Applied Analysis
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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 ... -
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 $u=a_i$, $0<\alpha<2$. ... -
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^ ... -
A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows
(2022-10-19)In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of the Euler equations, also the tangential ... -
Various results concerning homogenisation of nematic liquid crystals
(2022-10-17)In this thesis we present various results concerning homogenisation of nematic liquid crystals: two of them are in perforated domains, while the other one concerns rates of convergence for boundary homogenisation. The first ... -
Motion of a rigid body in a compressible fluid with Navier-slip boundary condition
(2022-11-25)In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface as well as at the boundary of the ... -
Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange
(2022-01-01)In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which ... -
Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system
(2022)The anisotropic Ginzburg-Landau system $\Delta u+\delta \nabla (div u) +\delta curl^*(curl u)=(|u|^2-1) u$, for $u\colon\mathbb R^2\to\mathbb R^2$ and $\delta\in (-1,1)$, models the formation of vortices in liquid crystals. ... -
Cubic microlattices embedded in nematic liquid crystals: A Landau-de Gennes study
(2021-01-01)We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not ... -
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 ... -
The Two Dimensional Liquid Crystal Droplet Problem with Tangential Boundary Condition
(2022-01-18)This paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a tangential anchoring boundary condition ... -
On the uniqueness of minimisers of Ginzburg-Landau functionals
(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 ... -
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 ... -
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 ... -
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 ... -
Cavity Volume and Free Energy in Many-Body Systems
(2021-10-01)Within this work, we derive and analyse an expression for the free energy of a single-species system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable ... -
Hölder regularity and convergence for a non-local model of nematic liquid crystals in the large-domain limit
(2022-02-01)We consider a non-local free energy functional, modelling a competition between entropy and pairwise interactions reminiscent of the second order virial expansion, with applications to nematic liquid crystals as a particular ... -
Nondegeneracy of heteroclinic orbits for a class of potentials on the plane
(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
(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
(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 ...