Turbulent Time and Length Scale Measurements in High-Velocity Open Channel Flows

In high-velocity open channel flows, the measurements of air-water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air-water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8 E+5 to 7.1 E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air-water depth Y90. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95 to 0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.

Investigation of the role of cadmium sulfide in the surface passivation of lead sulfide quantum dots

Surface passivation of PbS nanocrystals (NC), resulting in strong photoluminescence, can be achieved by the introduction of CdS precursors. The role of CdS in the surface passivation of PbS NCs is uncertain, as the crystalline structure of CdS and PbS are different, which should impede effective epitaxial overgrowth. Absorption spectroscopy is used to show that the CdS precursors strongly interact with the PbS NC surface. Electron microscopy reveals that the introduction of CdS precursors results in an increased particle size, consistent with overcoating. However, we also find the process to be highly non-uniform. Nevertheless, evidence for epitaxial growth is found, suggesting that effective surface passivation may be possible.

Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants

We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular lattices, using high-temperature series expansions. We consider a model with two exchange constants J1 and J2 on a lattice that interpolates between the limits of a square lattice (J1=0), a triangular lattice (J2=J1), and decoupled linear chains (J2=0). In all cases, the susceptibility, which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature Tp. Scaling the exchange constants to get the same peak temperature shows that the susceptibilities for the square lattice and linear chain limits have similar magnitudes near the peak. Maximum deviation arises near the triangular-lattice limit, where frustration leads to much smaller susceptibility and with a flatter temperature dependence. We compare our results to the inorganic materials Cs2CuCl4 and Cs2CuBr4 and to a number of organic molecular crystals. We find that the former (Cs2CuCl4 and Cs2CuBr4) are weakly frustrated and their exchange parameters determined through the temperature dependence of the susceptibility are in agreement with neutron-scattering measurements. In contrast, the organic materials considered are strongly frustrated with exchange parameters near the isotropic triangular-lattice limit.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Half-Filled Layered Organic Superconductors and the Resonating-Valence-Bond Theory of the Hubbard-Heisenberg Model

We present a resonating-valence-bond theory of superconductivity for the Hubbard-Heisenberg model on an anisotropic triangular lattice. Our calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta('), kappa, and lambda phases of (BEDT-TTF)(2)X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)(2)X [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a d(x)(2)-y(2) superconductor with a small superfluid stiffness and a pseudogap with d(x)(2)-y(2) symmetry.

On the relationship between the critical temperature and the London penetration depth in layered organic superconductors

We present an analysis of previously published measurements of the London penetration depth of layered organic superconductors. The predictions of the BCS theory of superconductivity are shown to disagree with the measured zero temperature, in plane, London penetration depth by up to two orders of magnitude. We find that fluctuations in the phase of the superconducting order parameter do not determine the superconducting critical temperature as the critical temperature predicted for a Kosterlitz–Thouless transition is more than an order of magnitude greater than is found experimentally for some materials. This places constraints on theories of superconductivity in these materials.

Random numbers from astronomical imaging

This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined.

Achromatic optical phase shifter/modulator

We propose and demonstrate, theoretically and experimentally, a novel achromatic optical phase shifter modulator based on a frequency-domain optical delay line configured to maintain zero group delay as variable phase delay is generated by means of tilting a mirror. Compared with previously reported phase shifter modulators, e.g., based on the Pancharatnam (geometric) phase, our device is high speed and polarization insensitive and produces a large, bounded phase delay that, uniquely, is one-to-one mapped to a measurable parameter, the tilt angle.

Development of a physical and genetic map of the virulent Wolbachia strain wMelPop

We report here the construction of a physical and genetic map of the virulent Wolbachia strain, wMelPop. This map was determined by ordering 28 chromosome fragments that resulted from digestion with the restriction endonucleases FseI, ApaI, SmaI, and AscI and were resolved by pulsed-field gel electrophoresis. Southern hybridization was done with 53 Wolbachia-specific genes as probes in order to determine the relative positions of these restriction fragments and use them to serve as markers. Comparison of the resulting map with the whole genome sequence of the closely related benign Wolbachia strain, wMel, shows that the two genomes are largely conserved in gene organization with the exception of a single inversion in the chromosome.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

A two-phase strategy for detecting recombination in nucleotide sequences

Genetic recombination can produce heterogeneous phylogenetic histories within a set of homologous genes. Delineating recombination events is important in the study of molecular evolution, as inference of such events provides a clearer picture of the phylogenetic relationships among different gene sequences or genomes. Nevertheless, detecting recombination events can be a daunting task, as the performance of different recombination-detecting approaches can vary, depending on evolutionary events that take place after recombination. We previously evaluated the effects of post-recombination events on the prediction accuracy of recombination-detecting approaches using simulated nucleotide sequence data. The main conclusion, supported by other studies, is that one should not depend on a single method when searching for recombination events. In this paper, we introduce a two-phase strategy, applying three statistical measures to detect the occurrence of recombination events, and a Bayesian phylogenetic approach to delineate breakpoints of such events in nucleotide sequences. We evaluate the performance of these approaches using simulated data, and demonstrate the applicability of this strategy to empirical data. The two-phase strategy proves to be time-efficient when applied to large datasets, and yields high-confidence results.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.

Hysteresis and phase transitions in a single partially internally wetted catalyst pellet: Thermogravimetric studies

The hydrogenation of cyclohexene over palladium supported in a microporous gamma-alumina pellet is studied thermogravimetrically with a view to measuring the extent of partial internal wetting associated with the different steady state branches. As many as three steady state branches having significantly different degrees of internal wetting and reaction rates, with transitions between them, are confirmed from observations of catalyst weight change. It is seen that with reduction in catalyst activity the middle branch, obtained by condensation from a vapor filled pellet, is much more prominent without showing an evaporative transition for the range of hydrogen partial pressures used here. The catalyst activity is therefore an important parameter affecting the structure of the steady state branches. Hysteresis effects are found to occur, and the thermogravimetric results also confirm the importance of history in determining the catalyst state. The measured degree of wetting is in accordance with that estimated from a mathematical model incorporating capillary condensation effects in addition to reaction-diffusion phenomena. The same model also satisfactorily interprets the reaction rate variations and transitions seen in the present work.