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
(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 $u=a_i$, $0<\alpha<2$. ... 
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^ ... 
A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows
(20221019)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
(20221017)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 Navierslip boundary condition
(20221125)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 Navierslip boundary condition at the interface as well as at the boundary of the ... 
Existence of a weak solution to a nonlinear fluidstructure interaction problem with heat exchange
(20220101)In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heatconducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a timedependent domain which ... 
Entire vortex solutions of negative degree for the anisotropic GinzburgLandau system
(2022)The anisotropic GinzburgLandau system $\Delta u+\delta \nabla (div u) +\delta curl^*(curl u)=(u^21) u$, 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 Landaude Gennes study
(20210101)We consider a Landaude 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
(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 ... 
The Two Dimensional Liquid Crystal Droplet Problem with Tangential Boundary Condition
(20220118)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 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 ... 
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 ... 
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 ... 
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 ... 
Cavity Volume and Free Energy in ManyBody Systems
(20211001)Within this work, we derive and analyse an expression for the free energy of a singlespecies 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 nonlocal model of nematic liquid crystals in the largedomain limit
(20220201)We consider a nonlocal 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 wellknown 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
(20210701)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 ...