• 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 ...

• Leaky Cell Model of Hard Spheres 

  Fai, Tomas G.; Taylor, J.M.; Virga, Epifanio G.; Zheng, Xiaoyu; Palffy-Muhoray, Peter (9-03-20)

  We study packings of hard spheres on lattices. The partition function, and therefore the pressure, may be written solely in terms of the accessible free volume, i.e., the volume of space that a sphere can explore without ...

• Double layered solutions to the extended Fisher–Kolmogorov P.D.E. 

  Smyrnelis, P.A. (2021-06-22)

  We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work ...

• The Well Order Reconstruction Solution for Three-Dimensional Wells, in the Landau-de Gennes theory. 

  Canevari, G.; Harris, J.; Majumdar, A.; Wang, Y. (2019)

  We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solu- tions (WORS) as a function of the well size, characterized by λ, and the well height denoted by ε. The WORS ...

• Symmetry and Multiplicity of Solutions in a Two-Dimensional Landau–de Gennes Model for Liquid Crystals 

  Ignat, R.; Nguyen, L.; Slastikov, V.; Zarnescu, A. (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 ...

• Landau-de Gennes Corrections to the Oseen-Frank Theory of Nematic Liquid Crystals 

  Di Fratta, G.; Robbins, J.M.; Slastikov, V.; Zarnescu, A. (2020-01-03)

  We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, ...

• A Scaling Limit from the Wave Map to the Heat Flow Into S2 

  Jiang, N.; Luo, Y.-L.; Tang, S.; Zarnescu, A. (2019-07-08)

  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 ...

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