The European Journal of Applied Mathematics and Cambridge University Press are pleased to award the 2020 John Ockendon Prize to B. Matejczyk, J. Pietschmann, M. Wolfram and G. Richardson for their paper Asymptotic models for transport in large aspect ratio nanopores, published in EJAM’s 30th volume. Editor Martin Burger discusses the winning paper below.

Synthetic Nanopores are an interesting type of sensing devices, which receive strong attention in particular for DNA sequencing.

In order to produce improved pores for such tasks it is of strong importance to derive quantitative mathematical models and efficient simulation tools for the transport of particles through such pores. An effort in this direction is made in the winning paper of the John Ockendon Prize: Asymptotic models for transport in large aspect ratio nanopores by Matejczyk, Pietschmann, Wolfram and Richardson.

The authors exploit the fact that typical nanopores have a rather large aspect ratio in order to derive a quasi one-dimensional model, which is amenable to efficient numerical simulations. In their convincing analysis they consider asymptotics of the ratio pore radius divided by pore length tending to zero in a higher dimensional Poisson-Nernst-Planck model with surface charges.

In addition they analyze the challenging case of a Debye length being of similar size as the pore radius. Their findings are strongly supported by their numerical simulations, which allow to compare the full solution of the Poisson-Nernst-Planck equations for pore geometries relevant in practice to the quasi one-dimensional model.

The paper is a convincing contribution on the topic, which highlights the usefulness of parameter asymptotics to derive reduced models and put forward simulation and design. Thus, it carries on a tradition of bringing asymptotic analysis to practical relevance, which can be traced back to the beginnings of EJAM. For practitioners in the field it gives clear indications which model to use in which parameter ranges.

Access Asymptotic models for transport in large aspect ratio nanopores for free through 30th September 2020.

For more on the John Ockendon Prize, read about the 2016 and 2018 winners.