Related papers: Point defects in 2-D liquid crystals with singular…
Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter,…
In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the…
We consider the geometric inverse problem of determining a closed Riemannian manifold from measurements of the heat kernel in an open subset of the manifold. In this paper we analyze the stability of this problem in the class of…
We study stable surfaces, i.e., second order minima of the area for variations of fixed volume, in sub-Riemannian space forms of dimension $3$. We prove a stability inequality and provide sufficient conditions ensuring instability of…
The 2-sets convex feasibility problem aims at finding a point in the intersection of two closed convex sets $A$ and $B$ in a normed space $X$. More generally, we can consider the problem of finding (if possible) two points in $A$ and $B$,…
We consider a two-dimensional, pure capillary drop of nearly-circular shape, having constant vorticity. We write the Craig-Sulem equations on the unit circle, then on the flat torus. We show their Hamiltonian structure and we then observe…
We study finite-time blowup for a nonlinear wave equation for maps from the Minkowski space $\mathbb{R}^{1+d}$ into the 1-sphere $\mathbb{S}^1$, whose nonlinearity exhibits a null-form structure. We construct, for every dimension $d \geq…
We study the $k$-center problem in a kinetic setting: given a set of continuously moving points $P$ in the plane, determine a set of $k$ (moving) disks that cover $P$ at every time step, such that the disks are as small as possible at any…
We investigate stability properties of the radially symmetric solution corresponding to the vortex defect (so called "melting hedgehog") in the framework of the Landau - de Gennes model of nematic liquid crystals. We prove local stability…
The dynamical stability of three-dimensional (3D) Lennard-Jones (LJ) crystals has been studied for many years. The face-centered-cubic and hexagonal close packed structures are dynamically stable, while the body-centered cubic structure is…
An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at…
We demonstrate a novel method of introducing point defects (mono and di-vacancies) in a confined mono-layer colloidal crystal by manipulating individual particles with optical tweezers. Digital video microscopy is used to study defect…
We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…
Within the Landau-de Gennes theory of liquid crystals, we study theoretically the equilibrium configurations with uniaxial symmetry. We show that the uniaxial symmetry constraint is very restrictive and can in general not be satisfied,…
Topological point defects on orientationally ordered spheres, and on deformable fluid vesicles have been partly motivated by their potential applications in creating super-atoms with directional bonds through functionalization of the…
We present a symmetry result regarding stationary solutions of the 2D Euler equations in a disk. We prove that in a disk, a steady flow with only one stagnation point and tangential boundary conditions is a circular flow, which confirms a…
We provide a short proof of the $L^2$-orbital stability of a class of explicit steady Euler flows in a disk by establishing a quantitative estimate. The main idea is to exploit the conserved quantities of the Euler equation, including the…
We establish various qualitative properties of liquid Lane-Emden stars in $\mathbb{R}^d$, including bounds for its density profile $\rho$ and radius $R$. Using them we prove that against radial perturbations, the liquid Lane-Emden stars are…
We investigate the stability of stars with a density discontinuity between a high-density core and a very low density mantle. Previous work on "strange dwarfs" suggested that such a discontinuity could stabilize stars that would have been…
We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau--de Gennes framework in terms of two geometry-dependent variables: half short edge length…