Multivariate Diophantine equations with many solutions

We show that for each n-tuple of positive rational integers (a_1,..,a_n) there are sets of primes S of arbitrarily large cardinality s such that the solutions of the equation a_1x_1+...+a_nx_n=1 with the x_i all S-units are not contained in fewer than exp((4+o(1))s^{1/2}(log s)^{-1/2}) proper linear subspaces of C^n. This generalizes a result of Erdos, Stewart and Tijdeman for m=2 [Compositio 36 (1988), 37-56]. Furthermore we prove that for any algebraic number field K of degree n, any integer m with 1<=m<n, and any sufficiently large s there are integers b_0,...,b_m in a number field which are linearly independent over the rationals, and prime numbers p_1,...,p_s, such that the norm polynomial equation |N_{K/Q}(b_0+b_1x_1+...+b_mx_m)|=p_1^{z_1}...p_s^{z_s} has at least exp{(1+o(1)){n/m}s^{m/n}(log s)^{-1+m/n}) solutions in integers x_1,..,x_m,z_1,..,z_s. This generalizes a result of Moree and Stewart [Indag. Math. 1 (1990), 465-472]. Our main tool, also established in this paper, is an effective lower bound for the number of ideals in a number field K of norm <=X composed of prime ideals which lie outside a given finite set of prime ideals T and which have norm <=Y. This generalizes a result of Canfield, Erdos and Pomerance [J. Number Th. 17 (1983), 1-28], and of Moree and Stewart (see above).Comment: 29 page

Numerical and experimental studies of the natural convection within a horizontal cylinder

Numerical solutions are obtained for the quasi-compressible Navier-Stokes equations governing the time-dependent natural convection within a horizontal cylinder. The early flow development and wall heat transfer are obtained after a uniformly cold wall is imposed as a boundary condition on the cylinder. Results are also obtained for a time-varying cold wall as a boundary condition with windward explicit differencing used for the numerical solutions. The viscous truncation error associated with this scheme is controlled so that first-order accuracy is maintained in time and space. Experiments within a small-scale instrumented horizontal cylinder revealed the time development of the temperature distribution across the boundary layer as well as the decay of wall heat transfer with time. Agreement between temperature distributions obtained experimentally and numerically was generally good. The time decay of the dimensionless ratio of the Nusselt number to the one-fourth power of the Grashof number is found both numerically and experimentally, and good agreement is obtained between these two results over most of the cylinder wall

p-wave Feshbach molecules

We have produced and detected molecules using a p-wave Feshbach resonance between 40K atoms. We have measured the binding energy and lifetime for these molecules and we find that the binding energy scales approximately linearly with magnetic field near the resonance. The lifetime of bound p-wave molecules is measured to be 1.0 +/- 0.1 ms and 2.3 +/- 0.2 ms for the m_l = +/- 1 and m_l = 0 angular momentum projections, respectively. At magnetic fields above the resonance, we detect quasi-bound molecules whose lifetime is set by the tunneling rate through the centrifugal barrier

Heat Capacity Measurements in Pulsed Magnetic Fields

The new NHMFL 60T quasi-continuous magnet produces a flat-top field for a period of 100 ms at 60 Tesla, and for longer time at lower fields, e.g. 0.5 sec at 35 Tesla. We have developed for the first time the capability to measure heat capacity at very high magnetic fields in the NHMFL 60 T quasi-continuous magnet at LANL, using a probe built out of various plastic materials. The field plateau allows us to utilize a heat-pulse method to obtain heat capacity data. Proof-of-principle heat capacity experiments were performed on a variety of correlated electron systems. Both magnet performance characteristics and physical properties of various materials studied hold out a promise of wide application of this new tool.Comment: 6 pages, 3 figures, World Scientific Pub. Co., to be publishe

Data Mining to Uncover Heterogeneous Water Use Behaviors From Smart Meter Data

Knowledge on the determinants and patterns of water demand for different consumers supports the design of customized demand management strategies. Smart meters coupled with big data analytics tools create a unique opportunity to support such strategies. Yet, at present, the information content of smart meter data is not fully mined and usually needs to be complemented with water fixture inventory and survey data to achieve detailed customer segmentation based on end use water usage. In this paper, we developed a data‐driven approach that extracts information on heterogeneous water end use routines, main end use components, and temporal characteristics, only via data mining existing smart meter readings at the scale of individual households. We tested our approach on data from 327 households in Australia, each monitored with smart meters logging water use readings every 5 s. As part of the approach, we first disaggregated the household‐level water use time series into different end uses via Autoflow. We then adapted a customer segmentation based on eigenbehavior analysis to discriminate among heterogeneous water end use routines and identify clusters of consumers presenting similar routines. Results revealed three main water end use profile clusters, each characterized by a primary end use: shower, clothes washing, and irrigation. Time‐of‐use and intensity‐of‐use differences exist within each class, as well as different characteristics of regularity and periodicity over time. Our customer segmentation analysis approach provides utilities with a concise snapshot of recurrent water use routines from smart meter data and can be used to support customized demand management strategies.TU Berlin, Open-Access-Mittel - 201

TETRA Observation of Gamma Rays at Ground Level Associated with Nearby Thunderstorms

Terrestrial Gamma ray Flashes (TGFs) -- very short, intense bursts of electrons, positrons, and energetic photons originating from terrestrial thunderstorms -- have been detected with satellite instruments. TETRA, an array of NaI(Tl) scintillators at Louisiana State University, has now been used to detect similar bursts of 50 keV to over 2 MeV gamma rays at ground level. After 2.6 years of observation, twenty-four events with durations 0.02- 4.2 msec have been detected associated with nearby lightning, three of them coincident events observed by detectors separated by ~1000 m. Nine of the events occurred within 6 msec and 3 miles of negative polarity cloud-to-ground lightning strokes with measured currents in excess of 20 kA. The events reported here constitute the first catalog of TGFs observed at ground level in close proximity to the acceleration site.Comment: To be published in Journal of Geophysical Research: Space Phys. 118,

Laser spot welding of laser textured steel to aluminium

Laser welding of dissimilar metals (steel and aluminium) was investigated with the aim to increase the maximum tensile shear load of the Fe-Al joints. The increase was achieved by texturing the surface of steel prior to the laser spot welding process which was performed in a lap-joint configuration with the steel positioned on top of the aluminium and with a texture faced down to the aluminium surface. This configuration enabled an increase of the bonding area of the joints, because the molten aluminium filled in the gaps of the texture, without the need of increasing the process energy which typically leads to the growth of the intermetallic compounds. Different textures (containing hexagonally arranged craters, parallel lines, grid and spiral patterns) were tested with different laser welding parameters. The Fe-Al joints obtained with the textured steel were found to have up to 25% higher maximum tensile-shear load than the joints obtained with the untextured steel