Applied Analysis
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The Well Order Reconstruction Solution for Three-Dimensional Wells, in the Landau-de Gennes theory.
(University of Strathclyde Glasgow, 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
(Archive for Rational Mechanics and Analysis, 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
(Archive for Rational Mechanics and Analysis, 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
(Communications in Mathematical Sciences, 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
(SIAM Journal on Mathematical Analysis, 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
(Mathematical Models and Methods in Applied Sciences, 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
(International Journal of Non-Linear Mechanics, 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
(Computer Physics Communications, 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
(SIAM Journal of Applied Mathematics, 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
(Archive for Rational Mechanics and Analysis, 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
(Journal of Nonlinear Science, 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
(Calculus of Variations and Partial Differential Equations, 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
(SIAM Journal on Applied Mathematics, 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
(Journal of Physics A: Mathematical and Theoretical, 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
(Physica D, 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 ... -
On the influence of gravity on density-dependent incompressible periodic fluids
(J. Differential Equations, 2019)The present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number $\varepsilon$ goes to zero. We consider the very general case where the initial data do not have ... -
A Global well-posedness result for the Rosensweig system of ferrofluids
(Rev. Mat. Iberoam., 2019)In this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this ... -
Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
(Comptes Rendus Mathematique, 2018-09-01)For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ... -
Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals
(Proceedings of the Royal Society A-Mathematical, Physical and Engineering Sciences, 2018-02-14)We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in ... -
Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals
(Archive for Rational Mechanics and Analysis, 2018-08-10)We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the ...
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