42 citations · 98 across the 20 of their papers we have counts for
4 papers · 1 filter
On quadrature rules for solving Partial Differential Equations using Neural Networks
Jon A. Rivera, Jamie M. Taylor, Ángel J. Omella +1
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate v…
Effective surface energies in nematic liquid crystals as homogenised rugosity effects
Razvan-Dumitru Ceuca, Jamie M. Taylor, Arghir Zarnescu
We study the effect of boundary rugosity in nematic liquid crystalline systems. We consider a highly general formulation of the problem, able to simultaneously deal with several li…
Cavity volume and free energy in many-body systems
Jamie M. Taylor, Thomas G. Fai, Epifanio G. Virga +2
Within this work we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exac…
Hölder regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit
Giacomo Canevari, Jamie M. Taylor
We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with application…