Two-dimensional turbulence on a sphere

Following Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) we undertake a spectral analysis of a non-divergent flow on a sphere. It is shown that the spherical harmonic energy spectrum is invariant under rotations of the polar axis of the spherical harmonic system and argued that a constraint of isotropy would not simplify the analysis but only exclude low-order modes. The spectral energy equation is derived and it is shown that the viscous term has a slightly different form than given in previous studies. The relations involving energy transfer within a triad of modes, which Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) derived under the condition that energy transfer is restricted to three modes, are derived under general conditions. These relations show that there are two types of interaction within a triad. The first type is where the middle mode acts as a source for the two other modes and the second type is where it acts as a sink. The inequality indicating cascade directions which was derived by Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) in Fourier space under the assumptions of narrow band forcing and stationarity is derived in spherical harmonic space under the assumption of dominance of first type interactions. The double cascade theory of Kraichnan (Phys. Fluids, vol. 10, 1967, pp. 1417–1423) is discussed in the light of the derived equations and it is hypothesised that in flows with limited scale separation the two cascades may, to a large extent, be produced by the same triad interactions. Finally, we conclude that the spherical geometry is the optimal test ground for exploration of two-dimensional turbulence by means of simulations.

Effects of the external magnetic field on the Lense–Thirring precession

In this paper, we study the effects of the external magnetic field on the Lense–Thirring (LT) precession of a test gyroscope attached to an observer in magnetized black hole spacetime. For this, we consider a Kerr–Newman black hole embedded in the external magnetic field. The LT precession of a test gyroscope diverges near the ergosurface and remains finite everywhere outside the ergosurface. It is seen that by increasing the external magnetic field, the LT precession frequency in the region of large [Formula: see text] decreases as [Formula: see text] increases, while the precession frequency in the region of small [Formula: see text] increases as [Formula: see text] increases, whereas it increases with increasing the charge of the black hole. The LT precession of a test gyroscope attached to observers moving along the directions close to the polar axis is greater than that of the observer moving in the equatorial plane.

Calculation of nonlinear optical properties of lithium niobate crystals

The coefficients of the second-order nonlinear optical tensor for lithium niobate crystal with a composition close to stoichiometric were calculated. The calculated results show that the contribution of the Li-O group to the optical effects of the second harmonic was greater than the contribution of the Nb-O group. The results also showed that the most efficient frequency conversion occurred along the polar axis of the crystal

X-RAY studies of ferroelectric lithium niobate crystals doped with rare earth elements

The lattice structural distortions of LiNbO3 crystals doped with samarium with a concentration of 1.0, 1.9, 2.5 mol. % were studied by X-ray diffraction methods. It was found that the samarium atoms and some of the niobium atoms occupied the vacant positions of lithium in the crystal lattice, and some of the niobium atoms were located in the empty octahedron. The octahedra of SmLiO6 was distorted more strongly than octahedra of NbLiO6 when niobium atoms entered the vacant positions of lithium. The smallest changes in the bond lengths in the octahedra of the main motif and in the defect region as well as along the polar axis in the lithium niobate lattice were observed in the sample with a samarium concentration of 2.5 mol. %.

Effect of plant growth regulators on two different types of eggplant flowers regarding style length and fruit setting

Aim of study: (i) to explore differences between eggplant flowers capable of setting fruit including long (LGs) and medium style flowers (MEs) and those which suffer from severe problems with fertility and fruit setting including short style ones (SRTs); (ii) to study the effect of plant growth regulators on floral morphology and fruit setting. Area of study: Isfahan University of Technology, Isfahan, Iran, 2017 and 2018. Material and methods: First the floral morphology and initial fruit setting of 13 eggplant genotypes from Iran were investigated. Then the differences between LGs and SRTs of two genotypes were explored. Finally, the effect of 1-naphthaleneacetic acid (NAA) and spermidine (Spd) on floral morphology and initial and final fruit setting of these two genotypes was determined. Main results: Results showed SRTs were not capable of fruit setting. Compared to SRTs, LGs had larger central canals, higher protein, total sugar, reducing sugar and K concentrations, as well as longer polar axis and pollen tubes and greater pollen viability. Although 1.5 mM Spd and 20 mg L-1 NAA resulted in increasing of LGs and MEs, and also total initial fruit set, surprisingly, no significant differences were observed in the final yield and final fruit set between the control and these treatments. Researching highlights: Since the rate of fruit dropping was higher in those treatments compared to the control, plants with more SRTs likely regulate their final load by abscising their flowers, and plants with more LGs regulate them by abscising their fruits.

Electroresistance in multipolar antiferroelectric Cu2Se semiconductor

Electric field-induced changes in the electrical resistance of a material are considered essential and enabling processes for future efficient large-scale computations. However, the underlying physical mechanisms of electroresistance are currently remain largely unknown. Herein, an electrically reversible resistance change has been observed in the thermoelectric α-Cu2Se. The spontaneous electric dipoles formed by Cu+ ions displaced from their positions at the centers of Se-tetrahedrons in the ordered α-Cu2Se phase are examined, and α-Cu2Se phase is identified to be a multipolar antiferroelectric semiconductor. When exposed to the applied voltage, a reversible switching of crystalline domains aligned parallel to the polar axis results in an observed reversible resistance change. The study expands on opportunities for semiconductors with localized polar symmetry as the hardware basis for future computational architectures.

Flowering Biology of Rhododendron pulchrum

To study the flowering biology of Rhododendron pulchrum, we used scanning electron microscopy (SEM) and paraffin sectioning to observe the microstructures of its floral organs, a methyl thiazolyl tetrazolium (MTT) colorimetric assay to detect pollen viability in different periods, continuous observations to study flowering phenology, and artificial pollination and a benzidine-hydrogen peroxide method to determine stigma receptivity. R. pulchrum exhibited a centralized flowering phenology. The protogynous stigmas of R. pulchrum were able to receive pollen before flowering. The pollen grains of R. pulchrum fused into tetrads, the average ratio of the polar axis length to the equatorial axis length (P/E) was 1.05, and the pollen viability was highest in the initial flowering period, reaching 88.98%. The pollen/ovule (P/O) ratio was 266–328, and the outcrossing index (OCI) was 4; the vitality of R. pulchrum pollen remained high in the initial flowering and blooming periods. Compared with the lifespan of a single flower, pollen vitality remained high for most of the experimental period, thereby improving male fitness. The P/O ratio suggests that R. pulchrum may have a facultative outcrossing breeding system. The OCI estimation suggests that R. pulchrum is partially self-compatible, most likely requiring pollinators to complete pollination.

Photon boomerang in a nearly extreme Kerr metric

The Kerr rotating black hole metric has unstable photon orbits that orbit around the hole at fixed values of the Boyer-Lindquist coordinate r that depend on the axial angular momentum of the orbit, as well as on the parameters of the hole. For zero orbital axial angular momentum, these orbits cross the rotational axes at a fixed value of r that depends on the mass M and angular momentum J of the black hole. Nonzero angular momentum of the hole causes the photon orbit to rotate so that its direction when crossing the north polar axis changes from one crossing to the next by an angle I shall call ∆φ, which depends on the black hole dimensionless rotation parameter a/M = cJ/(GM2) by an equation involving a complete elliptic integral of the first kind. When the black hole has a/M ≈ 0.994 341 179 923 26, which is nearly maximally rotating, a photon sent out in a constant-r direction from the north polar axis at r ≈ 2.423 776 210 035 73 GM/c2returns to the north polar axis in precisely the opposite direction (in a frame nonrotating with respect to the distant stars), a photon boomerang.

Tracking Fungal Growth: Establishment of Arp1 as a Marker for Polarity Establishment and Active Hyphal Growth in Filamentous Ascomycetes

Polar growth is a key characteristic of all filamentous fungi. It allows these eukaryotes to not only effectively explore organic matter but also interact within its own colony, mating partners, and hosts. Therefore, a detailed understanding of the dynamics in polar growth establishment and maintenance is crucial for several fields of fungal research. We developed a new marker protein, the actin-related protein 1 (Arp1) fused to red and green fluorescent proteins, which allows for the tracking of polar axis establishment and active hyphal growth in microscopy approaches. To exclude a probable redundancy with known polarity markers, we compared the localizations of the Spitzenkörper (SPK) and Arp1 using an FM4-64 staining approach. As we show in applications with the coprophilous fungus Sordaria macrospora and the hemibiotrophic plant pathogen Colletotrichum graminicola, the monitoring of Arp1 can be used for detailed studies of hyphal growth dynamics and ascospore germination, the interpretation of chemotropic growth processes, and the tracking of elongating penetration pegs into plant material. Since the Arp1 marker showed the same dynamics in both fungi tested, we believe this marker can be broadly applied in fungal research to study the manifold polar growth processes determining fungal life.