Related papers: Hyperuniformity on spherical surfaces
We study hyperuniform properties for the square-triangle tilings. The tiling is generated by a local growth rule, where squares or triangles are iteratively attached to its boundary. The introduction of the probability $p$ in the growth…
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to…
The concept of typical and weighted typical spherical faces for tessellations of the $d$-dimensional unit sphere, generated by $n$ independent random great hyperspheres distributed according to a non-degenerate directional distribution, is…
Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. However, automating them, e.g., for high-throughput applications, does rarely involve…
Disordered hyperuniform systems are exotic states of matter that completely suppress large-scale density fluctuations like crystals, and yet possess no Bragg peaks similar to liquids or glasses. Such systems have been discovered in a…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…
In this paper, we study the special curves and ruled surfaces on helix hypersurface whose tangent planes make a constant angle with a fixed direction in Euclidean n-space Besides, we observe some special ruled surfaces in and give…
An extended interference pattern close to surface may result in both a transmissive or evanescent surface fields for large area manipulation of trapped particles. The affinity of differing particle sizes to a moving standing wave light…
We present a novel particle management method using the Characteristic Mapping framework. In the context of explicit evolution of parametrized curves and surfaces, the surface distribution of marker points created from sampling the…
We consider random geometric graphs on the plane characterized by a non-uniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disc with positions, in polar…
We consider random genus-0 hyperbolic surfaces $\mathcal{S}_n$ with $n + 1$ punctures, sampled according to the Weil-Petersson measure. We show that, after rescaling the metric by $n^{-1/4}$, the surface $\mathcal{S}_n$ converges in…
In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of…
We show that the theory of varifolds can be suitably enriched to open the way to applications in the field of discrete and computational geometry. Using appropriate regularizations of the mass and of the first variation of a varifold we…
Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…
Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial…
We study notions of hyperuniformity for invariant locally square-integrable point processes in regular trees. We show that such point processes are never geometrically hyperuniform, and if the diffraction measure has support in the…
Non-spherical emulsion droplets can be stabilized by densely packed colloidal particles adsorbed at their surface. In order to understand the microstructure of these surface packings, the ordering of hard spheres on ellipsoidal surfaces is…
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion.…
We present designs of 2D isotropic, disordered photonic materials of arbitrary size with complete band gaps blocking all directions and polarizations. The designs with the largest gaps are obtained by a constrained optimization method that…
Interfacial instability would be aroused on a spherical liquid droplet when it is subject to external vertical vibration. In this paper, a linear analysis was conducted on this instability problem. The polar-angle dependent acceleration in…