Related papers: Diamond-Kite Adaptive Quadrilateral Meshing
Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterised by their director profile. In certain confined, colloidal and even more prominently in chiral nematics, the director profile may…
Many soft matter systems exhibit ordered, polycontinuous network morphologies, such as the cubic (double) gyroid or diamond, as well as disordered network morphologies known generically as ``random sponges". While presumed to share similar…
We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
We investigate nearest-neighbor valence-bond wave functions on bipartite three-dimensional lattices. By performing large-scale Monte Carlo simulations, we find that long-range magnetic order coexists with dipolar four-spin correlations on…
We classify the dihedral edge-to-edge tilings of the sphere by squares and rhombi.
In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In…
We study the electronic properties of the glide set of dislocations in diamond from first principles using hybrid exchange correlation functionals and find that the atomic-scale dislocation core states give rise to a prototypical…
We study the conformation and topological properties of cyclical star polymers with $f$ ring arms, each made of $n$ beads. We find that the conformational properties of unlinked cyclical star polymers are compatible to those of linear star…
Transformations between group coordinates of three--dimensional conformal sigma models in the flat background and their flat, i.e. Riemannian coordinates enable to find general dilaton fields for three-dimensional flat sigma models. By the…
Using evolutionary algorithm and first-principles calculations, we predict a family group of two-dimensional node-line semimetals MX (M=Pd, Pt; X=S, Se, Te), which has zig-zag type mono-layer structure in Pmm2 layer group. Band structure…
An upward equilateral triangle of side $n$ can be partitioned into $n$ unit upward equilateral triangles and $\frac{n(n-1)}{2}$ unit rhombi with $60^{\circ}$ and $120^{\circ}$ angles. In this paper, we focus on understanding such partitions…
Finite element codes typically use data structures that represent unstructured meshes as collections of cells, faces, and edges, each of which require associated coordinate systems. One then needs to store how the coordinate system of each…
Hexagonal diamond has been predicted computationally to display extraordinary physical properties including a hardness that exceeds cubic diamond. However, a recent electron microscopy study has shown that so-called hexagonal diamond…
We study symplectic structures on four-dimensional small covers. Our main result shows that every symplectic four-dimensional small cover is aspherical. We then classify symplectic small covers over products of two polygons, proving that…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
This paper describes in detail the construction of a local right-handed, orthogonal curvilinear coordinate system whose axes are along the local tangent, the local azimuth and the local normal of an analytically defined 3D surface of…
Graphite and diamond are two well-known allotropes of carbon with distinct physical properties due to different atomic connectivity. Graphite has a layered structure in which the honeycomb carbon sheets can easily glide, while atoms in…
Block copolymers often create droplets when placed on a substrate. Such nanostructured droplets can be arranged into regular microstructured arrays, thereby forming hierarchically organized materials that can be used in microelectronics,…
We propose two general operations on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods. The first operation, called DoF-transfer, moves edge…