The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros

CMB observations in LTB universes: Part I: Matching peak positions in the CMB spectrum

Acoustic peaks in the spectrum of the cosmic microwave background in spherically symmetric inhomogeneous cosmological models are studied. At the photon-baryon decoupling epoch, the universe may be assumed to be dominated by non-relativistic matter, and thus we may treat radiation as a test field in the universe filled with dust which is described by the Lema\^itre-Tolman-Bondi (LTB) solution. First, we give an LTB model whose distance-redshift relation agrees with that of the concordance $\Lambda$CDM model in the whole redshift domain and which is well approximated by the Einstein-de Sitter universe at and before decoupling. We determine the decoupling epoch in this LTB universe by Gamow's criterion and then calculate the positions of acoustic peaks. Thus obtained results are not consistent with the WMAP data. However, we find that one can fit the peak positions by appropriately modifying the LTB model, namely, by allowing the deviation of the distance-redshift relation from that of the concordance $\Lambda$CDM model at $z>2$ where no observational data are available at present. Thus there is still a possibility of explaining the apparent accelerated expansion of the universe by inhomogeneity without resorting to dark energy if we abandon the Copernican principle. Even if we do not take this extreme attitude, it also suggests that local, isotropic inhomogeneities around us may seriously affect the determination of the density contents of the universe unless the possible existence of such inhomogeneities is properly taken into account.Comment: 20 pages, 5 figure

The isotope effect on divertor conditions and neutral pumping in horizontal divertor configurations in JET-ILW Ohmic plasmas

In the past at JET, with the MkI divertor, a systematic study of the influence of X-point height and poloidal flux expansion has been conducted [1,2] showing minor differences in the radiation distribution, whereas in [3] experiment and simulations have shown enhancement of detachment as the flux expansion was increased. More recently at JET, equipped with the ITER-like wall (ILW), radiative seeded scenarios have been studied and a maximum radiation fraction 75% has been achieved. EDGE2D-EIRENE [4–6] simula- tions [7,8] have already shown that the divertor heat fluxes can be reduced with N2 injection, qualita- tively consistent with experimental observations [9] , by adjusting the impurity injection rate to reproduce the measured divertor radiation. In this paper we will present edge predictive simulations on the assess- ment of effects of poloidal flux expansion and recycling on radiation distribution and X-point peaking on JET-ILW nitrogen seeded plasmas

Pedestal evolution physics in low triangularity JET tokamak discharges with ITER-like wall

The pressure gradient of the high confinement pedestal region at the edge of tokamak plasmas rapidly collapses during plasma eruptions called edge localised modes (ELMs), and then re-builds over a longer time scale before the next ELM. The physics that controls the evolution of the JET pedestal between ELMs is analysed for 1.4 MA, 1.7 T, low triangularity, δ = 0.2, discharges with the ITER-like wall, finding that the pressure gradient typically tracks the ideal magneto-hydrodynamic ballooning limit, consistent with a role for the kinetic ballooning mode. Furthermore, the pedestal width is often influenced by the region of plasma that has second stability access to the ballooning mode, which can explain its sometimes complex evolution between ELMs. A local gyrokinetic analysis of a second stable flux surface reveals stability to kinetic ballooning modes; global effects are expected to provide a destabilising mechanism and need to be retained in such second stable situations. As well as an electronscale electron temperature gradient mode, ion scale instabilities associated with this flux surface include an electro-magnetic trapped electron branch and two electrostatic branches propagating in the ion direction, one with high radial wavenumber. In these second stability situations, the ELM is triggered by a peeling-ballooning mode; otherwise the pedestal is somewhat below the peeling-ballooning mode marginal stability boundary at ELM onset. In this latter situation, there is evidence that higher frequency ELMs are paced by an oscillation in the plasma, causing a crash in the pedestal before the peeling-ballooning boundary is reached. A model is proposed in which the oscillation is associated with hot plasma filaments that are pushed out towards the plasma edge by a ballooning mode, draining their free energy into the cooler plasma there, and then relaxing back to repeat the process. The results suggest that avoiding the oscillation and maximising the region of plasma that has second stability access will lead to the highest pedestal heights and, therefore, best confinement—a key result for optimising the fusion performance of JET and future tokamaks, such as ITER.EURATOM 633053EPSRC EP/K504178/1EPSRC EP/L01663X/1Plasma HEC Consortium EPSRCV EP/L000237/

Vortex nucleation in Bose-Einstein condensates in time-dependent traps

Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. It is found that this theory is able to describe the creation of vortices, but not the crystallization of a vortex lattice. In the case of a rotating, slightly anisotropic harmonic potential, the numerical results reproduce experimental findings, thereby showing that finite temperatures are not necessary for vortex excitation below the quadrupole frequency. In the case of a condensate subject to stirring by a narrow rotating potential, the process of vortex excitation is described by a classical model that treats the multitude of vortices created by the stirrer as a continuously distributed vorticity at the center of the cloud, but retains a potential flow pattern at large distances from the center.Comment: 22 pages, 7 figures. Changes after referee report: one new figure, new refs. No conclusions altere

Quality of cherry ‘Sweetheart’ from different regions of Portugal and Spain (Cova da Beira, Portalegre and Valle del Jerte).

Sweet cherries (Prunus avium L.) ‘Sweetheart’ were harvested at different production regions from Portugal (Cova da Beira and Portalegre) and Spain (Valle de Jerte). Cherries were harvested at their commercial maturation according to the empirical knowledge of external color corresponding to good quality. Fruits were stored and evaluated in order to study their quality on the harvest day and during a period of 21 days, at cold storage (1 ºC, 95% RH). The sweet cherry ‘Sweetheart’ is a well known variety and a highly appreciated one but fruits present a short shelf life. On the other hand the effect of different “terroir” on cherry characteristics should be known and clarified. Fruits from day 0, considered without storage, were kept at 20ºC and analyzed. Every weak, 3 replicas were randomly picked up and 10 fruits from each one were submitted to several analyses after fruit temperature stabilized at 20ºC. Several quality parameters were evaluated: external color (L*, a*, b*), texture, soluble solids content (SSC), titratable acidity (TA) and the ratio between soluble solid contents (SSC) and tritratable acidity (TA). Fruits from different orchards and locations were significantly different according to these parameters. Fruits from Cova da Beira were less firm comparing with other two regions, Valle de Jerte and Portalegre, which may indicate a higher maturation rate at harvest in those fruits. This is in accordance with SSC/titratable acidity rate suggesting a late harvest in Cova da Beira comparing with other two orchards, however fruits from Cova da Beira exhibit a poor color at harvest. These results clearly showed a lower correlation between SSC and firmness considering fruits origin

Testing the Void against Cosmological data: fitting CMB, BAO, SN and H0

In this paper, instead of invoking Dark Energy, we try and fit various cosmological observations with a large Gpc scale under-dense region (Void) which is modeled by a Lemaitre-Tolman-Bondi metric that at large distances becomes a homogeneous FLRW metric. We improve on previous analyses by allowing for nonzero overall curvature, accurately computing the distance to the last-scattering surface and the observed scale of the Baryon Acoustic peaks, and investigating important effects that could arise from having nontrivial Void density profiles. We mainly focus on the WMAP 7-yr data (TT and TE), Supernova data (SDSS SN), Hubble constant measurements (HST) and Baryon Acoustic Oscillation data (SDSS and LRG). We find that the inclusion of a nonzero overall curvature drastically improves the goodness of fit of the Void model, bringing it very close to that of a homogeneous universe containing Dark Energy, while by varying the profile one can increase the value of the local Hubble parameter which has been a challenge for these models. We also try to gauge how well our model can fit the large-scale-structure data, but a comprehensive analysis will require the knowledge of perturbations on LTB metrics. The model is consistent with the CMB dipole if the observer is about 15 Mpc off the centre of the Void. Remarkably, such an off-center position may be able to account for the recent anomalous measurements of a large bulk flow from kSZ data. Finally we provide several analytical approximations in different regimes for the LTB metric, and a numerical module for CosmoMC, thus allowing for a MCMC exploration of the full parameter space.Comment: 70 pages, 12 figures, matches version accepted for publication in JCAP. References added, numerical values in tables changed due to minor bug, conclusions unaltered. Numerical module available at http://web.physik.rwth-aachen.de/download/valkenburg

Split-merge cycle, fragmented collapse, and vortex disintegration in rotating Bose-Einstein condensates with attractive interactions

The dynamical instabilities and ensuing dynamics of singly- and doubly-quantized vortex states of Bose-Einstein condensates with attractive interactions are investigated using full 3D numerical simulations of the Gross-Pitaevskii equation. With increasing the strength of attractive interactions, a series of dynamical instabilities such as quadrupole, dipole, octupole, and monopole instabilities emerge. The most prominent instability depends on the strength of interactions, the geometry of the trapping potential, and deviations from the axisymmetry due to external perturbations. Singly-quantized vortices split into two clusters and subsequently undergo split-merge cycles in a pancake-shaped trap, whereas the split fragments immediately collapse in a spherical trap. Doubly-quantized vortices are always unstable to disintegration of the vortex core. If we suddenly change the strength of interaction to within a certain range, the vortex splits into three clusters, and one of the clusters collapses after a few split-merge cycles. The vortex split can be observed using a current experimental setup of the MIT group.Comment: 11 pages, 10 figure