Thin-film flow in helically wound rectangular channels with small torsion

Laminar gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section with small torsion in which the fluid depth is small is considered. Neglecting the entrance and exit regions we obtain the steady-state solution that is independent of position along the axis of the channel, so that the flow, which comprises a primary flow in the direction of the axis of the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity and pressure in terms of the free-surface shape, the latter satisfying a non-linear ordinary differential equation that has a simple exact solution in the special case of a channel of rectangular cross-section. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier–Stokes equations. The present work has particular relevance to spiral particle separators used in the mineral-processing industry. The validity of an assumption commonly used in modelling flow in spiral separators, namely that the flow in the outer region of the separator cross-section is described by a free vortex, is shown to depend on the problem parameters

Order parameters in the Verwey phase transition

The Verwey phase transition in magnetite is analyzed on the basis of the Landau theory. The free energy functional is expanded in a series of components belonging to the primary and secondary order parameters. A low-temperature phase with the monoclinic P2/c symmetry is a result of condensation of two order parameters X_3 and \Delta_5 . The temperature dependence of the shear elastic constant C_44 is derived and the mechanism of its softening is discussed.Comment: 4 pages, 1 figur

Screen-printed potentiometric Ag/AgCl chloride sensors: Lifetime performance and their use in soil salt measurements

Silver – silver chloride electrodes (Ag/AgCl) for the detection of chloride ions were fabricated using thick-film technology. Five different formulations were prepared and chloride responses were investigated over time. Almost identical and near Nernstian responses were observed over the first 162 days with an average chloride sensitivity for all formulations of -51.12 mV ± 0.45 mV per decade change in chloride concentration compared with a value of -50.59 mV ± 0.01 mV over 388 days for the best two formulations. After 6-months continuous immersion in tap water, pastes formulated with a glass binder began to exhibit a loss in sensitivity whilst those formulated from a commercial thick-film dielectric paste remained functional for the best part of a year. This difference in lifetime performance is attributed to the inclusion of proprietary additives in the commercial paste aiding adhesion and minimising AgCl leaching. The mechanical and chemical robustness of these electrodes has been demonstrated through their ability to detect changing levels of chloride when immersed in soil columns. This particular capacity will make them an invaluable tool in the fields of hydrology, agricultural science, soil science and environmental science

Analytical modeling of the structureborne noise path on a small twin-engine aircraft

The structureborne noise path of a six passenger twin-engine aircraft is analyzed. Models of the wing and fuselage structures as well as the interior acoustic space of the cabin are developed and used to evaluate sensitivity to structural and acoustic parameters. Different modeling approaches are used to examine aspects of the structureborne path. These approaches are guided by a number of considerations including the geometry of the structures, the frequency range of interest, and the tractability of the computations. Results of these approaches are compared with experimental data

How Peclet number affects microstructure and transient cluster aggregation in sedimenting colloidal suspensions

We study how varying the P \'eclet number (Pe) affects the steady state sedimentation of colloidal particles that interact through short-ranged attractions. By employing a hybrid molecular dynamics simulation method we demonstrate that the average sedimentation velocity changes from a non- monotonic dependence on packing fraction {\phi} at low Pe numbers, to a monotonic decrease with {\phi} at higher Pe numbers. At low Pe number the pair correlation functions are close to their equilibrium values, but as the Pe number increases, important deviations from equilibrium forms are observed. Although the attractive forces we employ are not strong enough to form permanent clusters, they do induce transient clusters whose behaviour is also affected by Pe number. In particular, clusters are more likely to fragment and less likely to aggregate at larger Pe numbers, and the probability of finding larger clusters decreases with increasing Pe number. Interestingly, the life-time of the clusters is more or less independent of Pe number in the range we study. Instead, the change in cluster distribution occurs because larger clusters are less likely to form with increasing Pe number. These results illustrate some of the subtleties that occur in the crossover from equilibrium like to purely non-equilibrium behaviour as the balance between convective and thermal forces changes.Comment: 8 page

Measuring atomic NOON-states and using them to make precision measurements

A scheme for creating NOON-states of the quasi-momentum of ultra-cold atoms has recently been proposed [New J. Phys. 8, 180 (2006)]. This was achieved by trapping the atoms in an optical lattice in a ring configuration and rotating the potential at a rate equal to half a quantum of angular momentum . In this paper we present a scheme for confirming that a NOON-state has indeed been created. This is achieved by spectroscopically mapping out the anti-crossing between the ground and first excited levels by modulating the rate at which the potential is rotated. Finally we show how the NOON-state can be used to make precision measurements of rotation.Comment: 14 preprint pages, 7 figure

Air Shower Simulation and Hadronic Interactions

The aim of this report of the Working Group on Hadronic Interactions and Air Shower Simulation is to give an overview of the status of the field, emphasizing open questions and a comparison of relevant results of the different experiments. It is shown that an approximate overall understanding of extensive air showers and the corresponding hadronic interactions has been reached. The simulations provide a qualitative description of the bulk of the air shower observables. Discrepancies are however found when the correlation between measurements of the longitudinal shower profile are compared to that of the lateral particle distributions at ground. The report concludes with a list of important problems that should be addressed to make progress in understanding hadronic interactions and, hence, improve the reliability of air shower simulations.Comment: Working Group report given at UHECR 2012 Symposium, CERN, Feb. 2012. Published in EPJ Web of Conferences 53, 01007 (2013

Predictive and prognostic modelling and simulation of coating failures due to corrosion and mechanical failures

This research presents analytical and mathematical modelling of coating failures within industrial components, structures, mobile assets and systems due to corrosive degradation and mechanical fracture. These failures lead to serval surface problems, therefore contact mechanics and electrochemistry approaches incorporating induced residual stresses have been adopted to develop a comprehensive solution for the prediction prognostic of such failures. Experimental study of film cracking and its propagation into substrates, interfacial transient behaviours and film-substrate system has been conducted. A parallel study of corrosive degradation to include cathodic delamination, cathodic blistering and tribo-corrosion of films has been conducted. Experimental and analytical studies of induced residual stresses within the coating and their effects on failure mechanisms and propagation have been completed. A detailed investigation of elastic mismatch at the interfacial contact and interfacial crack tip field has been performed and a complex stress intensity factor is presented. Mathematical derivation of oscillatory singularity, mode mix and interfacial fracture criterion to include adhesion are presented. This paper presents novel mathematical modelling incorporating interfacial crack propagating, diffusion of corrosive species and cathodic blistering for prediction and prognoses of coating failures

Qudit Quantum State Tomography

Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First we show how non-orthogonal measurement allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum state tomography can be performed for multi qudits with a specific example illustrating how to achieve this in one and two qutrit systems.Comment: 6 pages, 4 figures, submitted to PR

Self Interacting Dark Matter in the Solar System

Weakly coupled, almost massless, spin 0 particles have been predicted by many extensions of the standard model of particle physics. Recently, the PVLAS group observed a rotation of polarization of electromagnetic waves in vacuum in the presence of transverse magnetic field. This phenomenon is best explained by the existence of a weakly coupled light pseudoscalar particle. However, the coupling required by this experiment is much larger than the conventional astrophysical limits. Here we consider a hypothetical self-interacting pseudoscalar particle which couples weakly with visible matter. Assuming that these pseudoscalars pervade the galaxy, we show that the solar limits on the pseudoscalar-photon coupling can be evaded.Comment: 17 pages, 2 figure