Related papers: Scalar Representation of 2D Steady Vector Fields
In this study we revisit the problem of computing steady Navier-Stokes flows in two-dimensional unbounded domains. Precise quantitative characterization of such flows in the high-Reynolds number limit remains an open problem of theoretical…
Approximate streamsurfaces of a 3D velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical…
The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional…
Instantaneous features of three-dimensional velocity fields are most directly visualized via streamsurfaces. It is generally unclear, however, which streamsurfaces one should pick for this purpose, given that infinitely many such surfaces…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
Topological abstractions offer a method to summarize the behavior of vector fields but computing them robustly can be challenging due to numerical precision issues. One alternative is to represent the vector field using a discrete approach,…
In this paper, we prove that every planar graph has a 1-string $B_2$-VPG representation---a string representation using paths in a rectangular grid that contain at most two bends. Furthermore, two paths representing vertices $u,v$ intersect…
We propose a new approach to compute correlators of quantum fields in de Sitter space. It is based on nonequilibrium field theory techniques, and exploits de Sitter symmetries so as to partially reduce the number of independent variables of…
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
We examine the decay of passive scalars with small, but non zero, diffusivity in bounded 2D domains. The velocity fields responsible for advection are smooth (i.e., they have bounded gradients) and of a single large scale. Moreover, the…
3D Gaussian splats have emerged as a revolutionary, effective, learned representation for static 3D scenes. In this work, we explore using 2D Gaussian splats as a new primitive for representing videos. We propose GSVC, an approach to…
We present a covariant formalism for studying nonlinear perturbations of scalar fields. In particular, we consider the case of two scalar fields and introduce the notion of adiabatic and isocurvature covectors. We obtain differential…
We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the…
Even though the analysis of unsteady 2D flow fields is challenging, fluid mechanics experts generally have an intuition on where in the simulation domain specific features are expected. Using this intuition, showing similar regions enables…
The stationary velocity field (SVF) approach allows to build parametrizations of invertible deformation fields, which is often a desirable property in image registration. Its expressiveness is particularly attractive when used as a block…
This paper presents a practical approach for the optimization of topological simplification, a central pre-processing step for the analysis and visualization of scalar data. Given an input scalar field f and a set of "signal" persistence…
Differentiable vector graphics (VGs) are widely used in image vectorization and vector synthesis, while existing representations are costly to optimize and struggle to achieve high-quality rendering results for high-resolution images. This…
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
We integrate smoothing B-splines into a standard differentiable vector graphics (DiffVG) pipeline through linear mapping, and show how this can be used to generate smooth and arbitrarily long paths within image-based deep learning systems.…