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Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
We develop an analytical framework for self-stabilizing optical manipulation of freestanding metasurfaces in three dimensions. Our framework reveals that the challenging problem of stabilization against translational and rotational…
Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…
We compute the the Balmer spectra of compact objects of tensor triangulated categories whose objects are filtered or graded objects of (or sheaves valued in) another tensor triangulated category. Notable examples include the filtered…
Two types of finite element spaces on a tetrahedron are constructed for divdiv conforming symmetric tensors in three dimensions. The key tools of the construction are the decomposition of polynomial tensor spaces and the characterization of…
Motivated by the dynamical sampling problem, we study frames in an infinite dimensional Hilbert space generated by the iterates of a bounded operator T, also known as dynamical frames. We first characterize the operators that generate…
Neural implicit representation, the parameterization of a continuous distance function as a Multi-Layer Perceptron (MLP), has emerged as a promising lead in tackling surface reconstruction from unoriented point clouds. In the presence of…
A renormalizable rigid supersymmetry for the four dimensional antisymmetric tensor field model in a curved space-time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the…
In this article, we study the problem of recovering symmetric $m$-tensor fields (including vector fields) supported in a unit disk $\mathbb{D}$ from a set of generalized V-line transforms, namely longitudinal, transverse, and mixed V-line…
Knotted fields enrich a variety of physical phenomena, ranging from fluid flows, electromagnetic fields, to textures of ordered media. Maxwell's electrostatic equations, whose vacuum solution is mathematically known as a harmonic field,…
This paper presents the development of a complete CAD-compatible framework for structural shape optimization in 3D. The boundaries of the domain are described using NURBS while the interior is discretized with B\'ezier tetrahedra. The…
We show that there are a finite number of possible pictures for a surface in a tetrahedron with local index $n$. Combined with previous results, this establishes that any topologically minimal surface can be transformed into one with a…
Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated,…
While neural radiance fields (NeRF) have shown promise in novel view synthesis, their implicit representation limits explicit control over object manipulation. Existing research has proposed the integration of explicit geometric proxies to…
In this article I give a rigorous construction of the classical and quantum photon field on non-compact manifolds with boundary and in possibly inhomogeneous media. Such a construction is complicated by the presence of zero-modes that may…
We consider three-dimensional elastic frames constructed out of Euler-Bernoulli beams and describe extension of matching conditions by relaxing the vertex-rigidity assumption and the case in which concentrated mass may exists. This…
Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a…
Topological field theory in three dimensions provides a powerful tool to construct correlation functions and to describe boundary conditions in two-dimensional conformal field theories.
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier…