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

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

A Novel Method of Solution for the Fluid Loaded Plate

We study the Cauchy problem associated with the equations governing a fluid loaded plate formulated on either the line or the half-line. We show that in both cases the problem can be solved by employing the unified approach to boundary value problems introduced by on of the authors in the late 1990s. The problem on the full line was analysed by Crighton et. al. using a combination of Laplace and Fourier transforms. The new approach avoids the technical difficulty of the a priori assumption that the amplitude of the plate is in $L^1_{dt}(R^+)$ and furthermore yields a simpler solution representation which immediately implies the problem is well-posed. For the problem on the half-line, a similar analysis yields a solution representation, but this formula involves two unknown functions. The main difficulty with the half-line problem is the characterisation of these two functions. By employing the so-called global relation, we show that the two functions can be obtained via the solution of a complex valued integral equation of the convolution type. This equation can be solved in closed form using the Laplace transform. By prescribing the initial data $\eta_0$ to be in $H^3(R^+)$, we show that the solution depends continuously on the initial data, and hence, the problem is well-posed.Comment: 17 pages, 3 figures. Minor adjustments made to the introductio