We report on observations of a free-Shercliff-layer instability in a Taylor-Couette experiment using a liquid metal over a wide range of Reynolds numbers, $Re\sim 10^3-10^6$. The free Shercliff layer is formed by imposing a sufficiently strong axial...
We study the geometry of gauge fluxes in four-dimensional F-theory vacua with gauge group SU(3)xSU(2)xU(1)xU(1) and its implications for phenomenology. The models are defined by a previously introduced class of elliptic fibrations whose fibre is give...
The PIP-II project at Fermilab, which includes an 800-MeV superconducting LINAC, demands rigorous radiation shielding optimization to meet safety requirements. We updated the MARS geometry model to reflect new magnet and collimator designs and introd...
We show that the Wynn recurrence (the missing identity of Frobenius of the Padé approximation theory) can be incorporated into the theory of integrable systems as a reduction of the discrete Schwarzian Kadomtsev-Petviashvili equation. This allows, i...
A certain type of integer grid, called here an echelon grid, is an object found both in coherent systems whose components have a finite or countable number of levels and in algebraic geometry. If α=(α_1,...,α_d) is an integer vector representing...
Lagrangian systems with nonholonomic constraints may be considered as singular differential equations defined by some constraints and some multipliers. The geometry, solutions, symmetries and constants of motion of such equations are studied within...
The importance of examining the structure of centre-vortex matter in the ground-state fields of nonabelian gauge-field theory has been demonstrated in the recent centre-vortex based discovery of a second finite-temperature transition in QCD associate...
Aug 19, 2025 · Over the last half 50 years, fractals have challenged ideas about geometry and pushed math, science and technology into unexpected areas.
A key question in the interaction of droplets with lubricated and liquid-infused surfaces is what determines the apparent contact angle of droplets. Previous work has determined this using measured values of the geometry of the `skirt' -- the meniscu...
The prominent Russian mathematician Igor Rostislavovich Shafarevich passed away on February 19, 2017. In this article we supply his biography, discuss his many important contributions to number theory, algebra and algebraic geometry, and also discuss...
We describe the geometry of Küchle varieties (i.e. Fano 4-folds of index 1 contained in the Grassmannians as zero loci of equivariant vector bundles) with Picard number greater than 1 and the structure of their derived categories....
We initiate the study of subpolytopes of the permutahedron that arise as the convex hulls of stack-sorting on permutations. We primarily focus on $Ln1$ permutations, i.e., permutations of length $n$ whose penultimate and last entries are $n$ and $1$,...
Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct...
A contamination in a 3-manifold is an object interpolating between the contact structure and the lamination. Contaminations seem to provide a link between 3-dimensional contact geometry and the classical topology of 3-manifolds, as described in a s...
Point cloud analysis is challenging due to irregularity and unordered data structure. To capture the 3D geometries, prior works mainly rely on exploring sophisticated local geometric extractors using convolution, graph, or attention mechanisms. These...
Coevolutionary Rate Geometry · Genomic Strategy Phase Transitions · Arms Race Bifurcation on the Fitness Interaction Manifold https://www.youtube.com/watch?v=IE1aHf34_PA (⭐ 0)
A convex geometry is a closure system satisfying the anti-exchange property. This paper, following the work of K. Adaricheva and M. Bolat (2016) and the Polymath REU 2020 team, continues to investigate representations of convex geometries on a 5-elem...
A convex geometry is a closure system satisfying the anti-exchange property. In this work we document all convex geometries on 4- and 5-element base sets with respect to their representation by circles on the plane. All 34 non-isomorphic geometries o...
Given an original distribution, its statistical and probabilistic attributs may be scanned by the associated escort distribution introduced by Beck and Schlogl and employed in the formulation of nonextensive statistical mechanics. Here, the geometr...
We introduce a deep generative network for 3D shape detailization, akin to stylization with the style being geometric details. We address the challenge of creating large varieties of high-resolution and detailed 3D geometry from a small set of exempl...