-induced-transparency media and that they are fully stable. Our approximate analytical calculation, backed and verified by direct numerical simulations, yields the multi-dimensional generalization of the one-dimensional Sine-Gordon soliton.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let

Optical and X-ray Observations of the Afterglow to XRF030723

The X-ray-flash XRF030723 was detected by the HETE satellite and rapidly disseminated, allowing for an optical transient to be detected ~1 day after the burst. We discuss observations in the optical with Magellan, which confirmed the fade of the optical transient. In a 2-epoch ToO observation with Chandra, we discovered a fading X-ray source spatially coincident with the optical transient. We present spectral fits to the X-ray data. We also discuss the possibility that the source underwent a rebrightening in the X-rays, as was observed in the optical. We find that the significance of a possible rebrightening is very low (~1 sigma).Comment: 4 pages, 2 figures, to appear in Santa Fe GRB Conference Proceedings, 200

Coronal hole boundaries at small scales: IV. SOT view Magnetic field properties of small-scale transient brightenings in coronal holes

We study the magnetic properties of small-scale transients in coronal hole. We found all brightening events are associated with bipolar regions and caused by magnetic flux emergence followed by cancellation with the pre-existing and newly emerging magnetic flux. In the coronal hole, 19 of 22 events have a single stable polarity which does not change its position in time. In eleven cases this is the dominant polarity. The dominant flux of the coronal hole form the largest concentration of magnetic flux in terms of size while the opposite polarity is distributed in small concentrations. In the coronal hole the number of magnetic elements of the dominant polarity is four times higher than the non-dominant one. The supergranulation configuration appears to preserve its general shape during approximately nine hours of observations although the large concentrations in the network did evolve and were slightly displaced, and their strength either increased or decreased. The emission fluctuations seen in the X-ray bright points are associated with reoccurring magnetic cancellation in the footpoints. Unique observations of an X-ray jet reveal similar magnetic behaviour in the footpoints, i.e. cancellation of the opposite polarity magnetic flux. We found that the magnetic flux cancellation rate during the jet is much higher than in bright points. Not all magnetic cancellations result in an X-ray enhancement, suggesting that there is a threshold of the amount of magnetic flux involved in a cancellation above which brightening would occur at X-ray temperatures. Our study demonstrates that the magnetic flux in coronal holes is continuously recycled through magnetic reconnection which is responsible for the formation of numerous small-scale transient events. The open magnetic flux forming the coronal-hole phenomenon is largely involved in these transient features.Comment: 19 pages, 18 figures, A&A in pres

Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions

Viscous fluid dynamical calculations require no-slip boundary conditions. Numerical calculations of turbulence, as well as theoretical turbulence closure techniques, often depend upon a spectral decomposition of the flow fields. However, such calculations have been limited to two-dimensional situations. Here we present a method that yields orthogonal decompositions of incompressible, three-dimensional flow fields and apply it to periodic cylindrical and spherical no-slip boundaries.Comment: 16 pages, 2 three-part figure

Relativity and EPR Entanglement: Comments

Recent experiment by Zhinden et al (Phys. Rev {\bf A} 63 02111, 2001) purports to test compatibility between relativity and quantum mechanics in the classic EPR setting. We argue that relativity has no role in the EPR argument based solely on non-relativistic quantum formalism. It is suggested that this interesting experiment may have significance to address fundamental questions on quantum probability.Comment: 6 pages, no figure; Submitted to Phys. Rev.

Gamma-Ray Bursts as a Probe of the Very High Redshift Universe

We show that, if many GRBs are indeed produced by the collapse of massive stars, GRBs and their afterglows provide a powerful probe of the very high redshift (z > 5) universe.Comment: To appear in Proc. of the 5th Huntsville Gamma-Ray Burst Symposium, 5 pages, LaTe