Related papers: Relieving nematic geometric frustration in the pla…

We study nonlinear resolvents of holomorphic generators of one-parameter semigroups acting in the open unit disk. The class of nonlinear resolvents can be studied in the framework of geometric function theory because it consists of…

Using Landau-de Gennes theory to describe nematic order, we study a frustrated cell consisting of nematic liquid crystal confined between two parallel plates. We prove the uniqueness of equilibrium states for a small cell width. Letting the…

Metric anomalies arising from a distribution of point defects (intrinsic interstitials, vacancies, point stacking faults), thermal deformation, biological growth, etc. are well known sources of material inhomogeneity and internal stress. By…

An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element…

In this paper we classify the solutions to the geometric Neumann problem for the Liouville equation in the upper half-plane or an upper half-disk, with the energy condition given by finite area. As a result, we classify the conformal…

We consider an integral equation in the plane, in which the leading operator is of convolution type, and we prove that monotone (or stable) solutions are necessarily one-dimensional.

We study quasiconformal mappings of the unit disk that have planar extension with controlled distortion. For these mappings we prove a bound for the modulus of continuity of the inverse map, which somewhat surprisingly is almost as good as…

Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…

In the article we generalise the quasisolution approach to the planar aerohydrodynamics problems to 3D case. We search for solution in the form of the linear spline.

Our object of study is non smooth vector fields on $\R^2$. We apply the techniques of geometric singular perturbations in non smooth vector fields after regularization and a blow$-$up. In this way we are able to bring out some results that…

We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form band gaps (ranges of frequency in which the…

We build two embedded resolution procedures of a quasi-ordinary singularity of complex analytic hypersurface, by using toric morphisms which depend only on the characteristic monomials associated to a quasi-ordinary projection of the…

Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the…

We consider discretization of the 'geometric cover problem' in the plane: Given a set $P$ of $n$ points in the plane and a compact planar object $T_0$, find a minimum cardinality collection of planar translates of $T_0$ such that the union…

We give a description of the intrinsic geometry of elastic distortions in three-dimensional nematic liquid crystals and establish necessary and sufficient conditions for a set of functions to represent these distortions by describing how…

A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…

In this article, we characterize the distortion elements of the group of smooth diffeomorphisms of the circle and of the group of compactly supported smooth diffeomorphisms of the real line. More precisely, we prove that, in this context,…

Nematic interfaces are thin fluid films, ideally two-dimensional, endowed with an in-plane degenerate nematic order. In this letter we examine a generalisation of the classical Plateau problem to an axisymmetric nematic interface bounded by…

We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers,…

A vector field similar to those separately introduced by Artstein and Dafermos is constructed from the tangent to a monotone increasing one-parameter family of non-concentric circles that touch at the common point of intersection taken as…