Oscillation damping of chiral string loops

Chiral cosmic string loop tends to the stationary (vorton) configuration due to the energy loss into the gravitational and electromagnetic radiation. We describe the asymptotic behaviour of near stationary chiral loops and their fading to vortons. General limits on the gravitational and electromagnetic energy losses by near stationary chiral loops are found. For these loops we estimate the oscillation damping time. We present solvable examples of gravitational radiation energy loss by some chiral loop configurations. The analytical dependence of string energy with time is found in the case of the chiral ring with small amplitude radial oscillations.Comment: 10 pages, 2 figures. Accepted for publication in Physical Review

Separability of Rotational Effects on a Gravitational Lens

We derive the deflection angle up to $O(m^2a)$ due to a Kerr gravitational lens with mass $m$ and specific angular momentum $a$. It is known that at the linear order in $m$ and $a$ the Kerr lens is observationally equivalent to the Schwarzschild one because of the invariance under the global translation of the center of the lens mass. We show, however, nonlinear couplings break the degeneracy so that the rotational effect becomes in principle separable for multiple images of a single source. Furthermore, it is distinguishable also for each image of an extended source and/or a point source in orbital motion. In practice, the correction at $O(m^2a)$ becomes $O(10^{-10})$ for the supermassive black hole in our galactic center. Hence, these nonlinear gravitational lensing effects are too small to detect by near-future observations.Comment: 12 pages (RevTeX); accepted for publication in Phys. Rev.

Cosmic String Cusps with Small-Scale Structure: Their Forms and Gravitational Waveforms

We present a method for the introduction of small-scale structure into strings constructed from products of rotation matrices. We use this method to illustrate a range of possibilities for the shape of cusps that depends on the properties of the small-scale structure. We further argue that the presence of structure at cusps under most circumstances leads to the formation of loops at the size of the smallest scales. On the other hand we show that the gravitational waveform of a cusp remains generally unchanged; the primary effect of small-scale structure is to smooth out the sharp waveform emitted in the direction of cusp motion.Comment: RevTeX, 8 pages. Replaced with version accepted for publication by PR

On the construction of a geometric invariant measuring the deviation from Kerr data

This article contains a detailed and rigorous proof of the construction of a geometric invariant for initial data sets for the Einstein vacuum field equations. This geometric invariant vanishes if and only if the initial data set corresponds to data for the Kerr spacetime, and thus, it characterises this type of data. The construction presented is valid for boosted and non-boosted initial data sets which are, in a sense, asymptotically Schwarzschildean. As a preliminary step to the construction of the geometric invariant, an analysis of a characterisation of the Kerr spacetime in terms of Killing spinors is carried out. A space spinor split of the (spacetime) Killing spinor equation is performed, to obtain a set of three conditions ensuring the existence of a Killing spinor of the development of the initial data set. In order to construct the geometric invariant, we introduce the notion of approximate Killing spinors. These spinors are symmetric valence 2 spinors intrinsic to the initial hypersurface and satisfy a certain second order elliptic equation ---the approximate Killing spinor equation. This equation arises as the Euler-Lagrange equation of a non-negative integral functional. This functional constitutes part of our geometric invariant ---however, the whole functional does not come from a variational principle. The asymptotic behaviour of solutions to the approximate Killing spinor equation is studied and an existence theorem is presented.Comment: 36 pages. Updated references. Technical details correcte

Residual Nitrate and Mineralizable Soil Nitrogen in Relation to Nitrogen Uptake by Irrigated Sugarbeets

Previously reported studies on N fertilization of sugarbeets (Beta vulgaris L.) in southern Idaho revealed considerable variation among sites in amounts of residual soil NO? and N mineralized during short-term laboratory incubations. Consequently, the amount of N fertilizer needed to achieve near-maximum yields of sucrose differed markedly. The purpose of this study was to determine the feasibility of estimating amounts of N mineralized in the root zone during the season, taking into account site variations in temperature and soil water regimes. Residual soil NO?--N and mineralizable N to approximate rooting depth were estimated for 21 field sites in 1971 and six sites in 1972. The relative contributions of these two N sources to total N uptake by the crop, in the absence of applied fertilizer N, were then assessed. Estimates of N mineralized in the upper 45- cm soil layer for each successive month, ?N, over a 6- month period were derived using the expression, ?N/ ?t kWN (k = fraction of N mineralized during each month, ?t, adjusted for average air temperature; and W the estimated soil water content expressed as a fraction of the available water storage capacity). Resulting estimates of the fraction of potentially mineralizable N converted to (NO?- + NH?+)-N between 1 April and 30 September ranged from 0.15 to 0.22 (mean ± S.D. = 0.18 ± 0.02) in 1971 and 1972. On the average, mature sugarbeets recovered about 73% of the estimated N mineralized (6 months) plus residual NO?--N. The relative contributions of these two sources of soil derived N, respectively, were approximately 66 and 75%, as estimated from multiple regression analyses

Residual Nitrate and Mineralizable Soil Nitrogen in Relation to Nitrogen Uptake by Irrigated Sugarbeets

Previously reported studies on N fertilization of sugarbeets (Beta vulgaris L.) in southern Idaho revealed considerable variation among sites in amounts of residual soil NO? and N mineralized during short-term laboratory incubations. Consequently, the amount of N fertilizer needed to achieve near-maximum yields of sucrose differed markedly. The purpose of this study was to determine the feasibility of estimating amounts of N mineralized in the root zone during the season, taking into account site variations in temperature and soil water regimes. Residual soil NO?--N and mineralizable N to approximate rooting depth were estimated for 21 field sites in 1971 and six sites in 1972. The relative contributions of these two N sources to total N uptake by the crop, in the absence of applied fertilizer N, were then assessed. Estimates of N mineralized in the upper 45- cm soil layer for each successive month, ?N, over a 6- month period were derived using the expression, ?N/ ?t kWN (k = fraction of N mineralized during each month, ?t, adjusted for average air temperature; and W the estimated soil water content expressed as a fraction of the available water storage capacity). Resulting estimates of the fraction of potentially mineralizable N converted to (NO?- + NH?+)-N between 1 April and 30 September ranged from 0.15 to 0.22 (mean ± S.D. = 0.18 ± 0.02) in 1971 and 1972. On the average, mature sugarbeets recovered about 73% of the estimated N mineralized (6 months) plus residual NO?--N. The relative contributions of these two sources of soil derived N, respectively, were approximately 66 and 75%, as estimated from multiple regression analyses

The nomenclature and application of the names Euphorbia candelabrum Welw. and Euphorbia ingens in tropical Africa

During the last 40 years, one of the most widespread and conspicuous succulent trees in East and north‐east Africa has been referred to as Euphorbia candelabrum Kotschy or as E. candelabrum Trémaux ex Kotschy. This name is a later homonym of E. candelabrum Welw., and consequently it is illegitimate. The species to which the name E. candelabrum Kotschy has been widely applied is shown to be conspecific with E. ingens, which occurs from southern Ethiopia to subtropical South Africa.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152821/1/tax12091_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152821/2/tax12091.pd

Neutron Scattering Study of Crystal Field Energy Levels and Field Dependence of the Magnetic Order in Superconducting HoNi2B2C

Elastic and inelastic neutron scattering measurements have been carried out to investigate the magnetic properties of superconducting (Tc~8K) HoNi2B2C. The inelastic measurements reveal that the lowest two crystal field transitions out of the ground state occurat 11.28(3) and 16.00(2) meV, while the transition of 4.70(9) meV between these two levels is observed at elevated temperatures. The temperature dependence of the intensities of these transitions is consistent with both the ground state and these higher levels being magnetic doublets. The system becomes magnetically long range ordered below 8K, and since this ordering energy kTN ~ 0.69meV << 11.28meV the magnetic properties in the ordered phase are dominated by the ground-state spin dynamics only. The low temperature structure, which coexists with superconductivity, consists of ferromagnetic sheets of Ho{3+ moments in the a-b plane, with the sheets coupled antiferromagnetically along the c-axis. The magnetic state that initially forms on cooling, however, is dominated by an incommensurate spiral antiferromagnetic state along the c-axis, with wave vector qc ~0.054 A-1, in which these ferromagnetic sheets are canted from their low temperature antiparallel configuration by ~17 deg. The intensity for this spiral state reaches a maximum near the reentrant superconducting transition at ~5K; the spiral state then collapses at lower temperature in favor of the commensurate antiferromagnetic state. We have investigated the field dependence of the magnetic order at and above this reentrant superconducting transition. Initially the field rotates the powder particles to align the a-b plane along the field direction, demonstrating that the moments strongly prefer to lie within this plane due to the crystal field anisotropy. Upon subsequently increasing the field atComment: RevTex, 7 pages, 11 figures (available upon request); Physica

Quantum correlated twin atomic beams via photo-dissociation of a molecular Bose-Einstein condensate

We study the process of photo-dissociation of a molecular Bose-Einstein condensate as a potential source of strongly correlated twin atomic beams. We show that the two beams can possess nearly perfect quantum squeezing in their relative numbers.Comment: Corrected LaTeX file layou