Geometric transport along circular orbits in stationary axisymmetric spacetimes

Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric spacetimes is described explicitly relative to Lie transport in terms of the electric and magnetic parts of the induced connection. The influence of both the gravitoelectromagnetic fields associated with the zero angular momentum observers and of the Frenet-Serret parameters of these orbits as a function of their angular velocity is seen on the behavior of parallel transport through its representation as a parameter-dependent Lorentz transformation between these two inner-product preserving transports which is generated by the induced connection. This extends the analysis of parallel transport in the equatorial plane of the Kerr spacetime to the entire spacetime outside the black hole horizon, and helps give an intuitive picture of how competing "central attraction forces" and centripetal accelerations contribute with gravitomagnetic effects to explain the behavior of the 4-acceleration of circular orbits in that spacetime.Comment: 33 pages ijmpd latex article with 24 eps figure

Geometry and arithmetic of Maschke's Calabi-Yau three-fold

Maschke's Calabi-Yau three-fold is the double cover of projective three space branched along Maschke's octic surface. This surface is defined by the lowest degree invariant of a certain finite group acting on a four-dimensional (4D) vector space. Using this group, we show that the middle Betti cohomology group of the three-fold decomposes into the direct sum of 150 2D Hodge substructures. We exhibit 1D families of rational curves on the three-fold and verify that the associated Abel-Jacobi map is non-trivial. By counting the number of points over finite fields, we determine the rank of the Neron-Severi group of Maschke's surface and the Galois representation on the transcendental lattice of some of its quotients. We also formulate precise conjectures on the modularity of the Galois representations associated to Maschke's three-fold (these have now been proven by M. Schutt) and to a genus 33 curve, which parametrizes rational curves in the three-fold

Species richness and beta-diversity of aquatic macrophytes assemblages in three floodplain tropical lagoons: evaluating the effects of sampling size and depth gradients

Using aquatic macrophyte data gathered in three lagoons of the Paraná River floodplain we showed a strong effect of sample size on species richness. Incidence-based species richness estimators (Chao 2, jackknife 1, jackknife 2, incidence-based coverage estimator and bootstrap) were compared to evaluate their performance in estimating the species richness throughout transect sampling rnethod. Our results suggest that the best estimate of the species richness was gave by jackknife 2 estimator. Nevertheless, the transect sampling design was considered inappropriate to estimate aquatic macrophytes species richness. Depth gradient was not a good predictor of the species richness and species turnover (beta diversity). The dynamics of these environments, subject to high water-level fluctuation prevents the formation and permanence of a clear floristic depth-related gradient

On gravitomagnetic precession around black holes

We compute exactly the Lense-Thirring precession frequency for point masses in the Kerr metric, for arbitrary black hole mass and specific angular momentum. We show that this frequency, for point masses at or close to the innermost stable orbit, and for holes with moderate to extreme rotation, is less than, but comparable to the rotation frequency. Thus, if the quasi periodic oscillations (QPOs) observed in the modulation of the X-ray flux from some black holes candidates are due to Lense-Thirring precession of orbiting material, we predict that a separate, distinct QPO ought to be observed in each object.Comment: Accepted for publication in MNRAS. MN-Latex, 2 figure

Kerr metric, static observers and Fermi coordinates

The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane, i.e., Fermi coordinates for the neighborhood of a static observer world line, is derived and discussed in a way which extends to any uniformly circularly orbiting observer there.Comment: 15 page latex iopart class documen

Mechanistic insights into the hydrocyanation reaction

The hydrocyanation of an alkene is a catalytic carbon-carbon bond formation reaction and the obtained nitriles can be converted into a variety of valuable products. The investigation of this reaction has mainly focused on the DuPont adiponitrile (AdN) process. This process is so far the only example of a large scale industrial application of an alkene hydrocyanation. Adiponitrile is produced from butadiene in 3 steps: the Ni-catalyzed hydrocyanation of butadiene leads to a mixture of 2-methyl-3-butenenitrile (2M3BN) and 3-pentenenitrile (3PN), obtained in varying ratio (typically 2:3) depending on the ligand employed. In a second step, the branched 2M3BN is isomerized to the desired linear 3PN in the presence of similar Ni-catalysts. The last step is the hydrocyanation of 3PN to AdN. The catalyst performance in this process still needs to be improved in terms of activity, especially for the hydrocyanation of 3PN, and, in selectivity for both hydrocyanation steps. Many investigations are also focusing on the hydrocyanation of vinylarenes. Several ligands have been applied in this reaction and their influence on activity, regio- and enantioselectivity has been considered. An overview on the hydrocyanation of alkenes is given in Chapter 1. The chemistry behind this reaction is discussed prevalently from a mechanistic point of view. The reactivity of different classes of substrates is underlined. Mainly examples of the Ni-catalyzed hydrocyanation are reported, along with a brief overview on catalysis based on other metals. In Chapter 2, a new route for the synthesis of the triptycene-based diphosphine ligand Tript(PPh2)2 is described, giving the desired compound in good yield. The corresponding Pt(II)- and Ni(0)-complexes are characterized. In butadiene hydrocyanation the [Ni(cod)(Tript(PPh2)2)] pre-catalyst leads to unprecedented high selectivities for the linear product 3PN, combining concurrently high activity for both, hydrocyanation and isomerization reaction. The double activity of the catalyst enables to reduce the synthesis of 3PN to a one-step procedure consisting of a hydrocyanation followed by an isomerization reaction. This new catalyst could be the key towards process intensification in the future. Chapter 3 describes for the first time an in situ FT-IR spectroscopic study of the isomerization of 2M3BN towards 3PN. The spectra were analyzed comprehensively to obtain conversion profiles from the different band dynamics. Each band was transformed to its second derivative to enhance peak resolution. Calculated spectra of the substrate and the products support the peak assignment. An average conversion profile was calculated from different bands of the substrate and the product, applying a "quasimultivariate analysis" technique to correlate different band dynamics. This approach was validated using advanced chemometrics. Furthermore, these profiles obtained by IR spectroscopic analysis of the formation of 3PN and the consumption of 2M3BN showed a zero order kinetic. The application of new tetraphenol-based diphosphite ligands (TP) in the hydrocyanation reaction is described in Chapter 4. Very high activities were observed in the hydrocyanation of 3-pentenenitrile. Surprisingly, these systems are neither active in the hydrocyanation of butadiene nor do they show any isomerization of 2M3BN. This peculiar behavior of the [Ni(TP)] catalysts was investigated by means of NMR and IR spectroscopy, considering the formation of s-alkyl and p-allyl intermediates. The s-alkyl species formation seems to be prevalent with the TP ligands, while the formation of p-allyl species is disfavored. Since the hydrocyanation of 3PN proceeds via s-alkyl intermediates and the first two steps of the DuPont process via the p-allyl species, these results provide an explanation for the observed catalytic activity. Moreover, the coordination of ZnCl2 to the [Ni(2M3BN)(TP2)] complex was studied by IR spectroscopy. The comparison with a binaphthol-based diphosphite (BIPPP) ligand, often applied in hydrocyanation reactions, is also presented in relation to the coordination and catalytic activity. Chapter 5 reports on the hydrocyanation of styrene. According to present knowledge, this reaction leads predominantly to the branched product 2-phenylpropionitrile (98%). A dramatic inversion of the regioselectivity upon addition of a Lewis acid is observed. Up to 83% of the linear product 3-phenylpropionitrile was obtained applying phosphite ligands in the presence of AlCl3. The mechanism of the Ni-catalyzed reaction and the influence of additional Lewis acids have been elucidated by means of deuterium labeling experiments, NMR studies, and DFT calculations. It was concluded that the selectivity towards the linear product 3-phenylpropionitrile in the presence of AlCl3 is due to the higher stability of the intermediate ¿3-benzyl complex. The selective stabilization of this intermediate in the presence of the Lewis acid leads to the formation of a "steady state" for the ¿3-benzyl intermediate and indirectly promotes the formation of the linear product 3-phenylpropionitrile via the s-alkyl intermediate. Furthermore, the influence of different Lewis acids, such as CuCN, could be predicted via DFT calculations. Chapter 6 deals with the hydrocyanation of simple monoalkenes. So far, this reaction did not attract much attention, due to the lower conversion generally obtained as compared to the hydrocyanation of 1,3-dienes and vinylarenes. Yet, this reaction leads to aliphatic nitriles, which are potentially valuable intermediates for both bulk and finechemical industry. The role of the Lewis acid in the mechanism of the reaction is still not completely clear; in particular its exact role in the increase of the reactivity and regioselectivity towards linear nitriles. A conversion of 89% in the hydrocyanation of 1-octene is reported, applying a binaphthol-based diphosphite (BIPPP) as ligand and AlCl3 as Lewis acid. The competition between ß-(H,D)-elimination and hydrocyanation in the reaction mechanism has been investigated by deuterium labeling experiments. Furthermore, preliminary DFT calculations have been performed to study the deactivation of the Ni-catalyst by formation of dicyano species

Circular holonomy in the Taub-NUT spacetime

Parallel transport around closed circular orbits in the equatorial plane of the Taub-NUT spacetime is analyzed to reveal the effect of the gravitomagnetic monopole parameter on circular holonomy transformations. Investigating the boost/rotation decomposition of the connection 1-form matrix evaluated along these orbits, one finds a situation that reflects the behavior of the general orthogonally transitive stationary axisymmetric case and indeed along Killing trajectories in general.Comment: 9 pages, LaTeX iopart class, no figure

Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry

We derive an exact general axi-symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation. The solution is characterized by four parameters $M$ (mass), $Q$ (charge), $a$ (rotation) and $L$ (NUT). We then, calculate the total exterior energy using the energy-momentum complex given by M{\o}ller in the framework of Weitzenb$\ddot{o}$ck geometry. We show that the energy contained in a sphere is shared by its interior as well as exterior. We also calculate the components of the spatial momentum to evaluate the angular momentum distribution. We show that the only non-vanishing components of the angular momentum is in the Z direction.Comment: Latex. Will appear in IJMP

Equivalent Mid-Term Results of Open vs Endoscopic Gluteal Tendon Tear Repair Using Suture Anchors in Forty-Five Patients.

BackgroundLittle is known about the relative efficacy of open (OGR) vs endoscopic (EGR) gluteal tendon repair of gluteal tendon tears in minimizing pain and restoring function. Our aim is to compare these 2 surgical techniques and quantify their impact on clinical outcomes.MethodsAll patients undergoing gluteal tendon tear repair at our institution between 2015 and 2018 were retrospectively reviewed. Pain scores, limp, hip abduction strength, and the use of analgesics were recorded preoperatively and at last follow-up. The Hip disability and Osteoarthritis Outcome Score Junior and Harris Hip Score Section1 were obtained at last follow-up. Fatty degeneration was quantified using the Goutallier-Fuchs Classification (GFC). Statistical analysis was conducted using one-way analysis of variance and t-tests.ResultsForty-five patients (mean age 66, 87% females) met inclusion criteria. Average follow-up was 20.3 months. None of the 10 patients (22%) undergoing EGR had prior surgery. Of 35 patients (78%) undergoing OGR, 12 (27%) had prior hip replacement (75% via lateral approach). The OGRs had more patients with GFC ≥2 (50% vs 11%, P = .02) and used more anchors (P = .03). Both groups showed statistical improvement (P ≤ .01) for all outcomes measured. GFC >2 was independently associated with a worst limp and Harris Hip Score Section 1 score (P = .05). EGR had a statistically higher opioid use reduction (P < .05) than OGR. Other comparisons between EGR and OGR did not reach statistical significance.ConclusionIn this series, open vs endoscopic operative approach did not impact clinical outcomes. More complex tears were treated open and with more anchors. Fatty degeneration adversely impacted outcomes. Although further evaluation of the efficacy of EGR in complex tears is indicated, both approaches can be used successfully