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

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

IonMonger: a free and fast planar perovskite solar cell simulator with coupled ion vacancy and charge carrier dynamics

Details of an open-source planar perovskite solar cell simulator, that includes ion vacancy migration within the perovskite layer coupled to charge carrier transport throughout the perovskite and adjoining transport layers in one dimension, are presented. The model equations are discretised in space using a finite element scheme and temporal integration of the resulting system of differential-algebraic equations is carried out in MATLAB. The user is free to modify device parameters, as well as the incident illumination and applied voltage. Time-varying voltage and/or illumination protocols can be specified, e.g. to simulate current-voltage sweeps, or to track the open-circuit conditions as the illumination is varied. Typical simulations, e.g. current-voltage sweeps, only require computation times of seconds to minutes on a modern personal computer. An example set of hysteretic current-voltage curves is presented

ACTIVE: a randomised feasibility trial of a behavioural intervention to reduce fatigue in women undergoing radiotherapy for early breast cancer: study protocol

Background Fatigue is rated as the most distressing side effect of radiotherapy treatment for curable breast cancer. About four in ten women treated experience fatigue, which can last for years after treatment. The impact of this debilitating tiredness is loss of independence and impaired physical and mental function. Our study will take a behavioural intervention with demonstrated effect in treating fatigue in a mixed group of chemotherapy patients and adapt it for women undergoing radiotherapy for early breast cancer. The purpose of this trial is to evaluate the feasibility of delivering the intervention in the radiotherapy pathway for patients at a high risk of fatigue and to explore participants’ experiences of the trial and intervention. Methods A pragmatic single-site non-blinded feasibility trial of a behavioural intervention. Main inclusion criteria are prescription of the UK standard 40 Gy in 15 fractions over 3 weeks of radiotherapy (± tumour bed boost) for early (stage 0–IIIa) breast cancer. The total projected sample size after attrition is 70. A previously developed fatigue risk score tool will be used to predict individual’s likelihood of experiencing fatigue. Thirty women predicted to be at a high risk of experiencing significant fatigue will be allocated in the ratio 2:1 to the behavioural intervention or education trial arms, respectively. These feasibility trial participants will be assessed at baseline, after 10 and 15 fractions of radiotherapy and 10 days, 3 weeks and 6 months after radiotherapy. A further 40 women predicted to be at a lower risk of fatigue will join a risk score validation group. Measures to assess feasibility include recruitment, retention and completion rates and variation in implementation of the intervention. Process evaluation with intervention providers and users includes fidelity and adherence checks and qualitative interviews to understand how changes in behaviour are initiated and sustained. Discussion This feasibility study collates data to both inform the progression to and design of a future definitive trial and to refine the intervention

Water transfer and crack regimes in nano-colloidal gels

International audienceDirect observations of the surface and shape of model nano-colloidal gels associated with measurements of the spatial distribution of water content during drying show that air starts to significantly penetrate the sample when the material stops shrinking. We show that whether the material fractures or not during desiccation, as air penetrates the porous body, the water saturation decreases but remains almost homogeneous throughout the sample. This air-invasion is at the origin of another type of fracture due to capillary effects; these results provide a new insight in the liquid dynamics at the nano-scale. PACS number(s): 47.56.+r, 68.03.Fg, 81.40.N

Implicit particle methods and their connection with variational data assimilation

The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothing as well as to data assimilation for perfect models. We show that the minimizations required by implicit particle methods are similar to the ones one encounters in variational data assimilation and explore the connection of implicit particle methods with variational data assimilation. In particular, we argue that existing variational codes can be converted into implicit particle methods at a low cost, often yielding better estimates, that are also equipped with quantitative measures of the uncertainty. A detailed example is presented

A reduced-order strategy for 4D-Var data assimilation

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul tivariate background error covariance matrix $\textbf{B}_r$, and an important decrease of the computational burden o f the method, due to the drastic reduction of the dimension of the control space. % An illustration of the feasibility and the effectiveness of this method is given in the academic framework of twin experiments for a model of the equatorial Pacific ocean. It is shown that the multivariate aspect of $\textbf{B}_r$ brings additional information which substantially improves the identification procedure. Moreover the computational cost can be decreased by one order of magnitude with regard to the full-space 4D-Var method

Radiological-pathological correlation of pleomorphic liposarcoma of the anterior mediastinum in a 17-year-old girl

Liposarcoma is a soft-tissue sarcoma typically seen in adults. It is extremely rare in children. It most often occurs in the extremities or in the retroperitoneum. We present a very rare case of an anterior mediastinal liposarcoma of the pleomorphic subtype in a 17-year-old girl, along with radiological and pathological correlation. The location, patient age and histological subtype are exceedingly uncommon for this tumor