Related papers: Diamond-Kite Adaptive Quadrilateral Meshing
One remarkable feature of virtual element methods (VEMs) is their great flexibility and robustness when used on almost arbitrary polytopal meshes. This very feature makes it widely used in both fitted and unfitted mesh methods. Despite…
Morphology and its stability are essential features to address physicochemical properties of metallic nanoparticles. By means of Molecular Dynamics based simulations we show a complex dependence on the size and material of common structural…
We consider domino tilings of the Aztec diamond. Using the Domino Shuffling algorithm introduced by Elkies, Kuperberg, Larsen, and Propp in arXiv:math/9201305, we are able to generate domino tilings uniformly at random. In this paper, we…
The inverse Kasteleyn matrix of a bipartite graph holds much information about the perfect matchings of the system such as local statistics which can be used to compute local and global asymptotics. In this paper, we consider three…
We formulate Dirac fermions on a (1+1)-dimensional lattice based on a Hamiltonian formalism. The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around…
We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…
Celestial diamonds encode the global conformal multiplets of the conformally soft sector, elucidating the role of soft theorems, symmetry generators and Goldstone modes. Upon adding supersymmetry they stack into a pyramid. Here we treat the…
Three dimensional waveguides within the bulk of diamond are manufactured using ultrafast laser fabrication. High intensities within the focal volume of the laser cause breakdown of the diamond into a graphitic phase leading to a stress…
Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any…
We construct smooth finite element de Rham complexes in two space dimensions. This leads to three families of curl-curl conforming finite elements, two of which contain two existing families. The simplest triangular and rectangular finite…
We report fabrication and results of high-resolution X-ray topography characterization of diamond single crystal plates with a large surface area (10$\times$10 mm$^2$) and (111) crystal surface orientation for applications in high-heat-load…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
Due to recent development of growing and processing techniques for high-quality single crystal diamond, the large scale production of diamond optomechanical crystal cavities becomes feasible, enabling optomechanical devices that can operate…
Cavity-optomechanical systems realized in single-crystal diamond are poised to benefit from its extraordinary material properties, including low mechanical dissipation and a wide optical transparency window. Diamond is also rich in…
We map certain highly correlated electron systems on lattices with geometrical frustration in the motion of added particles or holes to the spatial defect-defect correlations of dimer models in different geometries. These models are studied…
In situ studies under severe plastic deformation at high pressures, employing rotational/shear diamond anvil cells (RDAC), have recently gained much interest in the high-pressure community owing to their potential applications in material…
We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the…