Related papers: Measuring Lattices
Connes' distance formula is applied to endow linear metric to three 1D lattices of different topology, with a generalization of lattice Dirac operator written down by Dimakis et al to contain a non-unitary link-variable. Geometric…
We present a novel method to transport ultra cold atoms in a focused optical lattice over macroscopic distances of many Rayleigh ranges. With this method ultra cold atoms were transported over 5 cm in 250 ms without significant atom loss or…
Two-dimensional spatial solitonic lattices are generated and investigated experimentally and numerically in an SBN:Ce crystal. An enhanced stability of these lattices is achieved by exploiting the anisotropy of coherent soliton interaction,…
Bravais lattices are the most fundamental building blocks of crystallography. They are classified into groups according to their translational, rotational, and inversion symmetries. In computational analysis of Bravais lattices, fulfilment…
The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for…
Small displacement methods have been successfully used to calculate the lattice dynamical properties of crystals. It involves displacing atoms by a small amount in order to calculate the induced forces on all atoms in a supercell for the…
We present an adaptive geometry in which the yardstick co-deforms with space itself, formulated on cellular spaces where length is a count: distances are shortest cell-crossing counts. No cell shape, angles, or embedding are assumed; the…
Accurate distances to local molecular clouds are critical for understanding the star and planet formation process, yet distance measurements are often obtained inhomogeneously on a cloud-by-cloud basis. We have recently developed a method…
In this paper, we introduce a three-dimensional mathematical model of collagen contraction with microbuckling based on the two-dimensional model previously developed by the authors. The model both qualitatively and quantitatively replicates…
Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…
Synthetic dimensions alter one of the most fundamental properties in nature, the dimension of space. They allow, for example, a real three-dimensional system to act as effectively four-dimensional. Driven by such possibilities, synthetic…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the…
Sickle cell disease causes erythrocytes to become sickle-shaped, affecting their movement in the bloodstream and reducing oxygen delivery. It has a high global prevalence and places a significant burden on healthcare systems, especially in…
Most well-established and widely used color difference (CD) metrics are handcrafted and subject-calibrated against uniformly colored patches, which do not generalize well to photographic images characterized by natural scene complexities.…
Learning an effective representation of 3D point clouds requires a good metric to measure the discrepancy between two 3D point sets, which is non-trivial due to their irregularity. Most of the previous works resort to using the Chamfer…
We present a new code for solving the molecular and atomic excitation and radiation transfer problem in a molecular gas and predicting emergent spectra. This code works in arbitrary three dimensional geometry using unstructured Delaunay…
In this exploratory study, two photon decay widths of pseudo-scalar ($\eta_c$) and scalar ($\chi_{c0}$) charmonium are computed using two ensembles of $N_f=2$ twisted mass lattice QCD gauge configurations. The simulation is performed two…
The metric dimension of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. Applications of metric dimension include discovering the source of a spread in a network,…
Segmentation of cell nuclei in microscopy images is a prevalent necessity in cell biology. Especially for three-dimensional datasets, manual segmentation is prohibitively time-consuming, motivating the need for automated methods.…