Basins of attraction in nonsmooth models of gear rattle

This paper is concerned with the computation of the basins of attraction of a simple one degree-of-freedom backlash oscillator using cell-to-cell mapping techniques. This analysis is motivated by the modeling of order vibration in geared systems. We consider both a piecewise-linear stiffness model and a simpler infinite stiffness impacting limit. The basins reveal rich and delicate dynamics, and we analyze some of the transitions in the system's behavior in terms of smooth and discontinuity-induced bifurcations. The stretching and folding of phase space are illustrated via computations of the grazing curve, and its preimages, and manifold computations of basin boundaries using DsTool (Dynamical Systems Toolkit)

Revisiting Chandler on the theory of the firm

The essay provides a review of Alfred Chandler's contribution to the theory of the firm in his three main works: Strategy and Structure (1962), The Visible Hand (1977) and Scale and Scope (1990). Focusing on the economic components of Chandler's analysis, it examines linkages to subsequent developments in the theory of the firm, including the resource based view. It discusses possible extensions of the Chandlerian perspective incorporating elements of capital market transaction cost theor

Flow patterns and cleaning behaviour of horizontal liquid jets impinging on angled walls

Liquid jets are widely used in cleaning operations in the food sector. Morison and Thorpe (2002) reported an experimental investigation of the flow patterns and cleaning behaviour of horizontal jets impinging on vertical walls. The Wilson et al. (2012) model, which described Morison and Thorpe's flow pattern data well, is extended to describe the flow pattern generated by a liquid jet, approaching a surface at a given angle to the horizontal, impinging on a plate inclined at a known angle to the vertical. The results are compared with experimental data collected for horizontal water jets impinging on inclined Perspex and glass plates. Tests employed nozzle diameters of 1, 2 and 3mm at room temperature, using flow rates of 0.78–2.23gs−1, 3.7–9.9gs−1 and 7.1–17.3gs−1 (0.025–0.062m3h−1) respectively. These are lower than industrial cleaning flow rates. The angle at which the horizontal jet impinged on the plate was varied from 30° to 120°. Two important dimensions are evaluated: (i) the width of the fast moving radial flow zone on the plate (the region bounded by the film jump, the feature similar to a hydraulic jump) at the plane of impingement; (ii) the distance on the plate to which the radial flow zone extends above the point of impingement. Both are described reasonably well by the model. Empirical relationships are reported for the width of the wetted region at the level of impingement, and the maximum width of the draining film. A short study of cleaning of layers of washable paint on glass, similar to the tests reported by Morison and Thorpe, show that the cleaning model recently developed by Wilson et al. (2014) gives a good description of the initial cleaning of such layers using an impinging stationary coherent water jet.A PhD scholarship for TW from Chengda Engineering Co. is gratefully acknowledged.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.fbp.2014.09.00

Lead isotopes in deep-sea coral skeletons: ground-truthing and a first deglacial Southern Ocean record

Past changes in seawater lead (Pb) isotopes record the temporal evolution of anthropogenic pollution, continental weathering inp uts, and ocean current transport. To advance our ability to reconstruct this signature, we present methodological developments that allow us to make precise and accurate Pb isoto pe measurements on deep-sea coral aragonite, and apply our approach to generate the f irst Pb isotope record for the glacial to deglacial mid-depth Southern Ocean. Our refined methodology includes a two-step anion e xchange chemistry procedure and measurement using a 207 Pb- 204 Pb double spike on a ThermoFinnigan Triton TIMS instrument. By employing a 10 12 Ω resistor (in place of a 10 Ω resistor) to measure the low- abundance 204 Pb ion beam, we improve the internal precision on 206,207,208 Pb/ 204 Pb for a 2 ng load of NIST-SRM-981 Pb from typically ~420 ppm to ~260 ppm (2 s.e.), and the long term external reproducibility from ~960 ppm to ~580 ppm (2 s.d.). Furthermore, for a typical 500 mg coral sample with low Pb concentrations (~6-10 p pb yielding ~3-5 ng Pb for analysis), we obtain a comparable internal precision of ~150-250 ppm for 206,207,208 Pb/ 204 Pb, indicating a good sensitivity for tracing natural Pb sources to the oceans. Successful extraction of a seawater signal from deep-sea coral aragonite furth er relies on careful physical and chemical cleaning steps, which are necessary to remove anthr opogenic Pb contaminants and obtain results that are consistent with ferromanganese cru sts. Applying our approach to a collection of late glaci al and deglacial corals (~12-40 ka BP) from south of Tasmania at ~1.4-1.7 km water dep th, we generated the first intermediate water Pb isotope record from the Southern Ocean. Th at record reveals millennial timescale variability, controlled by binary mixing between tw o Pb sources, but no distinct glacial- interglacial Pb isotope shift. Mixing between natur al endmembers is fully consistent with our data and points to a persistence of the same Pb sou rces through time, although we cannot rule out a minor influence from recent anthropogenic Pb. Whereas neodymium (Nd) isotopes in the Southern Ocean respond to global ocean circulat ion changes between glacial and interglacial periods, Pb isotopes record more local ised mixing within the Antarctic Circumpolar Current, potentially further modulated by climate through changing terrestrial inputs from southern Africa or Australia. Such deco upling between Pb and Nd isotopes in the Southern Ocean highlights their potential to provid e complementary insights into past oceanographic variability

Cleaning of a model food soil from horizontal plates by a moving vertical water jet

The removal of layers of a model food soil (dried Xanthan gum containing fluorescent ZnS particles) by a vertical water jet impinging normally on to the plate, generated by a solid stream nozzle which moves across the plate was reported by Köhler et al. (2014). Their experiments investigated nozzle pressures from 0.5-2.0 barg; nozzle diameters from 0.84-2.66 mm, nozzle-layer separation of 20 mm, and nozzle traverse speeds of 2.1-126 mm s-1. The flow parameters and separation are smaller than those typical of industrial jet cleaning operations. The model developed by Wilson et al. (2014; Chem. Eng. Sci., 109, 183–196) for cleaning of similar layers by a stationary impinging jet was modified to describe the case of moving nozzle. This new model predicted the trends observed in the experiments, and analysis of the data yielded a similar cleaning rate constant to that obtained previously for cleaning of similar layers by stationary jets. The model predicted a non-circular cleaning front which matched that extracted from new experiments in which the flow was interrupted in order to capture this feature. The model allowed the cleaning performance indicators suggested by Köhler et al. (2014) to be expressed quantitatively: these indicated that higher nozzle traverse speeds give increased cleaning time, energy and liquid consumption performance.The work at TU Dresden was funded by the European Union and the Free State of Saxony as part of project SAB 080951793. A short vacation study grant for LC from Fitzwilliam College, Cambridge, is gratefully acknowledged.This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S000925091400630

Particle image velocimetry and modelling of horizontal coherent liquid jets impinging on and draining down a vertical wall

The flow patterns created by a coherent horizontal liquid jet impinging on a vertical wall at moderate flow rates (jet flowrates 0.5-4.0 L min-1, jet velocities 2.6-21 m s-1) are studied with water on glass, polypropylene and polymethylmethacrylate (acrylic, Perspex®) using a novel particle image velicometry (PIV) technique employing nearly opaque liquid doped with artificial pearlescence to track surface velocity. Flow patterns similar to those reported in previous studies are observed on each substrate: their dimensions differed owing to the influence of wall material on contact angle. The dimensions are compared with models for (i) the radial flow zone, reported by Wang et al. (2013b), and (ii) the part of the draining film below the jet impingement point where it narrows to a node. For (ii), the model presented by Mertens et al. (2005) is revised to include a simpler assumed draining film shape and an alternative boundary condition accounting for surface tension effects acting at the film edge. This revised model gives equally good or better fits to the experimental data as compared with the Mertens et al. model. The effective contact angle which gives good agreement with the data is found to lie between the measured quasi-static advancing and receding contact angles, at approximately half the advancing value. The PIV measurements confirmed the existence of a thin, fast moving film with radial flow surrounding the point of impingement, and a wide draining film bounded by ropes of liquid below the impingement point. While these measurements generally support the predictions of existing models, these models assume that the flow is steady. In contrast, surface waves were evident in both regions and this partly explains the difference between the measured surface velocity and the values estimated from the models.The apparatus was constructed by Tao Wang and Lee Pratt. Preparatory work by Huifeng Wu, and Nevile Research Fellowship for JRL from Magdalene College, Cambridge, are gratefully acknowledged.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.expthermflusci.2015.12.01

Influence of plate surface protuberance size and shape on the production of pellets by extrusion-spheronisation

The influence of spheroniser plate surface protuberance geometry on pellets produced from spheronisation of paste extrudates was investigated using a model paste material (45 wt% microcrystalline cellulose/water). Four cross-hatched pattern plates of different dimensions and/or shape of the surface protuberances were studied in terms of their effect on pellet water content, spheronisation yield, pellet size and shape distributions, and surface morphology. In addition, the effect of the relative size of extrudates to protuberances was investigated by comparing pellets generated from 1 and 2 mm diameter extrudates. In this study, all the plates have the same groove line arrangement but differ in surface protuberance dimensions and/or shape, and so the focus differs from that of Michie et al. (2012) who investigated plates of different groove line arrangement.This work was finically supported by the China Postdoctoral Science Foundation (Grant No.: 2014M550497).This is the author accepted manuscript. It is currently embargoed pending publication

Structural phase transition in IrTe2_2: A combined study of optical spectroscopy and band structure calculations

Ir$_{1-x}$Pt$_x$Te$_2$ is an interesting system showing competing phenomenon between structural instability and superconductivity. Due to the large atomic numbers of Ir and Te, the spin-orbital coupling is expected to be strong in the system which may lead to nonconventional superconductivity. We grew single crystal samples of this system and investigated their electronic properties. In particular, we performed optical spectroscopic measurements, in combination with density function calculations, on the undoped compound IrTe$_2$ in an effort to elucidate the origin of the structural phase transition at 280 K. The measurement revealed a dramatic reconstruction of band structure and a significant reduction of conducting carriers below the phase transition. We elaborate that the transition is not driven by the density wave type instability but caused by the crystal field effect which further splits/separates the energy levels of Te (p$_x$, p$_y$) and Te p$_z$ bands.Comment: 16 pages, 5 figure

Cleaning of soft-solid soil layers on vertical and horizontal surfaces by stationary coherent impinging liquid jets

The cleaning action of stationary coherent liquid jets impinging (a) vertically downwards on horizontal plates, and (b) horizontally on vertical plates, was investigated using three soft-solid model soil layers: (i) PVA glue on glass and polymethylmethacrylate (Perspex) substrates; (ii) Xanthan gum on stainless steel; and (iii) petroleum jelly on glass. The liquid stream nozzle sizes, mass and volumetric flow rates and mean jet velocities investigated were: PVA, 2 mm, 17-50 g s^-1 (0.06-0.139 m^3 h^-1), 5.3-15.9 m s^-1; Xanthan gum, 0.39-3.3 mm, 2.1-148 g s^-1 (0.008-0.53 m^3 h^-1); 4.5-31.7 m s^-1; petroleum jelly, 2 mm, 7.8-50 g s^-1 (0.06-0.139 m^3 h^-1); 2.5-15.9 m s^-1. For all three soils, rapid initial removal of soil from the jet footprint was followed by the growth of a nearly circular, clean region centred at the point of jet impingement. The rate of removal of soil decreased sharply when the cleaning front reached the hydraulic or film jump. The data for the radial growth removal stage were compared with a mathematical model describing removal of the adhesive soil layer, where the force on the cleaning front was evaluated using the result reported by Wilson et al. (2011): their theory gave the momentum of the liquid film; this momentum was balanced against the soil strength, giving a simple relation between the cleaned radius and time. All three soils showed reasonable agreement with the model, across the range of flow rates and temperatures studied. The kinetic constant in the model was sensitive to soil layer thickness and the nature of the soil. Cleaning tests on the petroleum jelly soils at different temperatures, and separate rheological measurements, showed that the kinetic time constant for coating removal was proportional to the (critical shear stress)^-1.8. There was good agreement between results obtained with vertical and horizontal plates for the PVA and Xanthan gum soil layers. The petroleum jelly results differed, which is partly attributed to differences in preparing the layers of this rheologically complex material.This is the author's accepted manuscript and is under embargo until 3/2/16. The final published version can be found in Chemical Engineering Science here: http://www.sciencedirect.com/science/article/pii/S000925091400044X