Related papers: Meshless Approximation and Helmholtz-Hodge Decompo…
In this paper we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data to a graph structure and use tools designed for automatic, unsupervised analysis of graphs.…
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…
Recent point-based differentiable rendering techniques have achieved significant success in high-fidelity reconstruction and fast rendering. However, due to the unstructured nature of point-based representations, they are difficult to apply…
A discrete boundary-sensitive Hodge decomposition is proposed as a central tool for the analysis of wall shear stress (WSS) vector fields in aortic blood flows. The method is based on novel results for the smooth and discrete…
We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region,…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
In this article, we propose a strategy for the active manipulation of scalar Helmholtz fields in bounded near field regions of an active source while maintaining desired radiation patterns in prescribed far field directions. This control…
A robust and efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector Helmholtz…
In this paper, we present a new compositing approach to obtain stylized reflections and refractions with a simple control. Our approach does not require any mask or separate 3D rendering. Moreover, only one additional image is sufficient to…
We propose DeepMetaHandles, a 3D conditional generative model based on mesh deformation. Given a collection of 3D meshes of a category and their deformation handles (control points), our method learns a set of meta-handles for each shape,…
Multicellular tissues, such as the epithelium coating a developing embryo, often combine complex tissue shapes with heterogeneity in the spatial arrangement of individual cells. Discrete approximations, such as the cell vertex model, can…
The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Ampere's law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence…
We study a holographic p-wave superconductor model in a four dimensional Einstein-Maxwell-complex vector field theory with a negative cosmological constant. The complex vector field is charged under the Maxwell field. We solve the full…
This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. In many applications, the spatial distribution of a field needs to be…
A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold $M$ and the dynamics of Hamiltonian systems. It is shown that for a given…
An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is…
Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…
Complex 3D magnetic textures in nanomagnets exhibit rich physical properties, for example in their dynamic interaction with external fields and currents, and play an increasing role for current technological challenges such as…
Classical vector waves can possess intricate spin angular momenta (SAM), which are \emph{perpendicular} to the propagation direction, as revealed by the recent recognition of surprisingly transverse SAM in electromagnetic (EM) fields. In…
We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…