Brian R. Duffy

TL;DR: In this article, the tanh-function method for finding explicit travelling solitary wave solutions to non-linear evolution equations is described, and a Mathematica package ATFM is presented to deal with the tedious algebra and outputs directly the required solutions.

TL;DR: In this paper, the authors report the results of physical experiments that demonstrate the strong influence of the thermal conductivity of the substrate on the evaporation of a pinned droplet and show that this behaviour can be captured by a mathematical model including the variation of the saturation concentration with temperature, and hence coupling the problems for the vapour concentration in the atmosphere and the temperature in the liquid and the substrate.

TL;DR: In this paper, an explicit travelling solitary wave solution to a compound KdV-Burgers equation is obtained by using an automated method. And a two-dimensional generalization is discussed.

TL;DR: In this paper, the sn-and cn-function methods for finding nonsingular periodic-wave solutions to nonlinear evolution equations are described in a form suitable for automation, where sn and cn are the elliptic Jacobi snoidal andcnoidal functions, respectively.

TL;DR: In this article, the lifetime of a droplet on a solid substrate evaporating in a'stick-slide' mode is described and the unexpectedly subtle relationship between the life cycle of a single droplet and the lifetimes of initially identical droplets in the extreme modes (namely the constant contact radius and constant contact angle modes) is described.