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The stray- and demagnetization tensor field for a homogeneously magnetized tetrahedron is found analytically. The tetrahedron is a special case of four triangular faces with constant magnetization-charge surface density, for which we also…
The underlying structural disorder renders the concept of topological defects in amorphous solids difficult to apply and hinders a first-principle identification of the microscopic carriers of plasticity and of the regions more prone to…
State-of-the-art methods for driving-scene LiDAR-based perception (including point cloud semantic segmentation, panoptic segmentation and 3D detection, \etc) often project the point clouds to 2D space and then process them via 2D…
This paper introduces a 3D shape generative model based on deep neural networks. A new image-like (i.e., tensor) data representation for genus-zero 3D shapes is devised. It is based on the observation that complicated shapes can be well…
We analyze human poses and motion by introducing three sequences of easily calculated surface descriptors that are invariant under reparametrizations and Euclidean transformations. These descriptors are obtained by associating to each…
Our goal in this paper is to apply the topological signal processing (TSP) framework to the analysis of 3D Point Clouds (PCs) represented on simplicial complexes. Building on Discrete Exterior Calculus (DEC) theory for vector fields, we…
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…
This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity…
We measure the deformation of particles made of several slender arms in a two-dimensional (2D) linear shear and a three-dimensional (3D) turbulent flow. We show how these measurements of arm deformations along with the rotation rate of the…
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and…
Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and…
A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D…
Tensor network states are expected to be good representations of a large class of interesting quantum many-body wave functions. In higher dimensions, their utility is however severely limited by the difficulty of contracting the tensor…
Physical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or…
The triple decomposition of a velocity gradient tensor is studied with direct numerical simulations of homogeneous isotropic turbulence, where the velocity gradient tensor is decomposed into three components representing an irrotational…
Textured 3D meshes jointly represent geometry, topology, and appearance, yet their irregular structure poses significant challenges for deep-learning-based semantic segmentation. While a few recent methods operate directly on meshes without…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…
The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry. Point features, however, are not available…
In recent years, substantial progress has been achieved in learning-based reconstruction of 3D objects. At the same time, generative models were proposed that can generate highly realistic images. However, despite this success in these…