Renormalized energy between vortices in some Ginzburg–Landau models on 2-dimensional Riemannian manifolds

R Ignat, RL Jerrard - Archive for Rational Mechanics and Analysis, 2021 - Springer
We study a variational Ginzburg–Landau type model depending on a small parameter ε> 0
ε> 0 for (tangent) vector fields on a 2-dimensional Riemannian manifold S. As ε → 0 ε→ 0 …

Nematic liquid crystals on curved surfaces: a thin film limit

I Nitschke, M Nestler, S Praetorius… - Proceedings of the …, 2018 - royalsocietypublishing.org
We consider a thin film limit of a Landau–de Gennes Q-tensor model. In the limiting process,
we observe a continuous transition where the normal and tangential parts of the Q-tensor …

Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation

G Canevari, A Zarnescu - … Models and Methods in Applied Sciences, 2020 - World Scientific
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 …

The antiferromagnetic XY model on the triangular lattice: topological singularities

A Bach, M Cicalese, L Kreutz, G Orlando - arXiv preprint arXiv:2011.10445, 2020 - arxiv.org
We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the
two-dimensional triangular lattice in the vortex regime. Within this regime, the spin system …

The antiferromagnetic XY model on the triangular lattice: chirality transitions at the surface scaling

A Bach, M Cicalese, L Kreutz, G Orlando - Calculus of Variations and …, 2021 - Springer
We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the
two-dimensional triangular lattice. The system is fully frustrated and displays two families of …

Polydispersity and surface energy strength in nematic colloids

G Canevari, A Zarnescu - arXiv preprint arXiv:1910.03342, 2019 - arxiv.org
We consider a Landau-de Gennes model for a polydisperse, inhomogeneous suspension of
colloidal inclusions in a nematic host, in the dilute regime. We study the homogenised limit …

Rigid and deformable bodies in nematic liquid crystals

TGJ Chandler, SE Spagnolie - Physical Review Fluids, 2024 - APS
A nematic liquid crystal, a phase of matter composed of rodlike molecules, exhibits a
tendency towards uniform molecular alignment. Bodies inserted into such a fluid can disturb …

[HTML][HTML] Interaction energy between vortices of vector fields on Riemannian surfaces

R Ignat, RL Jerrard - Comptes Rendus Mathematique, 2017 - Elsevier
We study a variational Ginzburg–Landau-type model depending on a small parameter ε> 0
for (tangent) vector fields on a 2-dimensional Riemannian surface. As ε→ 0, the vector fields …

Landau-de Gennes corrections to the Oseen-Frank theory of nematic liquid crystals

G Di Fratta, JM Robbins, V Slastikov… - Archive for Rational …, 2020 - Springer
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 …

Active nematic fluids on Riemannian 2-manifolds

C Zhu, D Saintillan, A Chern - arXiv preprint arXiv:2405.06044, 2024 - arxiv.org
Recent advances in cell biology and experimental techniques using reconstituted cell
extracts have generated significant interest in understanding how geometry and topology …