42 citations · 98 across the 20 of their papers we have counts for
21 papers
Bound excited states of Fröhlich polarons in one dimension
Jamie Taylor, Matija Čufar, David Mitrouskas +3
The one-dimensional Fröhlich model describing the motion of a single electron interacting with optical phonons is a paradigmatic model of quantum many-body physics. We predict the…
A confined rod: mean field theory for hard rod-like particles
Jamie M. Taylor, Thomas G. Fai, Epifanio G. Virga +2
In this paper, we model the configurations of a system of hard rods by viewing each rod in a cell formed by its neighbors. By minimizing the free energy in the model and performing…
Interaction energies in paranematic colloids
Dmitry Golovaty, Jamie Taylor, Raghavendra Venkatraman +1
We consider a system of colloidal particles embedded in a paranematic -- an isotropic phase of a nematogenic medium above the temperature of the nematic-to-isotropic transition. In…
Deep Fourier Residual method for solving time-harmonic Maxwell's equations
Jamie M. Taylor, Manuela Bastidas, David Pardo +1
Solving PDEs with machine learning techniques has become a popular alternative to conventional methods. In this context, Neural networks (NNs) are among the most commonly used mach…
Machine Learning Discovery of Optimal Quadrature Rules for Isogeometric Analysis
Tomas Teijeiro, Jamie M. Taylor, Ali Hashemian +1
We propose the use of machine learning techniques to find optimal quadrature rules for the construction of stiffness and mass matrices in isogeometric analysis (IGA). We initially…
A Deep Fourier Residual Method for solving PDEs using Neural Networks
Jamie M. Taylor, David Pardo, Ignacio Muga
When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be made is the loss function to be minimised, which should ideally correspond to a norm of…
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…
Leaky Cell Model of Hard Spheres
Thomas G. Fai, Jamie M. Taylor, Epifanio G. Virga +2
We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e. the volume of…
On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
Francesco Della Porta, Angkana Rüland, Jamie M Taylor +1
Building on the work in \cite{BCH15,CH18,TIVP17}, in this article we propose and study a simple, geometrically constrained, probabilistic algorithm geared towards capturing some as…
-convergence of a mean-field model of a chiral doped nematic liquid crystal to the Oseen-Frank description of cholesterics
Jamie M. Taylor
Systems of elongated molecules, doped with small amounts of molecules lacking mirror symmetry can form macroscopically twisted cholesteric liquid crystal phases. The aim of this wo…
The excluded volume of two-dimensional convex bodies: Shape reconstruction and non-uniqueness
Jamie M. Taylor
In the Onsager model of one-component hard-particle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excl…
Contributions of Repulsive and Attractive Interactions to Nematic Order
Peter Palffy-Muhoray, Jamie M. Taylor, Epifanio G. Virga +1
Both repulsive and attractive molecular interactions can be used to explain the onset of nematic order. The object of this paper is to combine these two nematogenic molecular inter…
Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
Angkana Rüland, Jamie M. Taylor, Christian Zillinger
We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is two-fold, treating both rigidity and flexibility propert…
Oseen-Frank-type theories of ordered media as the -limit of a non-local mean-field free energy
Jamie M. Taylor
In this work we recover the Oseen-Frank theory of nematic liquid crystals as a -limit of a particular mean-field free energy as the sample size becomes infinitely large. The Fra…
Density functional theory for dense nematics with steric interactions
Eduardo S. Nascimento, Peter Palffy-Muhoray, Jamie M. Taylor +2
The celebrated work of Onsager on hard particle systems, based on the truncated second order virial expansion, is valid at relatively low volume fractions for large aspect ratio pa…
An analysis of equilibria in dense nematic liquid crystals
Jamie M. Taylor
This paper is concerned with the rigorous analysis of a recently proposed model of Zheng et. al. for describing nematic liquid crystals within the dense regime, with the orientatio…
Non-Gaussian chain statistics and finite extensibility in liquid crystal elastomers
Jamie M. Taylor
In this work we will derive an anisotropic generalisation of the finitely extensible chain model, due to Kuhn and Grün, which is well known in rubber elasticity. This provides a ch…
Maximum entropy methods as the bridge between macroscopic and microscopic theory
Jamie M. Taylor
This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of…