Related papers: Diamond-Kite Adaptive Quadrilateral Meshing
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
The recently discovered Hat tiling admits a 4-dimensional family of shape deformations, including the 1-parameter family already known to yield alternate monotiles. The continuous hulls resulting from these tilings are all topologically…
Two-dimensional lattices provide the arena for many physics problems of essential importance, a non-trivial symmetry in such lattices will help to reveal the underlying physics. Whether there is a directional scaling for the 2D lattices is…
We demonstrate the fabrication of sub-micron layers of single-crystal diamond suitable for subsequent processing as demonstrated by this test ring structure. This method is a significant enabling technology for nanomechanical and photonic…
We summarise three applications of the obstacle problem to membrane contact, elastoplastic torsion and cavitation modelling, and show how the resulting models can be solved using mixed finite elements. It is challenging to construct fixed…
Diamond 1 - 10 micrometers thick membranes are platform for photonic, quantum and opto-mechanic devices with applications across UV-IR spectral ranges. IR characterization of diamond gratings in reflection and transmission showed a change…
Micrometer-scale thin diamond devices are key components for various quantum sensing and networking experiments, including the integration of color centers into optical microcavities. In this work, we introduce a laser-cutting method for…
We present a new approach combining top down fabrication and bottom up overgrowth to create diamond photonic nanostructures in form of single-crystalline diamond nanopyramids. Our approach relies on diamond nanopillars, that are overgrown…
We use inverse methods of statistical mechanics and computer simulations to investigate whether an isotropic interaction designed to stabilize a given two-dimensional (2D) lattice will also favor an analogous three-dimensional (3D)…
We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…
In this paper we give a classification of tilings of the sphere by congruent quadrilaterals with exactly two equal edges. The tilings are the earth map tilings, $(p,q)$-earth map tilings and their flip modifications, and quadrilateral…
We present a multi-edge-length aperiodic tiling which exhibits 6--fold rotational symmetry. The edge lengths of the tiling are proportional to 1:$\tau$, where $\tau$ is the golden mean $\frac{1+\sqrt{5}}{2}$. We show how the tiling can be…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
We study exotic smoothings of open 4-manifolds using the minimal genus function and its analog for end homology. While traditional techniques in open 4-manifold smoothing theory give no control of minimal genera, we make progress by using…
A particular discrete rhombohedral lattice consisting of four symmetrically interlaced cuboctahedral point lattices is described that is interesting because of the high degree of symmetry it exhibits. The four constituent cuboctahedral…
Nitrogen-vacancy (NV) centers in diamond have attracted significant interest because of their excellent spin and optical characteristics for quantum information and metrology. To take advantage of the characteristics, the precise control of…
We present atomistic simulations for the mechanical response of ultra nanocrystalline diamond, a polycrystalline form of diamond with grain diameters of the order of a few nm. We consider fully three-dimensional model structures, having…
All-dielectric metamaterials consisting of high-dielectric inclusions in a low-dielectric matrix are considered as a low-loss alternative to resonant metal-based metamaterials. In this contribution we investigate the applicability of the…
Exploring nonminimal-rank quasicrystals, which have symmetries that can be found in both periodic and aperiodic crystals, often provides new insight into the physical nature of aperiodic long-range order in models that are easier to treat.…
We investigate symmetric grain boundaries in a lamellar diblock copolymer system. The form of the interface between two grains strongly depends on the angle $\theta$, between the normals of the grains. When this angle is small, the lamellae…