Related papers: Tetrahedral frame fields via constrained third ord…
Interaction between dipolar forces, such as permanent magnets, generally leads to the formation of one-dimensional chains and rings. We investigated whether it was possible to let dipoles self-assemble into three-dimensional structures by…
In the past year several constructions of non-invertible symmetries in Quantum Field Theory in $d\geq 3$ have appeared. In this paper we provide a unified perspective on these constructions. Central to this framework are so-called theta…
A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the…
We propose a class of models which generate three-dimensional random volumes, where each configuration consists of triangles glued together along multiple hinges. The models have matrices as the dynamical variables and are characterized by…
We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes and show their exactness on contractible domains. This complex includes vector fields and symmetric and traceless tensor fields, connected…
Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
We illustrate a rigorous approach to express the totally symmetric isotropic tensors of arbitrary rank in the $n$-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one…
We consider Trace finite element methods for the linear membrane problem on second order tetrahedral elements. To accomplish this, zero-level set reconstruction methods for second order tetrahedra are considered. For the higher order…
A family of conforming virtual element Hessian complexes on tetrahedral meshes are constructed based on decompositions of polynomial tensor spaces. They are applied to discretize the linearized time-independent Einstein-Bianchi system with…
We present a new approach for computing planar hexagonal meshes that approximate a given surface, represented as a triangle mesh. Our method is based on two novel technical contributions. First, we introduce Coordinate Power Fields, which…
In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of…
We propose a hybridized domain decomposition formulation of the discrete fracture network model, allowing for independent discretization of the individual fractures. A natural norm stabilization, obtained by penalizing the residual measured…
In this work we consider the issue of localization of antisymmetric tensor fields of arbitrary rank in a D dimensional Space-time with a codimension two. A string-like defect is used to simulate the membrane. The localization of massless…
It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…
The analysis and visualization of tensor fields is a very challenging task. Besides the cases of zeroth- and first-order tensors, most techniques focus on symmetric second-order tensors. Only a few works concern totally symmetric tensors of…
A new topography adapted mesh generation process tailored to simulate Atmospheric Boundary Layer (ABL) flows on complex terrains is presented. The mesher is fully automatic given: the maximum and minimum surface mesh size, the size of the…
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…
Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…