• Effective surface energies in nematic liquid crystals as homogenised rugosity effects 

  Ceuca, R.D.; Taylor, J.M.; Zarnescu, A. (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 

  Alikakos, N.; Geng, Z.; Zarnescu, A. (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 

  Geng, Z.; Zarnescu, A. (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 

  Geng, Z.; Granero-Belinchón, R. (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 

  Ceuca, R.D. (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 

  Necasova, S.; Ramaswamy, M.; Roy, A.; Schlömerkemper, A. (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 

  Mácha, V.; Muha, B.; Nečasová, S.; Roy, A.; Trifunović, S. (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 

  Kowalczyk, M.; Lamy, X.; Smyrnelis, P.A. (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 

  Ceuca, R.D. (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 

  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 ...

• The Two Dimensional Liquid Crystal Droplet Problem with Tangential Boundary Condition 

  Geng, Z.; Lin, F. (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 

  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 ...

• 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 ...

• 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 ...

• 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 ...

• Cavity Volume and Free Energy in Many-Body Systems 

  Taylor, J.M.; Fai, T.G.; Virga, E.G.; Zheng, X.; Palffy-Muhoray, P. (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 

  Canevari, G.; Taylor, J.M. (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 

  Jendrej, J.; Smyrnelis, P.A. (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 

  Della Porta, F.; Rüland, A.; Taylor, J.M.; Zillinger, C. (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 

  Smyrnelis, P.A. (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 ...

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