Related papers: Measuring Lattices
Precision measurement of small separations between two atoms or molecules has been of interest since the early days of science. Here, we discuss a scheme which yields spatial information on a system of two identical atoms placed in a…
A direct formulation of linear elasticity of cell complexes based on discrete exterior calculus is presented. The primary unknown are displacements, represented by primal vector-valued 0-cochain. Displacement differences and internal forces…
The decay B^0 -> DK^{*0} is well-known to provide excellent potential for a precise measurement of the Unitarity Triangle angle gamma in future experiments. It is noted that the sensitivity can be significantly enhanced by studying the…
Detached eclipsing double line spectroscopic binaries offer an opportunity to measure directly stellar parameters: mass, luminosity, radius, as well as the distance. The only non-trivial step is the need to determine surface brightness of…
In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of $\Gamma$-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi…
Cellular solids are a class of materials that have many interesting engineering applications, including ultralight structural materials. The traditional method for analyzing these solids uses convex uniform polyhedral honeycombs to…
In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater…
A technique is presented for the design of printed unit cells in aperiodic metasurface environments. The method begins with a solved matrix equation governing electromagnetic scattering from a homogenized metasurface design. The matrix…
We study three-dimensional microlensing where two lenses are located at different distances along the line of sight. We formulate the lens equation in complex notations and recover several previous results. There are in total either 4 or 6…
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…
Information on the lattice parameter of single crystals with known crystallographic structure allows for estimations of sample quality and composition. In many cases it is suffcient to determine one lattice parameter or the lattice spacing…
We propose a simple linear scaling expression in reciprocal space for evaluating the ion--electron potential of crystalline solids. The expression replaces the long-range ion--electron potential with an equivalent localized charge…
Parallax is the most important astronomical method for determining the distances from the Earth to nearby stars. We present two hands-on activities that explore the concepts and practice of parallax measurement. The first activity is a…
We propose a new method with $\mathcal{L}_2$ distance that maps one $N$-dimensional distribution to another, taking into account available information about correspondences. We solve the high-dimensional problem in 1D space using an…
Accurate and efficient methods to evaluate cosmological distances are an important tool in modern precision cosmology. In a flat $\Lambda$CDM cosmology, the luminosity distance can be expressed in terms of elliptic integrals. We derive an…
We derive an analytical closed expression to compute the minimum distance (quantified by the angle of separation measured from the center of the Earth) between any two satellites located at the same altitude and in circular orbits. We also…
A measurement technique is described which has the potential to map the atomic site occupancies of ultracold atoms in a short-period three-dimensional optical lattice. The method uses accordion and pinning lattices, together with…
This paper extends the recently obtained complete and continuous map of the Lattice Isometry Space (LISP) to the practical case of dimension 3. A periodic 3-dimensional lattice is an infinite set of all integer linear combinations of basis…
The coincidence site lattices (CSLs) of prominent 4-dimensional lattices are considered. CSLs in 3 dimensions have been used for decades to describe grain boundaries in crystals. Quasicrystals suggest to also look at CSLs in dimensions…
The measurement of the silicon lattice parameter by a separate-crystal triple-Laue x-ray interferometer is a key step for the kilogram realisation by counting atoms. Since the measurement accuracy is approaching nine significant digits, a…