Classical plume theory: 1937-2010 and beyond

Developing a theoretical description of turbulent plumes, the likes of which may be seen rising above industrial chimneys, is a daunting thought. Plumes are ubiquitous on a wide range of scales in both the natural and the man-made environments. Examples that immediately come to mind are the vapour plumes above industrial smoke stacks or the ash plumes forming particle-laden clouds above an erupting volcano. However, plumes also occur where they are less visually apparent, such as the rising stream of warmair above a domestic radiator, of oil from a subsea blowout or, at a larger scale, of air above the so-called urban heat island. In many instances, not only the plume itself is of interest but also its influence on the environment as a whole through the process of entrainment. Zeldovich (1937, The asymptotic laws of freely-ascending convective flows. Zh. Eksp. Teor. Fiz., 7, 1463-1465 (in Russian)), Batchelor (1954, Heat convection and buoyancy effects in fluids. Q. J. R. Meteor. Soc., 80, 339-358) and Morton et al. (1956, Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A, 234, 1-23) laid the foundations for classical plume theory, a theoretical description that is elegant in its simplicity and yet encapsulates the complex turbulent engulfment of ambient fluid into the plume. Testament to the insight and approach developed in these early models of plumes is that the essential theory remains unchanged and is widely applied today. We describe the foundations of plume theory and link the theoretical developments with the measurements made in experiments necessary to close these models before discussing some recent developments in plume theory, including an approach which generalizes results obtained separately for the Boussinesq and the non-Boussinesq plume cases. The theory presented - despite its simplicity - has been very successful at describing and explaining the behaviour of plumes across the wide range of scales they are observed. We present solutions to the coupled set of ordinary differential equations (the plume conservation equations) that Morton et al. (1956) derived from the Navier-Stokes equations which govern fluid motion. In order to describe and contrast the bulk behaviour of rising plumes from general area sources, we present closed-form solutions to the plume conservation equations that were achieved by solving for the variation with height of Morton's non-dimensional flux parameter Γ - this single flux parameter gives a unique representation of the behaviour of steady plumes and enables a characterization of the different types of plume. We discuss advantages of solutions in this form before describing extensions to plume theory and suggesting directions for new research. © 2010 The Author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Energy transfer and enhanced 1.54 μm emission in Erbium-Ytterbium disilicate thin films.

α-(Yb1-xErx)2Si2O7 thin films on Si substrates were synthesized by magnetron co-sputtering. The optical emission from Er3+ ions has been extensively investigated, evidencing the very efficient role of Yb-Er coupling. The energy-transfer coefficient was evaluated for an extended range of Er content (between 0.2 and 16.5 at.%) reaching a maximum value of 2 × 10⁻¹⁶ cm⁻³s⁻¹. The highest photoluminescence emission at 1535 nm is obtained as a result of the best compromise between the number of Yb donors (16.4 at.%) and Er acceptors (1.6 at.%), for which a high population of the first excited state is reached. These results are very promising for the realization of 1.54 μm optical amplifiers on a Si platform.

Synthesis and luminescence properties of erbium silicate thin films

We have studied the structure and the room temperature luminescence of erbium silicate thin films deposited by rf magnetron sputtering. Films deposited on silicon oxide layers are characterized by good structural properties and excellent stability. The optical properties of these films are strongly improved by rapid thermal annealing processes performed in the range of temperature 800-1250 °C. In fact through the reduction of the defect density of the material, a very efficient room temperature photoluminescence at 1535 nm is obtained. We have also investigated the influence of the annealing ambient, by finding that treatments in O2 atmosphere are significantly more efficient in improving the optical properties of the material with respect to processes in N2. Upconversion effects become effective only when erbium silicate is excited with high pump powers. The evidence that all Er atoms (about 1022 cm-3) in erbium silicate films are optically active suggests interesting perspectives for optoelectronic applications of this material. © 2007 Elsevier B.V. All rights reserved.

Erbium doped materials for a Si-based microphotonics

We have investigated the role of the Si excess on the photoluminescence properties of Er doped substoichiometric SiOx layers. We demonstrate that the Si excess has two competing roles: when agglomerated to form Si nanoclusters (Si-nc) it enhances the Er excitation efficiency but it also introduces new non-radiative decay channels. When Er is excited through an energy transfer from Si-nc, the beneficial effect on the enhanced excitation efficiency prevails and the Er emission increases with increasing Si content. Nevertheless the maximum excited Er fraction is only of the order of percent. In order to increase the concentration of excited Er ions, a different approach based on Er silicate thin film has been explored. Under proper annealing conditions, an efficient luminescence at 1535 nm is found and all of the Er ions in the material is optically active. The possibility to efficiently excite Er ions also through electron-hole mediated processes is demonstrated in nanometer-scale Er-Si-O/Si multilayers. These data are presented and discussed.

The Effect of Motivation on Movement: A Study of Bradykinesia in Parkinson's Disease

Background: Bradykinesia is a cardinal feature of Parkinson's disease (PD). Despite its disabling impact, the precise cause of this symptom remains elusive. Recent thinking suggests that bradykinesia may be more than simply a manifestation of motor slowness, and may in part reflect a specific deficit in the operation of motivational vigour in the striatum. In this paper we test the hypothesis that movement time in PD can be modulated by the specific nature of the motivational salience of possible action-outcomes. Methodology/Principal Findings: We developed a novel movement time paradigm involving winnable rewards and avoidable painful electrical stimuli. The faster the subjects performed an action the more likely they were to win money (in appetitive blocks) or to avoid a painful shock (in aversive blocks). We compared PD patients when OFF dopaminergic medication with controls. Our key finding is that PD patients OFF dopaminergic medication move faster to avoid aversive outcomes (painful electric shocks) than to reap rewarding outcomes (winning money) and, unlike controls, do not speed up in the current trial having failed to win money in the previous one. We also demonstrate that sensitivity to distracting stimuli is valence specific. Conclusions/Significance: We suggest this pattern of results can be explained in terms of low dopamine levels in the Parkinsonian state leading to an insensitivity to appetitive outcomes, and thus an inability to modulate movement speed in the face of rewards. By comparison, sensitivity to aversive stimuli is relatively spared. Our findings point to a rarely described property of bradykinesia in PD, namely its selective regulation by everyday outcomes. © 2012 Shiner et al.