Systematic derivation of a surface polarization model for planar perovskite solar cells

Increasing evidence suggests that the presence of mobile ions in perovskite solar cells can cause a current-voltage curve hysteresis. Steady state and transient current-voltage characteristics of a planar metal halide CH$_3$NH$_3$PbI$_3$ perovskite solar cell are analysed with a drift-diffusion model that accounts for both charge transport and ion vacancy motion. The high ion vacancy density within the perovskite layer gives rise to narrow Debye layers (typical width $\sim$2nm), adjacent to the interfaces with the transport layers, over which large drops in the electric potential occur and in which significant charge is stored. Large disparities between (I) the width of the Debye layers and that of the perovskite layer ($\sim$600nm) and (II) the ion vacancy density and the charge carrier densities motivate an asymptotic approach to solving the model, while the stiffness of the equations renders standard solution methods unreliable. We derive a simplified surface polarisation model in which the slow ion dynamic are replaced by interfacial (nonlinear) capacitances at the perovskite interfaces. Favourable comparison is made between the results of the asymptotic approach and numerical solutions for a realistic cell over a wide range of operating conditions of practical interest.Comment: 32 pages, 7 figure

Particle Impact Analysis of Bulk Powder During Pneumatic Conveyance

Fragmentation of powders during transportation is a common problem for manufacturers of food and pharmaceutical products. We illustrate that the primary cause of breakage is due to inter-particle collisions, rather than particle-wall impacts, and provide a statistical mechanics model giving the number of collisions resulting in fragmentation

On spherical twisted conjugacy classes

Let G be a simple algebraic group over an algebraically closed field of good odd characteristic, and let theta be an automorphism of G arising from an involution of its Dynkin diagram. We show that the spherical theta-twisted conjugacy classes are precisely those intersecting only Bruhat cells corresponding to twisted involutions in the Weyl group. We show how the analogue of this statement fails in the triality case. We generalize to good odd characteristic J-H. Lu's dimension formula for spherical twisted conjugacy classes.Comment: proof of Lemma 6.4 polished. The journal version is available at http://www.springerlink.com/content/k573l88256753640

Inverse approach to Einstein's equations for fluids with vanishing anisotropic stress tensor

We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class $B_1$. Although restricted, these spacetimes include many exact solutions of interest to compact object studies and to cosmological models studies. The question explored here is as follows: given a spacetime metric, what fluid flow (timelike congruence), if any, could generate the spacetime via Einstein's equations. We calculate the flow from the condition of a vanishing anisotropic stress tensor and give results in terms of the metric functions in the three canonical types of coordinates. A condition for perfect fluid sources is also provided. The framework developed is algorithmic and suited for the study and validation of exact solutions using computer algebra systems. The framework can be applied to solutions in comoving and non-comoving frames of reference, and examples in different types of coordinates are worked out.Comment: 15 pages, matches version to appear in Phys.Rev.

Magnetic Helicity Conservation and Astrophysical Dynamos

We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large scale fields in equipartition with the turbulent energy density. The prospects for driving a fast dynamo under these circumstances are uncertain, but if it is possible, then the field must be largely force-free. On the other hand, there is an efficient analog to the $\alpha-\Omega$ dynamo. Systems whose turbulence is driven by some anisotropic local instability in a shearing flow, like real stars and accretion disks, and some computer simulations, may successfully drive the generation of strong large scale magnetic fields, provided that $\partial_r\Omega>0$. We show that this criterion is usually satisfied. Such dynamos will include a persistent, spatially coherent vertical magnetic helicity current with the same sign as $-\partial_r\Omega$, that is, positive for an accretion disk and negative for the Sun. We comment on the role of random magnetic helicity currents in storing turbulent energy in a disordered magnetic field, which will generate an equipartition, disordered field in a turbulent medium, and also a declining long wavelength tail to the power spectrum. As a result, calculations of the galactic `seed' field are largely irrelevant.Comment: 28 pages, accepted by The Astrophysical Journa

Chandra X-ray Observations of the Quadruply Lensed Quasar RX J0911.4+0551

We present results from X-ray observations of the quadruply lensed quasar RX J0911.4+0551 using data obtained with the Advanced CCD Imaging Spectrometer (ACIS) on board the Chandra X-ray Observatory. The 29 ks observation detects a total of ~404 X-ray photons (0.3 to 7.0 keV) from the four images of the lensed quasar. Deconvolution of the aspect corrected data resolves all four lensed images, with relative positions in good agreement with optical measurements. When compared to contemporaneous optical data, one of the lensed images (component A3) is dimmer by a factor of ~6 in X-rays with respect to the 2 brighter images (components A1 and A2). Spectral fitting for the combined images shows significant intrinsic absorption in the soft (0.2 to 2.4 keV) energy band, consistent with the mini-BAL nature of this quasar, while a comparison with ROSAT PSPC observations from 1990 shows a drop of ~6.5 in the total soft bandpass flux. The observations also detect ~157 X-ray photons arising from extended emission of the nearby cluster (peaked ~42" SW of RXJ0911.4+0551) responsible for the large external shear present in the system. The Chandra observation reveals the cluster emission to be complex and non-spherical, and yields a cluster temperature of kT = 2.3^{+1.8}_{-0.8} keV and a 2.0 to 10 keV cluster luminosity within a 1 Mpc radius of L_X = 7.6_{-0.2}^{+0.6} x 10^{43} ergs/s (error bars denote 90% confidence limits). Our mass estimate of the cluster within its virial radius is 2.3^{+1.8}_{-0.7} x 10^{14} solar, and is a factor of 2 smaller than, although consistent with, previous mass estimates based on the observed cluster velocity dispersion.Comment: 16 pages, 3 figures (figure 1 is color ps). Accepted by Ap

Auto-calibration of ultrasonic lubricant-film thickness measurements

The measurement of oil film thickness in a lubricated component is essential information for performance monitoring and design. It is well established that such measurements can be made ultrasonically if the lubricant film is modelled as a collection of small springs. The ultrasonic method requires that component faces are separated and a reference reflection recorded in order to obtain a reflection coefficient value from which film thickness is calculated. The novel and practically useful approach put forward in this paper and validated experimentally allows reflection coefficient measurement without the requirement for a reference. This involves simultaneously measuring the amplitude and phase of an ultrasonic pulse reflected from a layer. Provided that the acoustic properties of the substrate are known, the theoretical relationship between the two can be fitted to the data in order to yield reflection coefficient amplitude and phase for an infinitely thick layer. This is equivalent to measuring a reference signal directly, but importantly does not require the materials to be separated. The further valuable aspect of this approach, which is demonstrated experimentally, is its ability to be used as a self-calibrating routine, inherently compensating for temperature effects. This is due to the relationship between the amplitude and phase being unaffected by changes in temperature which cause unwanted changes to the incident pulse. Finally, error analysis is performed showing how the accuracy of the results can be optimized. A finding of particular significance is the strong dependence of the accuracy of the technique on the amplitude of reflection coefficient input data used. This places some limitations on the applicability of the technique. © 2008 IOP Publishing Ltd

Supporting the learning of deaf students in higher education: a case study at Sheffield Hallam University

This article is an examination of the issues surrounding support for the learning of deaf students in higher education (HE). There are an increasing number of deaf students attending HE institutes, and as such provision of support mechanisms for these students is not only necessary but essential. Deaf students are similar to their hearing peers, in that they will approach their learning and require differing levels of support dependant upon the individual. They will, however, require a different kind of support, which can be technical or human resource based. This article examines the issues that surround supporting deaf students in HE with use of a case study of provision at Sheffield Hallam University (SHU), during the academic year 1994-95. It is evident that by considering the needs of deaf students and making changes to our teaching practices that all students can benefit

Characterizing the Rigidly Rotating Magnetosphere Stars HD 345439 and HD 23478

The SDSS III APOGEE survey recently identified two new $\sigma$ Ori E type candidates, HD 345439 and HD 23478, which are a rare subset of rapidly rotating massive stars whose large (kGauss) magnetic fields confine circumstellar material around these systems. Our analysis of multi-epoch photometric observations of HD 345439 from the KELT, SuperWASP, and ASAS surveys reveals the presence of a $\sim$0.7701 day period in each dataset, suggesting the system is amongst the faster known $\sigma$ Ori E analogs. We also see clear evidence that the strength of H-alpha, H I Brackett series lines, and He I lines also vary on a $\sim$0.7701 day period from our analysis of multi-epoch, multi-wavelength spectroscopic monitoring of the system from the APO 3.5m telescope. We trace the evolution of select emission line profiles in the system, and observe coherent line profile variability in both optical and infrared H I lines, as expected for rigidly rotating magnetosphere stars. We also analyze the evolution of the H I Br-11 line strength and line profile in multi-epoch observations of HD 23478 from the SDSS-III APOGEE instrument. The observed periodic behavior is consistent with that recently reported by Sikora and collaborators in optical spectra.Comment: Accepted in ApJ

Evolution of an elliptical bubble in an accelerating extensional flow

Mathematical models that describe the dynamical behavior of a thin gas bubble embedded in a glass fiber during a fiber drawing process have been discussed and analyzed. The starting point for the mathematical modeling was the equations presented in [1] for a glass fiber with a hole undergoing extensional flow. These equations were reconsidered here with the additional reduction that the hole, i.e. the gas bubble, was thin as compared to the radius of the fiber and of finite extent. The primary model considered was one in which the mass of the gas inside the bubble was fixed. This fixed-mass model involved equations for the axial velocity and fiber radius, and equations for the radius of the bubble and the gas pressure inside the bubble. The model equations assumed that the temperature of the furnace of the drawing tower was known. The governing equations of the bubble are hyperbolic and predict that the bubble cannot extend beyond the limiting characteristics specified by the ends of the initial bubble shape. An analysis of pinch-off was performed, and it was found that pinch-off can occur, depending on the parameters of the model, due to surface tension when the bubble radius is small. In order to determine the evolution of a bubble, a numerical method of solution was presented. The method was used to study the evolution of two different initial bubble shapes, one convex and the other non-convex. Both initial bubble shapes had fore-aft symmetry, and it was found that the bubbles stretched and elongated severely during the drawing process. For the convex shape, fore-aft symmetry was lost in the middle of the drawing process, but the symmetry was re-gained by the end of the drawing tower. A small amount of pinch-off was observed at each end for this case, so that the final bubble length was slightly shorter than its theoretical maximum length. For the non-convex initial shape, pinch-off occurred in the middle of the bubble resulting in two bubbles by the end of the fiber draw. The two bubbles had different final pressures and did not have fore-aft symmetry. An extension of the fixed-mass model was considered in which the gas in the bubble was allowed to diffuse into the surrounding glass. The governing equations for this leaky-mass model were developed and manipulated into a form suitable for a numerical treatment