Applied Analysis
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Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
Jendrej, J.; Smyrnelis, P.A.
(2021)
In the scalar case, the nondegeneracy of heteroclinic orbits is a well-known property, commonly used in problems involving nonlinear elliptic, parabolic or hyperbolic P.D.E. On the other hand, Schatzman proved that in the ... -
On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
Della Porta, F.; Rüland, A.; Taylor, J.M.; Zillinger, C. (2021-07-01)
Building on the work by Ball et al (2015 MATEC Web of Conf. 33 02008), Cesana and Hambly (2018 A probabilistic model for interfaces in a martensitic phase transition arXiv:1810.04380), Torrents et al (2017 Phys. Rev. E 95 ... -
A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores
Smyrnelis, P.A. (2021)
We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions ... -
Leaky Cell Model of Hard Spheres
Fai, Tomas G.; Taylor, J.M.; Virga, Epifanio G.; Zheng, Xiaoyu; Palffy-Muhoray, Peter (9-03-20)
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 space that a sphere can explore without ... -
Double layered solutions to the extended Fisher–Kolmogorov P.D.E.
Smyrnelis, P.A. (2021-06-22)
We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work ... -
The Well Order Reconstruction Solution for Three-Dimensional Wells, in the Landau-de Gennes theory.
(2019)We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solu- tions (WORS) as a function of the well size, characterized by λ, and the well height denoted by ε. The WORS ... -
Symmetry and Multiplicity of Solutions in a Two-Dimensional Landau–de Gennes Model for Liquid Crystals
(2020-05-20)We consider a variational two-dimensional Landau–de Gennes model in the theory of nematic liquid crystals in a disk of radius R. We prove that under a symmetric boundary condition carrying a topological defect of degree ... -
Landau-de Gennes Corrections to the Oseen-Frank Theory of Nematic Liquid Crystals
(2020-01-03)We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, ... -
A Scaling Limit from the Wave Map to the Heat Flow Into S2
(2019-07-08)In this paper we study a limit connecting a scaled wave map with the heat flow into the unit sphere 𝕊2. We show quantitatively how the two equations are connected by means of an initial layer correction. This limit is ... -
On a sharp Poincare-type inequality on the 2-sphere and its application in micromagnetics
(2019-08-21)The main aim of this note is to prove a sharp Poincaré-type inequality for vector-valued functions on $\mathbb{S}^2$ that naturally emerges in the context of micromagnetics of spherical thin films. -
Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation
(2020-02-01)We consider a Landau–de Gennes model for a suspension of small colloidal inclusions in a nematic host. We impose suitable anchoring conditions at the boundary of the inclusions, and we work in the dilute regime — i.e. the ... -
The Well Order Reconstruction Solution for three-dimensional wells, in the Landau–de Gennes theory
(2020-03-01)We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solutions (WORS) as a function of the well size, characterized by 𝜆, and the well height denoted by 𝜖. The WORS ... -
An optimal scaling to computationally tractable dimensionless models: Study of latex particles morphology formation
Rusconi, S.; Dutykh, D.; Zarnescu, A.; Sokolovski, D.; Akhmatskaya, E. (2020-02)
In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such ... -
Models for damped water waves
(2019)In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative ... -
Minimizers of a Landau-de Gennes energy with a subquadratic elastic energy
(2019)We study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional ... -
Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
Rüland, A.; Taylor, J.M.; Zillinger, C. (2019-03-30)
We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop- erties: Firstly, we relate the maximal ... -
Topological singular set of vector-valued maps, I: application to manifold-constrained Sobolev and BV spaces
(2019-03-30)We introduce an operator $\mathbf{S}$ on vector-valued maps $u$ which has the ability to capture the relevant topological information carried by $u$. In particular, this operator is defined on maps that take values in a ... -
Order Reconstruction for neatics on squares with isotropic inclusions: A Landau-de Gennes study
(2019-03-30)e study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional ... -
The excluded volume of two-dimensional convex bodies: shape reconstruction and non-uniqueness
Taylor, J.M. (2019-02-05)
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 excluded to one particle by another at this ... -
Asymptotic models for free boundary flow in porous media
(2019)We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ...
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