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Uniform profile near the point defect of Landau-de Gennes model
(2022-11-04)
For the Landau-de 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
(2022-09-15)
We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of Allen-Cahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim |u-a_i|^\alpha$ near $u=a_i$, $0<\alpha<2$. ...
Mathematical problems of nematic liquid crystals: between dynamical and stationary problems
(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 ...
Topics in the mathematical design of materials
(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 ...
Entire Minimizers of Allen–Cahn Systems with Sub-Quadratic Potentials
(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 ...
Weak sequential stability for a nonlinear model of nematic electrolytes
(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 ...
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 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 ...
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 ...
An optimal scaling to computationally tractable dimensionless models: Study of latex particles morphology formation
(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 ...