Constructions in Sasakian Geometry

We describe various constructions in Sasakian geometry. First we generalize the join construction of the first two authors to arbitrary Sasakian manifolds. We then give several examples, including ones which prove the existence of Sasakian-Einstein metrics on manifolds homeomorphic to $S^2\times S^5.$ Then we use a generalization of the join construction due to Lerman, namely contact fibre bundles, to give a theorem constructing toric Sasakian structures. Finally, we explicitly construct regular toric Sasakian structures on all simply connected regular contact manifolds in dimension five.Comment: Some minor errors corrected. References updated. To appear in Mathematische Zeitschrif

Native Language Identification on Text and Speech

This paper presents an ensemble system combining the output of multiple SVM classifiers to native language identification (NLI). The system was submitted to the NLI Shared Task 2017 fusion track which featured students essays and spoken responses in form of audio transcriptions and iVectors by non-native English speakers of eleven native languages. Our system competed in the challenge under the team name ZCD and was based on an ensemble of SVM classifiers trained on character n-grams achieving 83.58% accuracy and ranking 3rd in the shared task.Comment: Proceedings of the Workshop on Innovative Use of NLP for Building Educational Applications (BEA

Postbuckling response of long thick plates loaded in compression including higher order transverse shearing effects

Buckling and postbuckling results are presented for compression-loaded simply-supported aluminum plates and composite plates with a symmetric lay-up of thin + or - 45 deg plies composed of many layers. Buckling results for aluminum plates of finite length are given for various length-to-width ratios. Asymptotes to the curves based on buckling results give N(sub xcr) for plates of infinite length. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: Classical von Karman theory using the Kirchoff assumptions, first-order shear deformation theory, higher-order shear deformation theory, and 3-D flexibility theory. Present results indicate that the 3-D flexibility theory gives the lowest buckling loads. The higher-order shear deformation theory has fewer unknowns than the 3-D flexibility theory but does not take into account through-the-thickness effects. The figures presented show that small differences occur in the average longitudinal direct stress resultants from the four theories that are functions of applied end-shortening displacement

Can Non-Equilibrium Spin Hall Accumulation be Induced in Ballistic Nanostructures?

We demonstrate that flow of longitudinal unpolarized current through a ballistic two-dimensional electron gas with Rashba spin-orbit coupling will induce nonequilibrium spin accumulation which has opposite sign for the two lateral edges and it is, therefore, the principal observable signature of the spin Hall effect in two-probe semiconductor nanostructures. The magnitude of its out-of-plane component is gradually diminished by static disorder, while it can be enhanced by an in-plane transverse magnetic field. Moreover, our prediction of the longitudinal component of the spin Hall accumulation, which is insensitive to the reversal of the bias voltage, offers a smoking gun to differentiate experimentally between the extrinsic, intrinsic, and mesoscopic spin Hall mechanisms.Comment: 5 pages, 3 color EPS figures; published versio

Modeling of diffusion of injected electron spins in spin-orbit coupled microchannels

We report on a theoretical study of spin dynamics of an ensemble of spin-polarized electrons injected in a diffusive microchannel with linear Rashba and Dresselhaus spin-orbit coupling. We explore the dependence of the spin-precession and spin-diffusion lengths on the strengths of spin-orbit interaction and external magnetic fields, microchannel width, and orientation. Our results are based on numerical Monte Carlo simulations and on approximate analytical formulas, both treating the spin dynamics quantum-mechanically. We conclude that spin-diffusion lengths comparable or larger than the precession-length occur i) in the vicinity of the persistent spin helix regime for arbitrary channel width, and ii) in channels of similar or smaller width than the precession length, independent of the ratio of Rashba and Dresselhaus fields. For similar strengths of the Rashba and Dresselhaus fields, the steady-state spin-density oscillates or remains constant along the channel for channels parallel to the in-plane diagonal crystal directions. An oscillatory spin-polarization pattern tilted by 45$^{\circ}$ with respect to the channel axis is predicted for channels along the main cubic crystal directions. For typical experimental system parameters, magnetic fields of the order of Tesla are required to affect the spin-diffusion and spin-precession lengths.Comment: Replaced with final version (some explanations and figures improved). 8 pages, 6 figure