Toby Kay

Barrier crossing is a widespread phenomenon across natural and engineering systems. While abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process have yet to be linked quantitatively to easily measurable observables. We bridge this gap by developing a microscopic representation of Brownian motion in the presence of permeable barriers that allows us to treat barriers with constant asymmetric permeabilities.

Abstract The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we obtain such an equation from a microscopic description using a lattice random walk model.

The top walking trails in the UK have been revealed, according to a new travel study based on route type and accommodation metrics. Worthwhile Walking Routes: The Top UK Trails, created by Peak Cottages,  reveals which of the UK’s most popular trails tick all the boxes when it comes to intensity, accessibility and aesthetics, by looking at metrics such as rest stop frequency, elevation and Instagram worthiness.