The European Journal of Applied Mathematics and Cambridge University Press are pleased to award the 2018 John Ockendon Prize to G. Richardson, C.P. Please and V. Styles for their paper Derivation and solution of effective medium equations for bulk heterojunction organic solar cells, published in EJAM’s special issue: Big data and partial differential equations. Editor Martin Burger discusses the winning paper below.

The energy transition of the 21st century poses a lot of challenges to all kinds of sciences and mathematics. One of those, the transport behaviour in organic solar cells, is approached in the winning paper of the John Ockendon Prize: Derivation and solution of effective-medium equations for bulk heterojunction organic solar cells, by Richardson, Please, and Style.

Their paper investigates a Poisson-drift-diffusion model with recombination and photogeneration terms and interface conditions at the donor-acceptor boundary in a setup of heterojunction devices. Two important cases of heterojunctions are considered: a random mixing and elongated structures.

In order to derive an effective medium model, asymptotic expansions and homogenization techniques are applied to these two different setups, yielding simplified Poisson-drift-diffusion equations that can be used to compute current-voltage curves of the devices reasonably efficiently. In order to check the behaviour and validity of the approximation, appropriate finite element discretizations of both the original as well as the effective medium model are derived and implemented. The results clearly demonstrate the validity of the expansion and its limitations for large applied voltages.

The paper is a very nice combination of mathematical modelling, numerical simulation and model reduction by analytical techniques, which puts forward the theory of organic solar cells with heterojunctions and is expected to have a strong impact in the future design of such devices. It is very well written and allows a non-expert reader to dig into a modern application area.

Access Derivations and solution of effective-medium equations for bulk heterojunction organic solar cells for free through 30th September 2018.

Read more about the John Ockendon Prize, and the winning paper in 2016.

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