Vortex stabilization in a small rotating asymmetric Bose-Einstein condensate

We use a variational method to investigate the ground-state phase diagram of a small, asymmetric Bose-Einstein condensate with respect to the dimensionless interparticle interaction strength $\gamma$ and the applied external rotation speed $\Omega$. For a given $\gamma$, the transition lines between no-vortex and vortex states are shifted toward higher $\Omega$ relative to those for the symmetric case. We also find a re-entrant behavior, where the number of vortex cores can decrease for large $\Omega$. In addition, stabilizing a vortex in a rotating asymmetric trap requires a minimum interaction strength. For a given asymmetry, the evolution of the variational parameters with increasing $\Omega$ shows two different types of transitions (sharp or continuous), depending on the strength of the interaction. We also investigate transitions to states with higher vorticity; the corresponding angular momentum increases continuously as a function of $\Omega$

Stability of rotating states in a weakly-interacting Bose-Einstein condensate

We investigate the lowest state of a rotating, weakly-interacting Bose-Einstein condensate trapped in a harmonic confining potential that is driven by an infinitesimally asymmetric perturbation. Although in an axially-symmetric confining potential the gas has an axially-symmetric single-particle density distribution, we show that in the presence of the small asymmetric perturbation its lowest state is the one given by the mean-field approximation, which is a broken-symmetric state. We also estimate the rate of relaxation of angular momentum when the gas is no longer driven by the asymmetric perturbation and identify two regimes of "slow" and "fast" relaxation. States of certain symmetry are found to be more robust.Comment: 6 pages, RevTe

Stability of small amplitude normal modes of a Bose-Einstein condensate with a singly quantized vortex confined in an optical lattice

We study the dynamics of a BEC with a singly quantized vortex, placed in the combined potential of a 1-D (2-D) optical lattice and an axi-symmetric harmonic trap. A time-dependent variational Lagrangian analysis shows that an optical lattice helps to stabilize the vortex which in absence of the optical lattice is unstable. We find that the normal modes are stable only if the depth of the optical potential is more than a certain critical value. This critical value of the optical potential depends on the interaction parameter.In general higher the interaction parameter,lower the value of the optical potential required to stabilize the vortex. The BEC with the singly quantized vortex is found to be relatively more unstable in a 2-D optical lattice compared to a 1-D optical lattice.Comment: Revised version with 11 pages including 1 figur

The Ellipticity and Orientation of Clusters of Galaxies from N-Body Experiments

In this study we use simulations of 128$^3$ particles to study the ellipticity and orientation of clusters of galaxies in N-body simulations of differing power-law initial spectra (P(k) \propto k^n ,n = +1, 0, -1, -2$), and density parameters ($\Omega_0 = 0.2$to 1.0). Furthermore, unlike most theoretical studies we mimic most observers by removing all particles which lie at distances greater than 2 1/h Mpc from the cluster center of mass. We computed the axial ratio and the principal axes using the inertia tensor of each cluster. The mean ellipticity of clusters increases strongly with increasing$n$. We also find that clusters tend to become more spherical at smaller radii. We compared the orientation of a cluster to the orientation of neighboring clusters as a function of distance (correlation). In addition, we considered whether a cluster's major axis tends to lie along the line connecting it to a neighboring cluster, as a function of distance (alignment). Both alignments and correlations were computed in three dimensions and in projection to mimic observational surveys. Our results show that significant alignments exist for all spectra at small separations ($D < 15 h^{-1}$Mpc) but drops off at larger distance in a strongly$n-$dependent way.Comment: 22 pages, requires aaspp4.sty, flushrt.sty, and epsf.sty Revised manuscript, accepted for publication in Ap

The Growth Response of Two Diatom Species to Atmospheric Dust from the Last Glacial Maximum

Relief of iron (Fe) limitation in the surface Southern Ocean has been suggested as one driver of the regular glacial-interglacial cycles in atmospheric carbon dioxide (CO2). The proposed cause is enhanced deposition of Fe-bearing atmospheric dust to the oceans during glacial intervals, with consequent effects on export production and the carbon cycle. However, understanding the role of enhanced atmospheric Fe supply in biogeochemical cycles is limited by knowledge of the fluxes and ‘bioavailability’ of atmospheric Fe during glacial intervals. Here, we assess the effect of Fe fertilization by dust, dry-extracted from the Last Glacial Maximum portion of the EPICA Dome C Antarctic ice core, on the Antarctic diatom species Eucampia antarctica and Proboscia inermis. Both species showed strong but differing reactions to dust addition. E. antarctica increased cell number (3880 vs. 786 cells mL-1), chlorophyll a (51 vs. 3.9 μg mL-1) and particulate organic carbon (POC; 1.68 vs. 0.28 μg mL-1) production in response to dust compared to controls. P. inermis did not increase cell number in response to dust, but chlorophyll a and POC per cell both strongly increased compared to controls (39 vs. 15 and 2.13 vs. 0.95 ng cell-1 respectively). The net result of both responses was a greater production of POC and chlorophyll a, as well as decreased Si:C and Si:N incorporation ratios within cells. However, E, antarctica decreased silicate uptake for the same nitrate and carbon uptake, while P. inermis increased carbon and nitrate uptake for the same silicate uptake. This suggests that nutrient utilization changes in response to Fe addition could be driven by different underlying mechanisms between different diatom species. Enhanced supply of atmospheric dust to the surface ocean during glacial intervals could therefore have driven nutrient-utilization changes which could permit greater carbon fixation for lower silica utilization. Additionally, both species responded more strongly to lower amounts of direct Fe chloride addition than they did to dust, suggesting that not all the Fe released from dust was in a bioavailable form available for uptake by diatoms

Analytical results for a trapped, weakly-interacting Bose-Einstein condensate under rotation

We examine the problem of a repulsive, weakly-interacting and harmonically trapped Bose-Einstein condensate under rotation. We derive a simple analytic expression for the energy incorporating the interactions when the angular momentum per particle is between zero and one and find that the interaction energy decreases linearly as a function of the angular momentum in agreement with previous numerical and limiting analytical studies.Comment: 3 pages, RevTe

Dynamics of a Vortex in a Trapped Bose-Einstein Condensate

We consider a large condensate in a rotating anisotropic harmonic trap. Using the method of matched asymptotic expansions, we derive the velocity of an element of vortex line as a function of the local gradient of the trap potential, the line curvature and the angular velocity of the trap rotation. This velocity yields small-amplitude normal modes of the vortex for 2D and 3D condensates. For an axisymmetric trap, the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In a 2D condensate, the planar normal modes are degenerate, and their superposition can result in helical traveling waves, which differs from a 3D condensate. Including the effects of trap rotation allows us to find the angular velocity that makes the vortex locally stable. For a cigar-shape condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable normal mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shape condensate than in a disc-shape one. Normal modes with imaginary frequencies can occur for a nonaxisymmetric condensate (in both 2D and 3D). In connection with recent JILA experiments, we consider the motion of a straight vortex line in a slightly nonspherical condensate. The vortex line changes its orientation in space at the rate proportional to the degree of trap anisotropy and can exhibit periodic recurrences.Comment: 19 pages, 6 eps figures, REVTE

Weakly Interacting Bose-Einstein Condensates Under Rotation: Mean-field versus Exact Solutions

We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.Comment: 4 pages, RevTex, submitted to PR

Exploring the association of Brownfield remediation status with socioeconomic conditions in Wayne County, MI

Urban neighborhoods with locations of environmental contamination, known as brownfields, impact entire neighborhoods, but corrective environmental remedial action on brownfields is often tracked on an individual property basis, neglecting the larger neighborhood-level impact. This study addresses this impact by examining spatial differences between brownfields with unmitigated environmental concerns (open site) and sites that are considered fully mitigated or closed in urban neighborhoods (closed site) on the US census tract scale in Wayne County, MI. Michigan’s Department of Environment, Great Lakes, and Energy’s leaking underground storage tank (LUST) database provided brownfield information for Wayne County. Local indicators of spatial association (LISA) produced maps of spatial clustering and outliers. A McNemar’s test demonstrated significant discordances in LISA categories between LUST open and closed sites (p\u3c0.001). Geographically weighted regressions (GWR) evaluated the association between open and closed site spatial density (open-closed) with socioeconomic variables (population density, proportion of White or Black residents, proportion of college educated populations, the percentage of owner-occupied units, vacant units, rented units, and median household value). Final multivariate GWR showed that population density, being Black, college education, vacant units, and renter occupied units were significantly associated (p\u3c0.05) with open-closed, and that those associations varied across Wayne County. Increases in Black population was associated with increased open-closed. Increases in vacant units, renter-occupied units, and college education were associated with decreased open-closed. These results provide input for environmental justice research to identify inequalities and discover the distribution of environmental hazards among urban neighborhoods