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+34 946 567 842
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+34 946 567 842
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azarnescu@bcamath.org
Information of interest
 Orcid: 0000000236206196
My research focuses on the analytical study of fundamental models from condensed matter physics. After graduating from the University of Chicago, under the supervision of Prof. Peter Constantin, with a thesis on polymeric fluids, I moved to Oxford, for 5 years, working under the mentorship of Prof. John M. Ball, on variational theories of liquid crystals. After that I moved away from Oxford, and developed my independent directions of research, while at the University of Sussex, as a lecturer, for 5 years. Since 2016 I have been working as an Ikerbasque Research Professor in BCAM, as a researchleader of the Applied Analysis, while also holding a parttime position at the "Simion Stoilow" Institute of Mathematics, in Bucharest, Romania.

Reducing Model Complexity by Means of the Optimal Scaling: Population Balance Model for Latex Particles Morphology Formation.
(20230415)Rational computeraided design of multiphase polymer materials is vital for rapid progress in many important applications, such as: diagnostic tests, drug delivery, coatings , additives for constructing materials, cosmetics, ...

Uniform profile near the point defect of Landaude Gennes model
(20221104)For the Landaude Gennes functional on 3D domains, $$ I_\varepsilon(Q,\Omega):=\int_{\Omega}\left\{\frac12\nabla Q^2+\frac{1}{\varepsilon^2}\left( \frac{a^2}{2}\mathrm{tr}(Q^2)\frac{b^2}{3}\mathrm{tr}(Q^3)+\frac{c^ ...

Asymptotic behavior of the interface for entire vector minimizers in phase transitions
(20220915)We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of AllenCahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim ua_i^\alpha$ near $u=a_i$, $0<\alpha<2$. ...

A phenomenological model for interfacial water near hydrophilic polymers
(20220630)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 ...

Mathematical problems of nematic liquid crystals: between dynamical and stationary problems
(20210524)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 ...

Topics in the mathematical design of materials
(20210101)We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phasetransforming and shapemorphing materials, (ii) epitaxy as an ...

Entire Minimizers of Allen–Cahn Systems with SubQuadratic Potentials
(20210101)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 subquadratic behaviour locally near their minima. The corresponding ...

Weak sequential stability for a nonlinear model of nematic electrolytes
(20210101)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 ...

Effective surface energies in nematic liquid crystals as homogenised rugosity effects
(2021)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 liquid crystal theories. We use techniques ...

Symmetry and Multiplicity of Solutions in a TwoDimensional Landau–de Gennes Model for Liquid Crystals
(20200520)We consider a variational twodimensional 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 ...

Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation
(20200201)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 ...

An optimal scaling to computationally tractable dimensionless models: Study of latex particles morphology formation
(202002)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 ...

Landaude Gennes Corrections to the OseenFrank Theory of Nematic Liquid Crystals
(20200103)We study the asymptotic behavior of the minimisers of the Landaude Gennes model for nematic liquid crystals in a twodimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, ...

On the uniqueness of minimisers of GinzburgLandau functionals
(2020)We provide necessary and sufficient conditions for the uniqueness of minimisers of the GinzburgLandau functional for Rnvalued maps under a suitable convexity assumption on the potential and for H1=2 \ L1 boundary data ...

On a sharp Poincaretype inequality on the 2sphere and its application in micromagnetics
(20190821)The main aim of this note is to prove a sharp Poincarétype inequality for vectorvalued functions on $\mathbb{S}^2$ that naturally emerges in the context of micromagnetics of spherical thin films.

A Scaling Limit from the Wave Map to the Heat Flow Into S2
(20190708)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 ...

Uniqueness of degreeone Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
(20180901)For ε>0, we consider the GinzburgLandau functional for RNvalued 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 ...

Dynamics and flow effects in the BerisEdwards system modeling nematic liquid crystals
(20180810)We consider the BerisEdwards system modelling incompressible liquid crystal flows of nematic type. This couples a NavierStokes system for the fluid velocity with a parabolic reactionconvectiondiffusion equation for the ...

Shear flow dynamics in the BerisEdwards model of nematic liquid crystals
(20180214)We consider the BerisEdwards 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 ...

Spherevalued harmonic maps with surface energy and the K13 problem
(201711)We consider an energy functional motivated by the celebrated K13 problem in the OseenFrank theory of nematic liquid crystals. It is defined for spherevalued functions and appears as the usual Dirichlet energy with an ...

On a hyperbolic system arising in liquid crystal modelling
(201711)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 ...

Global wellposedness and twistwave solutions for the inertial QianSheng model of liquid crystals
(20171002)We consider the inertial QianSheng model of liquid crystals which couples a hyperbolictype equation involving a secondorder material derivative with a forced incompressible NavierStokes system. We study the energy law ...

Partial regularity and smooth topologypreserving approximations of rough domains
(20170101)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 ...

Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the oneconstant approximation
(20161231)We consider the twodimensional Landaude 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 ...