Geometric phases for corotating elliptical vortex patches

We describe a geometric phase that arises when two elliptical vortex patches corotate. Using the Hamiltonian moment model of Melander, Zabusky, and Styczek [J. Fluid Mech. 167, 95–115 (1986)] we consider two corotating uniform elliptical patches evolving according to the second order truncated equations of the model. The phase is computed in the adiabatic setting of a slowly varying Hamiltonian as in the work of Hannay [J. Phys. A 18, 221–230 (1985)] and Berry [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We also discuss the geometry of the symplectic phase space of the model in the context of nonadiabatic phases. The adiabatic phase appears in the orientation angle of each patch—it is similiar in form and is calculated using a multiscale perturbation procedure as in the point vortex configuration of Newton [Physica D 79, 416–423 (1994)] and Shashikanth and Newton [J. Nonlinear Sci. 8, 183–214 (1998)], however, an extra factor due to the internal stucture of the patch is present. The final result depends on the initial orientation of the patches unlike the phases in the works of Hannay and Berry [J. Phys. A 18, 221–230 (1985)]; [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We then show that the adiabatic phase can be interpreted as the holonomy of a connection on the trivial principal fiber bundle pi:T2×S1-->S1, where T2 is identified with the product of the momentum level sets of two Kirchhoff vortex patches and S1 is diffeomorphic to the momentum level set of two point vortex motion. This two point vortex motion is the motion that the patch centroids approach in the adiabatic limit

Challenges posed by non-standard neutrino interactions in the determination of δCP\delta_{CP} at DUNE

One of the primary objectives of Deep Underground Neutrino Experiment (DUNE) is to discover the leptonic CP violation and to identify it's source. In this context, we study the impact of non-standard neutrino interactions (NSIs) on observing the CP violation signal at DUNE. We explore the impact of various parameter degeneracies introduced by non-zero NSI and identify which of these can influence the CP violation sensitivity and CP precision of DUNE, by considering NSI both in data and in theory. In particular, we study how the CP sensitivity of DUNE is affected because of the intrinsic hierarchy degeneracy which occurs when the diagonal NSI parameter $\epsilon_{ee}=-1$ and $\delta_{CP}= \pm 90^{\circ}$

Discrete approximations for Markov-chain filters

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Structure of adsorbed organometallic rhodium: model single atom catalysts

We have determined the structure of a complex rhodium carbonyl chloride [Rh(CO)(2)Cl] molecule adsorbed on the TiO2 (110) surface by the normal incidence x-ray standing wave technique. The data show that the technique is applicable to reducible oxide systems and that the dominant adsorbed species is undissociated with Rh binding atop bridging oxygen and to the Cl found close to the fivefold coordinated Ti ions in the surface. A minority geminal dicarboryl species, where Rh-Cl bond scission has occurred, is found bridging the bridging oxygen ions forming a high-symmetry site

The Strong Levinson Theorem for the Dirac Equation

We consider the Dirac equation in one space dimension in the presence of a symmetric potential well. We connect the scattering phase shifts at E=+m and E=-m to the number of states that have left the positive energy continuum or joined the negative energy continuum respectively as the potential is turned on from zero.Comment: Submitted to Physical Review Letter

Flexible conformable hydrophobized surfaces for turbulent flow drag reduction

In recent years extensive work has been focused onto using superhydrophobic surfaces for drag reduction applications. Superhydrophobic surfaces retain a gas layer, called a plastron, when submerged underwater in the Cassie-Baxter state with water in contact with the tops of surface roughness features. In this state the plastron allows slip to occur across the surface which results in a drag reduction. In this work we report flexible and relatively large area superhydrophobic surfaces produced using two different methods: Large roughness features were created by electrodeposition on copper meshes; Small roughness features were created by embedding carbon nanoparticles (soot) into Polydimethylsiloxane (PDMS). Both samples were made into cylinders with a diameter under 12 mm. To characterize the samples, scanning electron microscope (SEM) images and confocal microscope images were taken. The confocal microscope images were taken with each sample submerged in water to show the extent of the plastron. The hydrophobized electrodeposited copper mesh cylinders showed drag reductions of up to 32% when comparing the superhydrophobic state with a wetted out state. The soot covered cylinders achieved a 30% drag reduction when comparing the superhydrophobic state to a plain cylinder. These results were obtained for turbulent flows with Reynolds numbers 10,000 to 32,500

Children with severe malnutrition: can those at highest risk of death be identified with the WHO protocol?

Background With strict adherence to international recommended treatment guidelines, the case fatality for severe malnutrition ought to be less than 5%. In African hospitals, fatality rates of 20% are common and are often attributed to poor training and faulty case management. Improving outcome will depend upon the identification of those at greatest risk and targeting limited health resources. We retrospectively examined the major risk factors associated with early (<48 h) and late in-hospital death in children with severe malnutrition with the aim of identifying admission features that could distinguish a high-risk group in relation to the World Health Organization (WHO) guidelines. Methods and Findings Of 920 children in the study, 176 (19%) died, with 59 (33%) deaths occurring within 48 h of admission. Bacteraemia complicated 27% of all deaths: 52% died before 48 h despite 85% in vitro antibiotic susceptibility of cultured organisms. The sensitivity, specificity, and likelihood ratio of the WHO-recommended “danger signs” (lethargy, hypothermia, or hypoglycaemia) to predict early mortality was 52%, 84%, and 3.4% (95% confidence interval [CI] = 2.2 to 5.1), respectively. In addition, four bedside features were associated with early case fatality: bradycardia, capillary refill time greater than 2 s, weak pulse volume, and impaired consciousness level; the presence of two or more features was associated with an odds ratio of 9.6 (95% CI = 4.8 to 19) for early fatality (p < 0.0001). Conversely, the group of children without any of these seven features, or signs of dehydration, severe acidosis, or electrolyte derangements, had a low fatality (7%). Conclusions Formal assessment of these features as emergency signs to improve triage and to rationalize manpower resources toward the high-risk groups is required. In addition, basic clinical research is necessary to identify and test appropriate supportive treatments

Levinson's theorem for the Schr\"{o}dinger equation in two dimensions

Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically symmetric potential in two dimensions is re-established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison with Levinson's theorem in non-critical case, the half bound state for $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of $P$ wave at zero energy to increase an additional $\pi$.Comment: Latex 11 pages, no figure and accepted by P.R.A (in August); Email: [email protected], [email protected]