A fast and robust numerical scheme for solving models of charge carrier transport and ion vacancy motion in perovskite solar cells

Drift-diffusion models that account for the motion of both electronic and ionic charges are important tools for explaining the hysteretic behaviour and guiding the development of metal halide perovskite solar cells. Furnishing numerical solutions to such models for realistic operating conditions is challenging owing to the extreme values of some of the parameters. In particular, those characterising (i) the short Debye lengths (giving rise to rapid changes in the solutions across narrow layers), (ii) the relatively large potential differences across devices and (iii) the disparity in timescales between the motion of the electronic and ionic species give rise to significant stiffness. We present a finite difference scheme with an adaptive time step that is posed on a non-uniform staggered grid that provides second order accuracy in the mesh spacing. The method is able to cope with the stiffness of the system for realistic parameters values whilst providing high accuracy and maintaining modest computational costs. For example, a transient sweep of a current-voltage curve can be computed in only a few minutes on a standard desktop computer.Comment: 22 pages, 8 figure

Reaction Diffusion and Ballistic Annihilation Near an Impenetrable Boundary

The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic propagation. It is shown that the effect of the boundary is quite different in both cases: diffusion-reaction leads to a density excess, whereas ballistic annihilation exhibits a density deficit, and in both cases the effect is not localized at the boundary but penetrates into the system. The field-theoretic renormalization group is used to obtain the universal properties of the density excess in two dimensions and below for the reaction-diffusion system. In one dimension the excess decays with the same exponent as the bulk and is found by an exact solution. In two dimensions the excess is marginally less relevant than the bulk decay and the density profile is again found exactly for late times from the RG-improved field theory. The results obtained for the diffusive case are relevant for Mg$^{2+}$ or Cd$^{2+}$ doping in the TMMC crystal's exciton coalescence process and also imply a surprising result for the dynamic magnetization in the critical one-dimensional Ising model with a fixed spin. For the case of ballistic reactants, a model is introduced and solved exactly in one dimension. The density-deficit profile is obtained, as is the density of left and right moving reactants near the impenetrable boundary.Comment: to appear in J. Phys.

Tri-literal verbs with a weak final radical y in Ugaritic

ihe purpose of this investigation is to examine whether the different spellings of some forms of III-y verbs in Ugaritic reflect differences in meaning. There are about fifty roots attested which end in y; it is not possible to be exactly sure of the number because the parsing of some forms is tentative. After surveying previous descriptions of the Ugaritic III-y verb (Chapter I) the meaning of the verbs in their contexts is discussed in detail (Chapter II). The examination of all the attested forms shows quite clearly that yqtl forms of III-y verbs describe past and future actions, whether or not the final radical is written, although there does seem to be a slight tendency for the shorter form to be used in past narration. Because of this apparent free variation in the use of final y in verbs, it was decided to investigate how consistently other words were spelled. Those passages that are repeated once or twice in the myths have, therefore, been closely examined and the variations within them have been tabulated (Chapter III). The place names that end in y have also been examined because they are sometimes written without the final –y (Chapter IV). Spelling variation seems to have existed in Ugaritic more than has generally been supposed. If this is so, it may be possible, to regard some forms of verbs of the pattern ybky and ybk as variant spellings of the same word

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

Aminoglycoside-Induced Phosphatidylserine Externalization in Sensory Hair Cells Is Regionally Restricted, Rapid, and Reversible

The aminophospholipid phosphatidylserine (PS) is normally restricted to the inner leaflet of the plasma membrane. During certain cellular processes, including apoptosis, PS translocates to the outer leaflet and can be labeled with externally applied annexin V, a calcium-dependent PS-binding protein. In mouse cochlear cultures, annexin V labeling reveals that the aminoglycoside antibiotic neomycin induces rapid PS externalization, specifically on the apical surface of hair cells. PS externalization is observed within ~75 s of neomycin perfusion, first on the hair bundle and then on membrane blebs forming around the apical surface. Whole-cell capacitance also increases significantly within minutes of neomycin application, indicating that blebbing is accompanied by membrane addition to the hair cell surface. PS externalization and membrane blebbing can, nonetheless, occur independently. Pretreating hair cells with calcium chelators, a procedure that blocks mechanotransduction, or overexpressing a phosphatidylinositol 4,5-biphosphate (PIP2)-binding pleckstrin homology domain, can reduce neomycin-induced PS externalization, suggesting that neomycin enters hair cells via transduction channels, clusters PIP2, and thereby activates lipid scrambling. The effects of short-term neomycin treatment are reversible. After neomycin washout, PS is no longer detected on the apical surface, apical membrane blebs disappear, and surface-bound annexin V is internalized, distributing throughout the supranuclear cytoplasm of the hair cell. Hair cells can therefore repair, and recover from, neomycin-induced surface damage. Hair cells lacking myosin VI, a minus-end directed actin-based motor implicated in endocytosis, can also recover from brief neomycin treatment. Internalized annexin V, however, remains below the apical surface, thereby pinpointing a critical role for myosin VI in the transport of endocytosed material away from the periphery of the hair cell

Rethinking professional practice: the logic of competition and the crisis of identity in housing practice

The relationship between professionalism, education and housing practice has become increasingly strained following the introduction of austerity measures and welfare reforms across a range of countries. Focusing on the development of UK housing practice, this article considers how notions of professionalism are being reshaped within the context of welfare retrenchment and how emerging tensions have both affected the identity of housing professionals and impacted on the delivery of training and education programmes. The article analyses the changing knowledge and skills valued in contemporary housing practice and considers how the sector has responded to the challenges of austerity. The central argument is that a dominant logic of competition has culminated in a crisis of identity for the sector. Although the focus of the article is on UK housing practice, the processes identified have a wider relevance for the analysis of housing and welfare delivery in developed economies

The Reaction Process A+A->O in Sinai Disorder

The single-species reaction-diffusion process $A+A\to O$ is examined in the presence of an uncorrelated, quenched random velocity field. Utilising a field-theoretic approach, we find that in two dimensions and below the density decay is altered from the case of purely diffusing reactants. In two-dimensions the density amplitude is reduced in the presence of weak disorder, yielding the interesting result that Sinai disorder can cause reactions to occur at an {\it increased} rate. This is in contrast to the case of long-range correlated disorder, where it was shown that the reaction becomes sub-diffusion limited. However, when written in terms of the microscopic diffusion constant it is seen that increasing the disorder has the effect of reducing the rate of the reaction. Below two dimensions, the effect of Sinai disorder is much more severe and the reaction is shown to become sub-diffusion limited. Although there is no universal amplitude for the time-dependence of the density, it is universal when expressed in terms of the disorder-averaged diffusion length. The appropriate amplitude is calculated to one-loop order.Comment: 12 pages, 2 figure

Gravitational field models for the earth (GEM 1 and 2)

Two models of the earth's gravitational field have been computed at Goddard Space Flight Center. The first, Goddard Earth Model 1 (GEM 1), has been derived from satellite tracking data. The second, Goddard Earth Model 2 (GEM 2), has been derived from a combination of satellite tracking and surface gravimetric data. The geopotential models are represented in spherical harmonics complete to degree and order 16 for the combined solution and complete to degree and order 12 for the satellite solution. Both solutions include zonal terms to degree 21 and related satellite resonant coefficients to degree 22. The satellite data consisted primarily of optical data processed on 300 weekly orbital arcs for 25 close earth satellites. Surface gravity data were employed in the form of 5 deg x 5 deg mean free-air gravity anomalies providing about 70% world coverage. Station locations were obtained for 46 tracking sites by combining electronic, laser, and additional optical tracking data with the above satellite data. Analysis of the radial positions of these stations and a value of mean gravity on the geoid indicated a mean equatorial radius for the earth of about 6378145 meters. Results of geopotential tests on satellite data not used in the solution show that better agreement was obtained with the GEM 1 and GEM 2 models than with the 1969 Smithsonian Standard Earth 2 model

Finite Density QCD in the Chiral Limit

We present the first results of an exact simulation of full QCD at finite density in the chiral limit. We have used a MFA (Microcanonical Fermionic Average) inspired approach for the reconstruction of the Grand Canonical Partition Function of the theory; using the fugacity expansion of the fermionic determinant we are able to move continuously in the ($\beta -\mu$) plane with $m=0$.Comment: 3 pages, LaTeX, 3 figures, uses espcrc2.sty, psfig. Talk presented by A. Galante at Lattice 97. Correction of some reference