The second generation of the open-source MATLAB-based software tool , for solving drift–diffusion models of charge transport in planar perovskite solar cells, is presented here. This version is based upon a generalisation of the original drift–diffusion model of charge carrier and ion motion in the perosvkite cell, as described in Courtier (J Comput Electron 18:1435–1449, 2019). The generalised model has the flexibility to capture (1) non-Boltzmann statistics of charge carriers in the transport layers, (2) steric effects for the ions in the perovskite layer, (3) generation of charge carriers from light made up of a spectrum of different wavelengths and, (4) Auger recombination. The updated software is significantly more stable than the original version and also adds the ability to simulate impedance spectroscopy measurements as well as transient voltage and/or illumination protocols. In addition, it is fully backwards compatible with the original version and displays improved performance through refinement of the underlying numerical methods. Furthermore, the software has been made accessible to a wider user base by the addition of , a version that leverages MATLAB’s live scripts and eliminates the need for a detailed knowledge of MATLAB’s syntax.

Spatial linguistic surveys often reveal well defined geographical zones where certain linguistic forms are dominant over their alternatives. It has been suggested that these patterns may be understood by analogy with coarsening in models of two dimensional physical systems. Here we investigate this connection by comparing data from the Cambridge Online Survey of World Englishes to the behaviour of a generalised zero temperature Potts model with long range interactions. The relative displacements of linguistically similar population centres reveals enhanced east-west affinity. Cluster analysis reveals three distinct linguistic zones. We find that when the interaction kernel is made anisotropic by stretching along the east-west axis, the model can reproduce the three linguistic zones for all interaction parameters tested. The model results are consistent with a view held by some linguists that, in the USA, language use is, or has been, exchanged or transmitted to a greater extent along the east-west axis than the north-south.

Low Earth Orbit is becoming crowded with satellites. Updating estimates of collision probabilities is important as new deployments are authorised but is difficult because only limited information is given. This report investigates developing analytic estimates of collision probabilities. A survey of approaches reported in the literature is carried out. A collision involving a satellite from the Iridium cluster is reviewed. A simple analytic expression for the collision probability between two satellites is derived using the smallness of several dimensionless ratios appearing in the problem. Single collision probabilities are then extended to orbital planes populated by n satellites with the aim of finding the optimal point at which to traverse such an orbit. This report demonstrates that analytic estimates relevant to the problem can be made. Further work should focus on: making these estimates rigorous by using a formal asymptotic approach, considering multiple orbital planes and introducing time dependence