Changes in precipitation and river flow in northeast Turkey: associations with the North Atlantic Oscillation

This paper explores the relationships between the North Atlantic Oscillation (NAO) index and precipitation and river flow over northeast Turkey. Precipitation totals and maximum, mean and minimum river flow are analysed at the seasonal scale for 12 and 10 stations, respectively. Pearson’s and Mann-Kendall correlation tests are applied to assess relationships between the NAO index and precipitation and river flow metrics, and to detect trends in time-series. Autumn precipitation totals display significant increasing trends, especially for coastal stations, while inland stations show significant increasing trends for spring precipitation. Minimum and maximum river flow decreases significantly for spring and summer. This tendency implies varying conditions towards a drier regime. Seasonal precipitation patterns show a negative association with the NAO for December–January–February (DJF), March–April–May (MAM) and September–October–November (SON) for some stations. Positive associations between the NAO and winter-extended winter (December–March) river flows are detected for some stations in northeast Turkey

Bowen-York Tensors

There is derived, for a conformally flat three-space, a family of linear second-order partial differential operators which send vectors into tracefree, symmetric two-tensors. These maps, which are parametrized by conformal Killing vectors on the three-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular these maps send source-free electric fields into TT-tensors. Moreover, if the original vector field is the Coulomb field on $\mathbb{R}^3\backslash \lbrace0\rbrace$, the resulting tensor fields on $\mathbb{R}^3\backslash \lbrace0\rbrace$ are nothing but the family of TT-tensors originally written down by Bowen and York.Comment: 12 pages, Contribution to CQG Special Issue "A Spacetime Safari: Essays in Honour of Vincent Moncrief

Multi-beam Energy Moments of Multibeam Particle Velocity Distributions

High resolution electron and ion velocity distributions, f(v), which consist of N effectively disjoint beams, have been measured by NASA's Magnetospheric Multi-Scale Mission (MMS) observatories and in reconnection simulations. Commonly used standard velocity moments generally assume a single mean-flow-velocity for the entire distribution, which can lead to counterintuitive results for a multibeam f(v). An example is the (false) standard thermal energy moment of a pair of equal and opposite cold particle beams, which is nonzero even though each beam has zero thermal energy. By contrast, a multibeam moment of two or more beams has no false thermal energy. A multibeam moment is obtained by taking a standard moment of each beam and then summing over beams. In this paper we will generalize these notions, explore their consequences and apply them to an f(v) which is sum of tri-Maxwellians. Both standard and multibeam energy moments have coherent and incoherent forms. Examples of incoherent moments are the thermal energy density, the pressure and the thermal energy flux (enthalpy flux plus heat flux). Corresponding coherent moments are the bulk kinetic energy density, the RAM pressure and the bulk kinetic energy flux. The false part of an incoherent moment is defined as the difference between the standard incoherent moment and the corresponding multibeam moment. The sum of a pair of corresponding coherent and incoherent moments will be called the undecomposed moment. Undecomposed moments are independent of whether the sum is standard or multibeam and therefore have advantages when studying moments of measured f(v).Comment: 27 single-spaced pages. Three Figure

Prolongations of Geometric Overdetermined Systems

We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on the dimension of the solution space.Comment: 22 pages. In the second version, a comparison with the classical theory of prolongations was added. In this third version more details were added concerning our construction and especially the use of Kostant's computation of Lie algebra cohomolog

Super-Alfv\'enic propagation of reconnection signatures and Poynting flux during substorms

The propagation of reconnection signatures and their associated energy are examined using kinetic particle-in-cell simulations and Cluster satellite observations. It is found that the quadrupolar out-of-plane magnetic field near the separatrices is associated with a kinetic Alfv\'en wave. For magnetotail parameters, the parallel propagation of this wave is super-Alfv\'enic (V_parallel ~ 1500 - 5500 km/s) and generates substantial Poynting flux (S ~ 10^-5 - 10^-4 W/m^2) consistent with Cluster observations of magnetic reconnection. This Poynting flux substantially exceeds that due to frozen-in ion bulk outflows and is sufficient to generate white light aurora in the Earth's ionosphere.Comment: Submitted to PRL on 11/1/2010. Resubmitted on 4/5/201

Invariants of Artinian Gorenstein Algebras and Isolated Hypersurface Singularities

We survey our recently proposed method for constructing biholomorphic invariants of quasihomogeneous isolated hypersurface singularities and, more generally, invariants of graded Artinian Gorenstein algebras. The method utilizes certain polynomials associated to such algebras, called nil-polynomials, and we compare them with two other classes of polynomials that have also been used to produce invariants.Comment: 13 page

Gauged vortices in a background

We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class of the abelian Higgs model approximately truncates to a finite-dimensional moduli space with a Kaehler structure. For the case where the vortices live on a 2-sphere, we explain how localisation formulas on the moduli spaces can be used to compute explicitly the partition function of the vortex gas interacting with a background potential. The coefficients of this analytic function provide geometrical data about the Kaehler structures, the simplest of which being their symplectic volume (computed previously by Manton using an alternative argument). We use the partition function to deduce simple results on the thermodynamics of the vortex system; in particular, the average height on the sphere is computed and provides an interesting effective picture of the ground state.Comment: Final version: 22 pages, LaTeX, 1 eps figur

Modelling and simulation of fluid-structure interactions in human snoring

Snoring noise is generated by vibration of the soft tissues of the upper airway, principally those that form the back of the roof of the mouth (the soft palate) and its conical extension (the uvula). In addition to discord with bed partners, snorers are at much greater risk of obstructive sleep apnoea. This sleep-related breathing disorder is characterised by episodic upper airway obstruction with accompanying sleep disruption and consequent excessive daytime sleepiness, as well as an elevated risk of accidents and cardiovascular disease. The instability that leads to flow-induced oscillations characteristic of inspiratory snoring in the human upper airway may be modelled using a cantilevered flexible plate in a mean channel flow. However, the cantilever in existing models strictly only captures the dynamics of the uvula. In a more complete model, these dynamics will be augmented by their interaction with the motions of the soft palate—itself a flexible structure of higher effective stiffness—from which the uvula extends. To investigate how the elasticity of the soft palate affects uvula motion and their combined susceptibility to flow-induced oscillation a modification is made to the standard model. In a one-dimensional cantilevered flexible plate we allow thickness to vary as a function of length, thus effecting local changes in inertia and flexural rigidity.The overall cantilever therefore comprises a section representing the soft palate followed by a section of lower thickness that represents the uvula. The cantilever is attached to a rigid wall (hard palate) separating upper (nasal) and lower (oral) inlets of a rigid-walled channel (pharynx) conveying a viscous flow. This model is formulated using the open-source finite-element software library oomph-lib. A parametric study is performed in which the uvula-to-soft palate length and thickness ratios are varied whilst keeping their combined length constant. Results show that there is a critical uvula-length fraction that determines whether the uvula stabilises or destabilises the system. A relatively ‘short’ uvula swings out of phase with the soft palate and these oscillations are observed to decay; the mode shapes involved are not predicted by a uniform-thickness plate model. By contrast, if the uvula is relatively ‘long’ the flexible plate motion is isolated to the uvular section and the oscillations grow in amplitude, indicating a net energy transfer from fluid to structure. Increasing the thickness, hence inertia and flexural rigidity, of a ‘short’ uvula, e.g., by oedema, makes the fluid-structure system more unstable. In this case if the oedema were aggrevated by the vibratory mechanical insult then it would be self-sustaining and imply a bidirectional relationship between snoring and oedema of the uvula.Anatomical variability is common in the lengths of the soft palate and uvula which may make some people more susceptible than others to uvulopalatal snoring. Palatal surgery for snoring has proved highly variable in its effectiveness. Modelling of palatal motion using this approach may help guide patient selection for and type of soft-palate surgery applied to treat this common and potentially disabling condition

Quantized Maxwell Theory in a Conformally Invariant Gauge

Maxwell theory can be studied in a gauge which is invariant under conformal rescalings of the metric, and first proposed by Eastwood and Singer. This paper studies the corresponding quantization in flat Euclidean 4-space. The resulting ghost operator is a fourth-order elliptic operator, while the operator P on perturbations of the potential is a sixth-order elliptic operator. The operator P may be reduced to a second-order non-minimal operator if a dimensionless gauge parameter tends to infinity. Gauge-invariant boundary conditions are obtained by setting to zero at the boundary the whole set of perturbations of the potential, jointly with ghost perturbations and their normal derivative. This is made possible by the fourth-order nature of the ghost operator. An analytic representation of the ghost basis functions is also obtained.Comment: 8 pages, plain Tex. In this revised version, the calculation of ghost basis functions has been amended, and the presentation has been improve