The Dirichlet problem for superdegenerate differential operators

Let $L$ be an infinitely degenerate second-order linear operator defined on a bounded smooth Euclidean domain. Under weaker conditions than those of H\"ormander, we show that the Dirichlet problem associated with $L$ has a unique smooth classical solution. The proof uses the Malliavin calculus. At present, there appears to be no proof of this result using classical analytic techniques

Integrated stratigraphy of the Kimmeridge Clay Formation (Upper Jurassic) based on exposures and boreholes in south Dorset, UK

For the purposes of a high-resolution multi-disciplinary study of the Upper Jurassic Kimmeridge Clay Formation, two boreholes were drilled at Swanworth Quarry and one at Metherhills, south Dorset, UK. Together, the cores represent the first complete section through the entire formation close to the type section. We present graphic logs that record the stratigraphy of the cores, and outline the complementary geophysical and analytical data sets (gamma ray, magnetic susceptibility, total organic carbon, carbonate, [delta]13Corg). Of particular note are the new borehole data from the lowermost part of the formation which does not crop out in the type area. Detailed logs are available for download from the Kimmeridge Drilling Project web-site at http://kimmeridge.earth.ox.ac.uk/. Of further interest is a mid-eudoxus Zone positive shift in the [delta]13Corg record, a feature that is also registered in Tethyan carbonate successions, suggesting that it is a regional event and may therefore be useful for correlation. The lithostratigraphy of the cores has been precisely correlated with the nearby cliff section, which has also been examined and re-described. Magnetic-susceptibility and spectral gamma-ray measurements were made at a regular spacing through the succession, and facilitate core-to-exposure correlation. The strata of the exposure and core have been subdivided into four main mudrock lithological types: (a) medium-dark–dark-grey marl; (b) medium-dark–dark grey–greenish black shale; (c) dark-grey–olive-black laminated shale; (d) greyish-black–brownish-black mudstone. The sections also contain subordinate amounts of siltstone, limestone and dolostone. Comparison of the type section with the cores reveals slight lithological variation and notable thickness differences between the coeval strata. The proximity of the boreholes and different parts of the type section to the Purbeck–Isle of Wight Disturbance is proposed as a likely control on the thickness changes

Candidates for a possible third-generation gravitational wave detector: comparison of ring-Sagnac and sloshing-Sagnac speedmeter interferometers

Speedmeters are known to be quantum non-demolition devices and, by potentially providing sensitivity beyond the standard quantum limit, become interesting for third generation gravitational wave detectors. Here we introduce a new configuration, the sloshing-Sagnac interferometer, and compare it to the more established ring-Sagnac interferometer. The sloshing-Sagnac interferometer is designed to provide improved quantum noise limited sensitivity and lower coating thermal noise than standard position meter interferometers employed in current gravitational wave detectors. We compare the quantum noise limited sensitivity of the ring-Sagnac and the sloshing-Sagnac interferometers, in the frequency range, from 5 Hz to 100 Hz, where they provide the greatest potential benefit. We evaluate the improvement in terms of the unweighted noise reduction below the standard quantum limit, and by finding the range up to which binary black hole inspirals may be observed. The sloshing-Sagnac was found to give approximately similar or better sensitivity than the ring-Sagnac in all cases. We also show that by eliminating the requirement for maximally-reflecting cavity end mirrors with correspondingly-thick multi-layer coatings, coating noise can be reduced by a factor of approximately 2.2 compared to conventional interferometers

Use of novel sensors combining local positioning and acceleration to measure feeding behavior differences associated with lameness in dairy cattle

Time constraints for dairy farmers are an important factor contributing to the under-detection of lameness, resulting in delayed or missed treatment of lame cows within many commercial dairy herds. Hence, a need exists for flexible and affordable cow-based sensor systems capable of monitoring behaviors such as time spent feeding, which may be affected by the onset of lameness. In this study a novel neck-mounted mobile sensor system that combines local positioning and activity (acceleration) was tested and validated on a commercial UK dairy farm. Position and activity data were collected over 5 consecutive days for 19 high-yield dairy cows (10 lame, 9 non-lame) that formed a subset of a larger (120 cow) management group housed in a freestall barn. A decision tree algorithm that included sensor-recorded position and accelerometer data was developed to classify a cow as doing 1 of 3 categories of behavior: (1) feeding, (2) not feeding, and (3) out of pen for milking. For each classified behavior the mean number of bouts, the mean bout duration, and the mean total duration across all bouts was determined on a daily basis, and also separately for the time periods in between milking (morning = 0630–1300 h; afternoon = 1430–2100 h; night = 2230–0500 h). A comparative analysis of the classified cow behaviors was undertaken using a Welch -test with Benjamini-t Hochberg post-hoc correction under the null hypothesis of no differences in the number or duration of behavioral bouts between the 2 test groups of lame and nonlame cows. Analysis showed that mean total daily feeding duration was significantly lower for lame cows compared with non-lame cows. Behavior was also affected by time of day with significantly lower mean total duration of feeding and higher total duration of nonfeeding in the afternoons for lame cows compared with nonlame cows. The results demonstrate how sensors that measure both position and acceleration are capable of detecting differences in feeding behavior that may be associated with lameness. Such behavioral differences could be used in the development of predictive algorithms for the prompt detection of lameness as part of a commercially viable automated behavioral monitoring system

Stability of π\pi junction configurations in ferromagnet-superconductor heterostructures

We investigate the stability of possible order parameter configurations in clean layered heterostructures of the $SFS...FS$ type, where $S$ is a superconductor and $F$ a ferromagnet. We find that for most reasonable values of the geometric parameters (layer thicknesses and number) and of the material parameters (such as magnetic polarization, wavevector mismatch, and oxide barrier strength) several solutions of the {\it self consistent} microscopic equations can coexist, which differ in the arrangement of the sequence of ``0'' and ``$\pi$'' junction types (that is, with either same or opposite sign of the pair potential in adjacent $S$ layers). The number of such coexisting self consistent solutions increases with the number of layers. Studying the relative stability of these configurations requires an accurate computation of the small difference in the condensation free energies of these inhomogeneous systems. We perform these calculations, starting with numerical self consistent solutions of the Bogoliubov-de Gennes equations. We present extensive results for the condensation free energies of the different possible configurations, obtained by using efficient and accurate numerical methods, and discuss their relative stabilities. Results for the experimentally measurable density of states are also given for different configurations and clear differences in the spectra are revealed. Comprehensive and systematic results as a function of the relevant parameters for systems consisting of three and seven layers (one or three junctions) are given, and the generalization to larger number of layers is discussed.Comment: 17 pages, including 14 Figures. Higher resolution figures available from the author

Methods to Determine Neutrino Flux at Low Energies:Investigation of the Low ν\nu Method

We investigate the "low-$\nu$" method (developed by the CCFR/NUTEV collaborations) to determine the neutrino flux in a wide band neutrino beam at very low energies, a region of interest to neutrino oscillations experiments. Events with low hadronic final state energy $\nu<\nu_{cut}$ (of 1, 2 and 5 GeV) were used by the MINOS collaboration to determine the neutrino flux in their measurements of neutrino ($\nu_\mu$) and antineutrino (\nub_\mu) total cross sections. The lowest $\nu_\mu$ energy for which the method was used in MINOS is 3.5 GeV, and the lowest \nub_\mu energy is 6 GeV. At these energies, the cross sections are dominated by inelastic processes. We investigate the application of the method to determine the neutrino flux for $\nu_\mu$, \nub_\mu energies as low as 0.7 GeV where the cross sections are dominated by quasielastic scattering and $\Delta$(1232) resonance production. We find that the method can be extended to low energies by using $\nu_{cut}$ values of 0.25 and 0.50 GeV, which is feasible in fully active neutrino detectors such as MINERvA.Comment: 25 pages, 32 figures, to be published in European Physics Journal

Entangled Quantum Clocks for Measuring Proper-Time Difference

We report that entangled pairs of quantum clocks (non-degenerate quantum bits) can be used as a specialized detector for precisely measuring difference of proper-times that each constituent quantum clock experiences. We describe why the proposed scheme would be more precise in the measurement of proper-time difference than a scheme of two-separate-quantum-clocks. We consider possibilities that the proposed scheme can be used in precision test of the relativity theory.Comment: no correction, 4 pages, RevTe

Kinetic theory of point vortices: diffusion coefficient and systematic drift

We develop a kinetic theory for point vortices in two-dimensional hydrodynamics. Using standard projection operator technics, we derive a Fokker-Planck equation describing the relaxation of a ``test'' vortex in a bath of ``field'' vortices at statistical equilibrium. The relaxation is due to the combined effect of a diffusion and a drift. The drift is shown to be responsible for the organization of point vortices at negative temperatures. A description that goes beyond the thermal bath approximation is attempted. A new kinetic equation is obtained which respects all conservation laws of the point vortex system and satisfies a H-theorem. Close to equilibrium this equation reduces to the ordinary Fokker-Planck equation.Comment: 50 pages. To appear in Phys. Rev.

Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes

Equations for submanifolds, which correspond to embeddings of the four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are presented in convenient form in general case. Several specific examples are considered.Comment: 7 pages, LaTeX, the mathematical part of this paper is based on the withdrawn preprint arXiv:1012.0320 [gr-qc