Energy spectra of vortex distributions in two-dimensional quantum turbulence

We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size characterized by the healing length $\xi$. We show that for the divergence-free portion of the superfluid velocity field, the kinetic energy spectrum over wavenumber $k$ may be decomposed into an ultraviolet regime ($k\gg \xi^{-1}$) having a universal $k^{-3}$ scaling arising from the vortex core structure, and an infrared regime ($k\ll\xi^{-1}$) with a spectrum that arises purely from the configuration of the vortices. The Novikov power-law distribution of intervortex distances with exponent -1/3 for vortices of the same sign of circulation leads to an infrared kinetic energy spectrum with a Kolmogorov $k^{-5/3}$ power law, consistent with the existence of an inertial range. The presence of these $k^{-3}$ and $k^{-5/3}$ power laws, together with the constraint of continuity at the smallest configurational scale $k\approx\xi^{-1}$, allows us to derive a new analytical expression for the Kolmogorov constant that we test against a numerical simulation of a forced homogeneous compressible two-dimensional superfluid. The numerical simulation corroborates our analysis of the spectral features of the kinetic energy distribution, once we introduce the concept of a {\em clustered fraction} consisting of the fraction of vortices that have the same sign of circulation as their nearest neighboring vortices. Our analysis presents a new approach to understanding two-dimensional quantum turbulence and interpreting similarities and differences with classical two-dimensional turbulence, and suggests new methods to characterize vortex turbulence in two-dimensional quantum fluids via vortex position and circulation measurements.Comment: 19 pages, 8 figure

Snell's Law for a vortex dipole in a Bose-Einstein condensate

A quantum vortex dipole, comprised of a closely bound pair of vortices of equal strength with opposite circulation, is a spatially localized travelling excitation of a planar superfluid that carries linear momentum, suggesting a possible analogy with ray optics. We investigate numerically and analytically the motion of a quantum vortex dipole incident upon a step-change in the background superfluid density of an otherwise uniform two-dimensional Bose-Einstein condensate. Due to the conservation of fluid momentum and energy, the incident and refracted angles of the dipole satisfy a relation analogous to Snell's law, when crossing the interface between regions of different density. The predictions of the analogue Snell's law relation are confirmed for a wide range of incident angles by systematic numerical simulations of the Gross-Piteavskii equation. Near the critical angle for total internal reflection, we identify a regime of anomalous Snell's law behaviour where the finite size of the dipole causes transient capture by the interface. Remarkably, despite the extra complexity of the surface interaction, the incoming and outgoing dipole paths obey Snell's law.Comment: 16 pages, 7 figures, Scipost forma

Storage stability of whole and nibbed, conventional and high oleic peanuts (<i>Arachis hypogeae </i>L.)

Peanuts are increasingly being used as nibbed ingredients in cereal bars, confectionery and breakfast cereals. However, studies on their oxidative stability in this format are limited. Storage trials to determine the stability to oxidation were carried out on whole and nibbed kernels of conventional (CP) and high oleic (HOP) peanuts, with respect to temperature and modified atmosphere packaging. HOP exhibited the highest oxidative stability, with a lag phase in whole kernels of 12–15 weeks before significant oxidation occurred. HOP also showed higher levels of intrinsic antioxidants, a trolox equivalent antioxidant capacity (TEAC) of 70 mMol equivalence and radical scavenging percentage (RSP) of 99.8 % at the beginning of storage trials, whereas CP showed values of 40 mMol and 81.2 %, respectively. The intrinsic antioxidants at the beginning of these storage trials were shown to affect the peroxide value (PV), where RSP and TEAC decreased, and PV increased. Therefore, in peanuts the processing format (nibbed or whole) had the highest influence on susceptibility of lipid oxidation, highest to lowest importance: processing format &gt; temperature &gt; atmospheric conditions

Species-habitat associations in a Sri Lankan dipterocarp forest

Forest structure and species distribution patterns were examined among eight topographically defined habitats for the 205 species with stems ≥ 1 cm dbh inhabiting a 25-ha plot in the Sinharaja rain forest, Sri Lanka. The habitats were steep spurs, less-steep spurs, steep gullies and less-steep gullies, all at either lower or upper elevations. Mean stem density was significantly greater on the upper spurs than in the lower, less-steep gullies. Stem density was also higher on spurs than in gullies within each elevation category and in each upper-elevation habitat than in its corresponding lower-elevation habitat. Basal area varied less among habitats, but followed similar trends to stem density. Species richness and Fisher\u27s alpha were lower in the upper-elevation habitats than in the lower-elevation habitats. These differences appeared to be related to the abundances of the dominant species. Of the 125 species subjected to torus-translation tests, 99 species (abundant and less abundant and those in different strata) showed at least one positive or negative association to one or more of the habitats. Species associations were relatively more frequent with the lower-elevation gullies. These and the previous findings on seedling ecophysiology, morphology and anatomy of some of the habitat specialists suggest that edaphic and hydrological variation related to topography, accompanied by canopy disturbances of varying intensity, type and extent along the catenal landscape, plays a major role in habitat partitioning in this forest. Copyright © 2006 Cambridge University Press

Scaling dynamics of the ultracold Bose gas

The large-scale expansion dynamics of quantum gases is a central tool for ultracold gas experiments and poses a significant challenge for theory. In this work we provide an exact reformulation of the Gross-Pitaevskii equation for the ultracold Bose gas in a coordinate frame that adaptively scales with the system size during evolution, enabling simulations of long evolution times during expansion or similar large-scale manipulation. Our approach makes no hydrodynamic approximations, is not restricted to a scaling ansatz, harmonic potentials, or energy eigenstates, and can be generalized readily to non-contact interactions via the appropriate stress tensor of the quantum fluid. As applications, we simulate the expansion of the ideal gas, a cigar-shaped condensate in the Thomas-Fermi regime, and a linear superposition of counter propagating Gaussian wavepackets. We recover known scaling for the ideal gas and Thomas-Fermi regimes, and identify a linear regime of aspect-ratio preserving free expansion; analysis of the scaling dynamics equations shows that an exact, aspect-ratio invariant, free expansion does not exist for nonlinear evolution. Our treatment enables exploration of nonlinear effects in matter-wave dynamics over large scale-changing evolution.Comment: 12 pages, 3 figures, 2 appendice

Assessing the effects of the first 2 years of industry-led badger culling in England on the incidence of bovine tuberculosis in cattle in 2013–2015

Culling badgers to control the transmission of bovine tuberculosis (TB) between this wildlife reservoir and cattle has been widely debated. Industry-led culling began in Somerset and Gloucestershire between August and November 2013 to reduce local badger populations. Industry-led culling is not designed to be a randomised and controlled trial of the impact of culling on cattle incidence. Nevertheless, it is important to monitor the effects of the culling and, taking the study limitations into account, perform a cautious evaluation of the impacts. A standardised method for selecting areas matched to culling areas in factors found to affect cattle TB risk has been developed to evaluate the impact of badger culling on cattle TB incidence. The association between cattle TB incidence and badger culling in the first two years has been assessed. Descriptive analyses without controlling for confounding showed no association between culling and TB incidence for Somerset, or for either of the buffer areas for the first two years since culling began. A weak association was observed in Gloucestershire for Year 1 only. Multivariable analysis adjusting for confounding factors showed that reductions in TB incidence were associated with culling in the first two years in both the Somerset and Gloucestershire intervention areas when compared to areas with no culling (IRR: 0.79, 95%CI: 0.72-0.87, p<0.001 and IRR: 0.42, 95%CI: 0.34-0.51, p<0.001 respectively). An increase in incidence was associated with culling in the 2 km buffer surrounding the Somerset intervention area (IRR: 1.38, 95%CI: 1.09-1.75, p=0.008), but not in Gloucestershire (IRR: 0.91, 95%CI: 0.77-1.07, p=0.243). As only two intervention areas with two years’ of data are available for analysis, and the biological cause-effect relationship behind the statistical associations is difficult to determine, it would be unwise to use these findings to develop generalisable inferences about the effectiveness of the policy at present

Screening men for abdominal aortic aneurysm: 10 year mortality and cost effectiveness results from the randomised Multicentre Aneurysm Screening Study

Objectives To assess whether the mortality benefit from screening men aged 65-74 for abdominal aortic aneurysm decreases over time, and to estimate the long term cost effectiveness of screening

Nitrogen Blanketing and Hydrogen Starvation in Dead-Ended-Anode Polymer Electrolyte Fuel Cells Revealed by Hydro-Electro-Thermal Analysis

Dead-ended anode operation has a number of practical advantages that simplify system complexity and lower cost for polymer electrolyte fuel cells. However, dead-ended mode leads to performance loss over time which can only be reversed by performing intermittent purge events. This work applies a combined hydro-electro-thermal analysis to an air-cooled open-cathode fuel cell, presenting experimental functional maps of water distribution, current density and temperature. This approach has allowed the identification of a 'nitrogen blanketing' effect due to nitrogen cross-over from the cathode and a 'bypass' effect where a peripheral gap between the gasket and the GDL offers a hydrogen flow 'short circuit' to the border of the electrode. A consequence of high local current density at the margin of the electrode, and resulting high temperatures, may impact the lifetime of the cell in dead-end mode