相关论文: Grassmannian spectral shooting
In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector form of the discrete nonlinear Schrodinger…
Consistency Guided Scene Flow Estimation (CGSF) is a self-supervised framework for the joint reconstruction of 3D scene structure and motion from stereo video. The model takes two temporal stereo pairs as input, and predicts disparity and…
We present a novel approach for solving the shallow water equations using a discontinuous Galerkin spectral element method. The method we propose has three main features. First, it enjoys a discrete well-balanced property, in a spirit…
Gaussian splatting has recently gained traction as a compelling map representation for SLAM systems, enabling dense and photo-realistic scene modeling. However, its application to monocular SLAM remains challenging due to the lack of…
In this paper we explore practicable ways for self-consistent calculations of spectral functions from analytically continued functional renormalization group (aFRG) flow equations. As a particularly straightforward one we propose to include…
This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin,…
We tackle the task of scene flow estimation from point clouds. Given a source and a target point cloud, the objective is to estimate a translation from each point in the source point cloud to the target, resulting in a 3D motion vector…
We present a novel spectral method for the Allen-Cahn equation on spheres, eliminating the reliance on conventional quadrature exactness conditions. By replacing these conditions with a restricted isometry relation derived from…
Persistent homology is constrained to purely topological persistence while multiscale graphs account only for geometric information. This work introduces persistent spectral theory to create a unified low-dimensional multiscale paradigm for…
An accurate system to study the stability of pipe flow that ensures regularity is presented. The system produces a spectrum that is as accurate as Meseguer \& Trefethen (2000), while providing flexibility to amend the boundary conditions…
In the spectral stability analysis of localized patterns to singular perturbed evolution problems, one often encounters that the Evans function respects the scale separation. In such cases the Evans function of the full linear stability…
We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…
The Evans function is a powerful tool for the stability analysis of viscous shock profiles; zeros of this function carry stability information. In the one-dimensional case, it is typical to compute the Evans function using Goodman's…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
We study by a combination of numerical and analytical Evans function techniques the stability of solitary wave solutions of the St. Venant equations for viscous shallow-water flow down an incline, and related models. Our main result is to…
We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation…
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles…
Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g. 2005, 2009b) has…
One of the difficulties associated with the scattering problems arising in connection with integrable systems is that they are frequently non-self-adjoint, making it difficult to determine where the spectrum lies. In this paper, we consider…
We propose a method for developing the flows of stochastic dynamical systems, posed as Ito's stochastic differential equations, on a Riemannian manifold identified through a suitably constructed metric. The framework used for the stochastic…