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In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…
Chiral nematic liquid crystals exhibit both a helical planar ground state with uniform twist and a metastable defect-rich focal conic texture, and can be switched between the two microstructures via application of transient voltage pulses.…
Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the…
The continuum mechanics of line defects representing singularities due to terminating discontinuities of the elastic displacement and its gradient field is developed. The development is intended for application to coupled phase…
Active nematics in two dimensions stir themselves efficiently through internally generated chaotic flows, largely driven by motile $+1/2$ disclinations. We investigate how this tendency toward chaotic fluid stirring can, counterintuitively,…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
We investigate channel-confined, nematic liquid crystals using the Beris-Edwards model of nematohydrodynamics. Using strong homeotropic anchoring at the walls, we find multistability i.e. multiple coexisting states where the uniform nematic…
Topological defects are increasingly being identified in various biological systems, where their characteristic flow fields and stress patterns are associated with continuous active stress generation by biological entities. Here, using…
We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…
We use analytic arguments and numerical solutions of the continuum, active nematohydrodynamic equations to study how friction alters the behaviour of active nematics. Concentrating on the case where there is nematic ordering in the passive…
We prove a structure theorem for the solutions of nonlinear thin two-membrane problems in dimension two. Using the theory of quasi-conformal maps, we show that the difference of the sheets is topologically equivalent to a solution of the…
We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain in $\mathbb{R}^2$. For…
Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the…
We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $\mathbb{R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
Exact solutions are derived for the problem of a two-dimensional, infinitely anisotropic, linear-elastic medium containing a periodic lattice of voids. The matrix material possesses either one infinitely soft, or one infinitely hard loading…
Increasing evidence suggests that active matter exhibits instances of mixed symmetry that cannot be fully described by either polar or nematic formalism. Here, we introduce a minimal model that integrates self-propulsion into the active…
Evolving from turbulent states the 2D fluids and the plasmas reach states characterized by a high degree of order, consisting of few vortices. These asymptotic states represent a small subset in the space of functions and are characterised…
We propose an agent-based model of active flexible rods. Inspired by cytoskeletal flows, we introduce activity by an internal flow that contributes to the dissipative forces. The active force between our agents is central and reciprocal,…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…