Related papers: Torque-operated gradient-index axicon

It has been a widely belief that for a planar convex domain with two coordinate axes of symmetry, the location of maximal norm of gradient of torsion function is either linked to contact points of largest inscribed circle or connected to…

Solar sails with the capability of generating a tangential radiation pressure at the sun-pointing attitude, such as refractive sails can provide more efficient methods for attitude and orbital control of sailcraft. This paper presents the…

We derive a general expression for the deformation-gradient tensor by invoking the standard definition of a gradient of a vector field in curvilinear coordinates. This expression shows the connection between the standard definition of a…

The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…

Motivated by the sampling problems and heterogeneity issues common in high- dimensional big datasets, we consider a class of discordant additive index models. We propose method of moments based procedures for estimating the indices of such…

This work aims at analysing the moment effects at the tool tip point and at the central axis, in the framework of a turning process. A testing device in turning, including a six-component dynamometer, is used to measure the complete torsor…

We use micromagnetic modelling to demonstrate the operation of graded index lenses designed to steer forward-volume magnetostatic spin waves by 90 and 180 degrees. The graded index profiles require the refractive index to diverge in the…

This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a…

This paper investigates fractional torsional rigidity on compact, connected metric graphs, a novel extension of the classical concept to nonlocal operators. The fractional torsional rigidity is defined as the $L^1$-norm of the fractional…

We use twisted relative Picard varieties to split Brauer classes on projective varieties over algebraically closed fields by torsors for a fixed abelian scheme independent of the Brauer class. The construction is also used to prove that the…

We investigate the location of the maximal gradient of the torsion function on certain non-symmetric planar domains. First, by establishing uniform estimates for convex narrow domains, we show that as a planar domain bounded by two graphs…

This work focuses on the gradient flow dynamics of a neural network model that uses correlation loss to approximate a multi-index function on high-dimensional standard Gaussian data. Specifically, the multi-index function we consider is a…

Twisting by a G-torsor an object endowed with an action of a group G is a classical tool. For instance one finds in the paragraph 5.3 of the book "cohomologie galoisienne" by Serre, the description of the "op\'eration de torsion" in a…

Statistical moments of velocity gradients provide fundamental information on the small-scale properties of turbulence. In this work, we propose a systematic method to derive exact expressions for statistical moments of arbitrary order for…

An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X. The main result is…

Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…

The optimization of physical parameters serves various purposes, such as system identification and efficiency in developing devices. Spin-torque oscillators have been applied to neuromorphic computing experimentally and theoretically, but…

We define analytic torsion of Z_2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a…

Purpose: This paper presents a full fourth-order model of the gravity gradient torque of spacecraft around asteroids by taking into consideration of the inertia integrals of the spacecraft up to the fourth order, which is an improvement of…

We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…