Modelling ion populations in astrophysical plasmas: carbon in the solar transition region

The aim of this work is to improve the modelling of ion populations in higher density, lower temperature astrophysical plasmas, of the type commonly found in lower solar and stellar atmospheres. Ion population models for these regions frequently employ the coronal approximation, which assumes conditions more suitable to the upper solar atmosphere, where high temperatures and lower densities prevail. Using the coronal approximation for modelling the solar transition region gives theoretical lines intensities for the Li-like and Na-like isoelectronic sequences which can be factors of 2-5 times lower than observed. The works of Burgess & Summers (1969) and Nussbaumer & Storey (1975) showed the important part ions in excited levels play when included in the modelling. Their models, however, used approximations for the atomic rates to determine the ion balance. Presented here is the first stage in updating these earlier models of carbon by using rates from up-to-date atomic calculations and more recent photo-ionising radiances for the quiet Sun. Where such atomic rates are not readily available, in the case of electron-impact direct ionisation and excitation--auto-ionisation, new calculations have been made and compared to theoretical and experimental studies. The effects each atomic process has on the ion populations as density changes is demonstrated, and final results from the modelling are compared to the earlier works. Lastly, the new results for ion populations are used to predict line intensities for the solar transition region in the quiet Sun, and these are compared with predictions from coronal-approximation modelling and with observations. Significant improvements in the predicted line intensities are seen in comparison to those obtained from zero-density modelling of carbon.Comment: Draft accepted by A&A, 13 pages, 15 figure

Experimental investigation of the turbulent axisymmetric wake with rotation generated by a wind turbine

An experimental investigation of the axial and azimuthal (swirl) velocity field in the wake of a single 3-bladed wind turbine with rotor diameter of 0.91m was conducted, up to 20 diameters downstream. The turbine was positioned in the free stream, near the entrance of the 6m x 2.7m cross section of the University of New Hampshire (UNH) Flow Physics Facility. Velocity measurements were conducted at different rotor loading conditions with blade tip-speed ratios from 2.0 to 2.8. A Pitot-static tube and constant temperature hot-wire anemometer with a multi-wire sensor were used to measure velocity fields. An equilibrium similarity theory for the turbulent axisymmetric wake with rotation was outlined, and first evidence for a new scaling function for the mean swirling velocity component, Wmax ∝ x-1 ∝ U3/2o a was found; where W represents swirl, x represents downstream distance, and Uo, represents the centerline velocity deficit in the wake

Designing Effective Questions for Classroom Response System Teaching

Classroom response systems (CRSs) can be potent tools for teaching physics. Their efficacy, however, depends strongly on the quality of the questions used. Creating effective questions is difficult, and differs from creating exam and homework problems. Every CRS question should have an explicit pedagogic purpose consisting of a content goal, a process goal, and a metacognitive goal. Questions can be engineered to fulfil their purpose through four complementary mechanisms: directing students' attention, stimulating specific cognitive processes, communicating information to instructor and students via CRS-tabulated answer counts, and facilitating the articulation and confrontation of ideas. We identify several tactics that help in the design of potent questions, and present four "makeovers" showing how these tactics can be used to convert traditional physics questions into more powerful CRS questions.Comment: 11 pages, including 6 figures and 2 tables. Submitted (and mostly approved) to the American Journal of Physics. Based on invited talk BL05 at the 2005 Winter Meeting of the American Association of Physics Teachers (Albuquerque, NM

Effects of density on the oxygen ionization equilibrium in collisional plasmas

The ion populations most frequently adopted for diagnostics in collisional plasmas are derived from the density independent coronal approximation. In higher density, lower temperature conditions, ionization rates are enhanced once metastable levels become populated, and recombination rates are suppressed if ions recombine into Rydberg levels. As a result, the formation temperatures of ions shift, altering the diagnostics of the plasma. To accurately model the effect of ionization from metastable levels, new electron impact ionization cross-sections have been calculated for oxygen, both for direct ionization and excitation–auto-ionization of the ground and metastable levels. The results have been incorporated into collisional radiative modelling to show how the ionization equilibrium of oxygen changes once metastable levels become populated. Suppression of dielectronic recombination has been estimated and also included in the modelling, demonstrating the shifts with density in comparison to the coronal approximation. The final results for the ionization equilibrium are used in differential emission measure modelling to predict line intensities for many lines emitted by O II–O VI in the solar transition region. The predictions show improved agreement by 15–40 per cent for O II, O VI, and the intercombination lines of O III–O V, when compared to results from coronal approximation modelling. While there are still discrepancies with observations of these lines, this could, to a large part, be explained by variability in the observations

The Deformation of an Elastic Substrate by a Three-Phase Contact Line

Young's classic analysis of the equilibrium of a three-phase contact line ignores the out-of-plane component of the liquid-vapor surface tension. While it has long been appreciated that this unresolved force must be balanced by elastic deformation of the solid substrate, a definitive analysis has remained elusive because conventional idealizations of the substrate imply a divergence of stress at the contact line. While a number of theories of have been presented to cut off the divergence, none of them have provided reasonable agreement with experimental data. We measure surface and bulk deformation of a thin elastic film near a three-phase contact line using fluorescence confocal microscopy. The out-of-plane deformation is well fit by a linear elastic theory incorporating an out-of-plane restoring force due to the surface tension of the gel. This theory predicts that the deformation profile near the contact line is scale-free and independent of the substrate elastic modulus.Comment: 4 pages, 3 figure

Pricing Derivatives the Martingale Way.

In recent years results from the theory of martingales has been successfully applied to problems in financial economics. In the present paper we show how efficient and elegant this "martingale technology" can be when solving for complex options. In particular we provide closed form solutions for several new classes of exotic options including the cliquet, the ladder, the discrete shout and the discrete lookback. We also provide a derivation of the price of an option on the maximum of n assets to demonstrate the power of the multi-dimensional Girsanov theorem. Although some of the results presented are well known, the treatment of the material in this paper is new in that it focuses on the application of the martingale technology to concrete problems in option pricing, methods that until now have mostly been used for purely theoretical purposes.