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We consider defining the embedding of a triangle mesh into $R^3$, up to translation, rotation, and scale, by its vector of dihedral angles. Theoretically, we show that locally, almost everywhere, the map from realizable vectors of dihedrals…
We have constructed the geometric phases emerging from the non-trivial topology of a space-dependent magnetic field, interacting with the spin magnetic moment of a neutral particle. Our basic tool is the local unitary transformation which…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace re- search community is working on next generation of CFD capacity that is accurate, automatic, and fast. A…
Triangle-hinge models [arXiv:1503.08812] are introduced to describe worldvolume dynamics of membranes. The Feynman diagrams consist of triangles glued together along hinges and can be restricted to tetrahedral decompositions in a large N…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
The squared Laplace operator acting on symmetric rank-two tensor fields is studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this fourth-order elliptic operator is obtained provided that such tensor fields and their…
Three-dimensional magnetic nanostructures are an emerging platform capable of creating complex topological magnetic fields. The control of localized nanoscale magnetic fields is seen to be of importance for diverse areas from…
In a model of nonlinear system of three scalar fields the problem on dynamics of a massive particle moving in effective potential provided by two relativistic fields is solving. The potentials for these fields are chosen in the form of…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
The concepts of controlled frames and it's dual in n-Hilbert spaces and their tensor products have been introduced and then some of their characterizations are given. We further study the relationship between controlled frame and bounded…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
The fundamental matrix and trifocal tensor are convenient algebraic representations of the epipolar geometry of two and three view configurations, respectively. The estimation of these entities is central to most reconstruction algorithms,…
For each object in a tensor triangulated category, we construct a natural continuous map from the object's support---a closed subset of the category's triangular spectrum---to the Zariski spectrum of a certain commutative ring of…
When obtaining interior 3D voxel data from triangular meshes, most existing methods fail to handle low quality meshes which happens to take up a big portion on the internet. In this work we present a robust voxelization method that is based…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
A continuum density-field formulation with particle-scale resolution is constructed to simultaneously incorporate the orientation dependence of interparticle interactions and the rotational invariance of the system, a fundamental but…
We introduce and study a new 3d Topological Field Theory which can be associated to any compact real manifold X. This TFT is analogous to the 2d A-model and reduces to it upon compactification on an interval with suitable boundary…
We investigate three-dimensional nonparaxial linear accelerating beams arising from the transverse Whittaker integral. They include different Mathieu, Weber, and Fresnel beams, among other. These beams accelerate along a semicircular…
We give a combinatorial characterization of minimally rigid planar frameworks with orientation-preserving crystallographic symmetry, under the constraint of forced symmetry. The main theorems are proved by extending the methods of the first…