Related papers: Integrable Frame Fields using Odeco Tensors
We discretize a tangential tensor field equation using a surface-finite element approach with a penalization term to ensure almost tangentiality. It is natural to measure the quality of such a discretization intrinsically, i.e., to examine…
We present Factor Fields, a novel framework for modeling and representing signals. Factor Fields decomposes a signal into a product of factors, each represented by a classical or neural field representation which operates on transformed…
We introduce a spin field approach, that is compatible with the Cartan moving frame method, to describe the submanifold in a flat space. In fact, we consider a kind of spin field $\psi$, that satisfies a Killing spin field equation…
Orbital angular momentum (OAM) detection underpins almost all aspects of vortex beams' advances such as communication and quantum analogy. Conventional schemes are frustrated by low speed, complicated system, limited detection range. Here,…
Embedding fields provide a way of coupling a background structure to a theory while preserving diffeomorphism-invariance. Examples of such background structures include embedded submanifolds, such as branes; boundaries of local subregions,…
An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…
Minkowski tensors are comprehensive shape descriptors that robustly capture n-point information in complex random geometries and that have already been extensively applied in the Euclidean plane. Here, we devise a novel framework for…
Octupolar tensors are third order, completely symmetric and traceless tensors. Whereas in 2D an octupolar tensor has the same symmetries as an equilateral triangle and can ultimately be identified with a vector in the plane, the symmetries…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
This paper is concerned with the inverse problem of reconstructing small and local perturbations of a planar surface using the field interaction between a known plasmonic particle and the planar surface. The aim is to perform a…
We classify, up to a natural equivalence relation, vector fields of the plane which belong to the kernel of a 1--form. This form can be closed, in which case the vector fields are integrable, or not, in which case the differential of the…
The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear…
We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers of independent linear forms, or equivalently, for decomposing symmetric tensors into sums of rank-1 symmetric tensors of linearly independent…
Multi-mode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication, sensing…
This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…
Geometric features, robust to noise, of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis. We apply the Fels-Olver's moving frame method (for geometric features) paired with…
We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on…
Optical levitation of nanoscale particles has emerged as a platform for precision measurement. Extremely low damping, together with optical interferometric position detection, makes possible exquisite force measurement and promises…
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the…
Maxwell's equations are formulated in arbitrary moving frames by means of tetrad fields, which are interpreted as reference frames adapted to observers in space-time. We assume the existence of a general distribution of charges and currents…