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+34 946 567 842
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+34 946 567 843
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azarnescu@bcamath.org
Information of interest
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Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation
Canevari, G.; Zarnescu, A.
(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 ...
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Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals
Hao, W.; Xiang, X.; Zarnescu, A. (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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Entire Minimizers of Allen–Cahn Systems with Sub-Quadratic Potentials
Alikakos, N.; Gazoulis, D.; Zarnescu, A. (2021-01-01)
We study entire minimizers of the Allen–Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with sub-quadratic behaviour locally near their minima. The corresponding ...
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Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals
De Anna, F.; Zarnescu, A. (2017-10-02)
We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ...
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Landau-de Gennes Corrections to the Oseen-Frank Theory of Nematic Liquid Crystals
Di Fratta, G.; Robbins, J.M.; Slastikov, V.; Zarnescu, A. (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, ...
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Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation
Kitavtsev, G.; Robbins, J.M.; Slastikov, V.; Zarnescu, A. (2016-12-31)
We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general $k$-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent ...
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Mathematical problems of nematic liquid crystals: between dynamical and stationary problems
Zarnescu, A. (2021-05-24)
Mathematical studies of nematic liquid crystals address in general two rather different perspectives: That of fluid mechanics and that of calculus of variations. The former focuses on dynamical problems while the latter ...
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On a hyperbolic system arising in liquid crystal modelling
Feireisl, E.; Rocca, E.; Schimperna, G.; Zarnescu, A. (2017-11)
We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ...
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On a sharp Poincare-type inequality on the 2-sphere and its application in micromagnetics
Fratta, G.D.I.; Slastikov, V.; Zarnescu, A. (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.
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On the uniqueness of minimisers of Ginzburg-Landau functionals
Ignat, R.; Nguyen, L.; Slastikov, V.; Zarnescu, A. (2020)
We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for Rn-valued maps under a suitable convexity assumption on the potential and for H1=2 \ L1 boundary data ...
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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 ...
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Partial regularity and smooth topology-preserving approximations of rough domains
Ball, J.M.; Zarnescu, A. (2017-01-01)
For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partial\Omega$ can be locally represented ...
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A phenomenological model for interfacial water near hydrophilic polymers
Earls, A.; Calderer, M.-C.; Desroches, M.; Zarnescu, A.; Rodrigues, S. (2022-06-30)
We propose a minimalist phenomenological model for the ‘interfacial water’ phenomenon that occurs near hydrophilic polymeric surfaces. We achieve this by combining a Ginzburg–Landau approach with Maxwell’s equations which ...
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A Scaling Limit from the Wave Map to the Heat Flow Into S2
Jiang, N.; Luo, Y.-L.; Tang, S.; Zarnescu, A. (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 ...
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Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals
Murza, A.C.; Teruel, A.E.; Zarnescu, A. (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 ...
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Sphere-valued harmonic maps with surface energy and the K13 problem
Day, S.; Zarnescu, A. (2017-11)
We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an ...
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Symmetry and Multiplicity of Solutions in a Two-Dimensional Landau–de Gennes Model for Liquid Crystals
Ignat, R.; Nguyen, L.; Slastikov, V.; Zarnescu, A. (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 ...
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Topics in the mathematical design of materials
Chen, X.; Fonseca, I.; Ravnik, M.; Slastikov, V.; Zannoni, C.; Zarnescu, A. (2021-01-01)
We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phase-transforming and shape-morphing materials, (ii) epitaxy as an ...
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Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
Ignat, R.; Nguyen, L.; Slastikov, V.; Zarnescu, A. (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 ...
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Weak sequential stability for a nonlinear model of nematic electrolytes
Fereisl, E.; Rocca, E.; Schimperna, G.; Zarnescu, A. (2021-01-01)
In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a ...