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

Implicit Simulations using Messaging Protocols

A novel algorithm for performing parallel, distributed computer simulations on the Internet using IP control messages is introduced. The algorithm employs carefully constructed ICMP packets which enable the required computations to be completed as part of the standard IP communication protocol. After providing a detailed description of the algorithm, experimental applications in the areas of stochastic neural networks and deterministic cellular automata are discussed. As an example of the algorithms potential power, a simulation of a deterministic cellular automaton involving 10^5 Internet connected devices was performed.Comment: 14 pages, 3 figure

Prompt energization of relativistic and highly relativistic electrons during a substorm interval: Van Allen Probes observations

Abstract On 17 March 2013, a large magnetic storm significantly depleted the multi-MeV radiation belt. We present multi-instrument observations from the Van Allen Probes spacecraft Radiation Belt Storm Probe A and Radiation Belt Storm Probe B at ~6 Re in the midnight sector magnetosphere and from ground-based ionospheric sensors during a substorm dipolarization followed by rapid reenergization of multi-MeV electrons. A 50% increase in magnetic field magnitude occurred simultaneously with dramatic increases in 100 keV electron fluxes and a 100 times increase in VLF wave intensity. The 100 keV electrons and intense VLF waves provide a seed population and energy source for subsequent radiation belt enhancements. Highly relativistic (\u3e2 MeV) electron fluxes increased immediately at L* ~ 4.5 and 4.5 MeV flux increased \u3e90 times at L* = 4 over 5 h. Although plasmasphere expansion brings the enhanced radiation belt multi-MeV fluxes inside the plasmasphere several hours postsubstorm, we localize their prompt reenergization during the event to regions outside the plasmasphere. Key Points Substorm dynamics are important for highly relativistic electron energization Cold plasma preconditioning is significant for rapid relativistic energization Relativistic / highly relativistic electron energization can occur in \u3c 5 hrs

Feeding, tentacle and gut morphology in five species of southern African intertidal holothuroids (Echinodermata)

Light, scanning and transmission electron microscopy were used to compare the structure of the tentacles and digestive tracts of four species of intertidal dendrochlrote (Roweia stephensoni, Pseudocneila sykion, Aslia spyridophora, R. frauenfeldi frauenfeldi),and one species of aspidochirote holothuroid (Neostichopus grammatus). In addition, gut lengths and contents of the five species were compared. Gut contents were sieved to determine the size of the particulate matter ingested. Roweia stephensoni, P. sykion and A. spyridophora were found to be suspension feeders using dendritic tentacles to capture and ingest food particles mostly <53 μm in size. Roweia f. frauenfeldi was also a suspension feeder but, had atypical (reduced) dendritic tentacles which captured food particles between 250 μm-1.18 mm in size. Neostichopus grammatus was a deposit feeder, ingesting sediments mostly between 106-500 μm using tentacles which are peltate with ramified processes. The gut lengths of the four suspension-feeding species were found to be significantly (p <0.001) longer than that of the deposit feeder. The digestive tract of all species was composed of four tissue layers, with the digestive epithelial layer of the anterior and posterior ends of the intestine of suspension feeders being significantly thicker (52 to 57 μm) than that of the deposit feeder (about 19 to 29 μm). In addition, the epithelial layer of the intestine of suspension feeders contained more highly vesicular enterocytes than that of the deposit feeder

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

Rehabilitation following rotator cuff repair: A nested qualitative study exploring the perceptions and experiences of participants in a randomised controlled trial

Objective: To investigate acceptability, barriers to adherence with the interventions, and which outcome measures best reflect the participants’ rehabilitation goals in a pilot and feasibility randomised controlled trial evaluating early patient-directed rehabilitation and standard rehabilitation, including sling immobilisation for four weeks, following surgical repair of the rotator cuff of the shoulder. Design: Nested qualitative study. Setting: Five English National Health Service Hospitals. Subjects: Nineteen patient participants who had undergone surgical repair of the rotator cuff and 10 healthcare practitioners involved in the trial. Method: Individual semi-structured interviews. Data were analysed thematically. Results: Four themes: (1) Preconceptions of early mobilisation; many participants were motivated to enter the trial for the opportunity of removing their sling and getting moving early. (2) Sling use and movement restrictions; for some, sling use for four weeks was unacceptable and contributed to their pain, rather than relieving it. (3) Tensions associated with early mobilisation; clinical tensions regarding early mobilisation and the perceived risk to the surgical repair were apparent. (4) Processes of running the trial; participants found the trial processes to be largely appropriate and acceptable, but withholding the results of the post-operative research ultrasound scan was contentious. Conclusion: Trial processes were largely acceptable, except for withholding results of the ultrasound scan. For some participants, use of the shoulder sling for a prolonged period after surgery was a reported barrier to standard rehabilitation whereas the concept of early mobilisation contributed tension for some healthcare practitioners due to concern about the effect on the surgical repair

Record statistics and persistence for a random walk with a drift

We study the statistics of records of a one-dimensional random walk of n steps, starting from the origin, and in presence of a constant bias c. At each time-step the walker makes a random jump of length \eta drawn from a continuous distribution f(\eta) which is symmetric around a constant drift c. We focus in particular on the case were f(\eta) is a symmetric stable law with a L\'evy index 0 < \mu \leq 2. The record statistics depends crucially on the persistence probability which, as we show here, exhibits different behaviors depending on the sign of c and the value of the parameter \mu. Hence, in the limit of a large number of steps n, the record statistics is sensitive to these parameters (c and \mu) of the jump distribution. We compute the asymptotic mean record number after n steps as well as its full distribution P(R,n). We also compute the statistics of the ages of the longest and the shortest lasting record. Our exact computations show the existence of five distinct regions in the (c, 0 < \mu \leq 2) strip where these quantities display qualitatively different behaviors. We also present numerical simulation results that verify our analytical predictions.Comment: 51 pages, 22 figures. Published version (typos have been corrected