Related papers: Repulsive Curves
We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…
It remains a challenge to simultaneously remove geometric distortion and space-time-varying blur in frames captured through a turbulent atmospheric medium. To solve, or at least reduce these effects, we propose a new scheme to recover a…
A numerical scheme for computing arc-length parametrized curves of low bending energy that are confined to convex domains is devised. The convergence of the discrete formulations to a continuous model and the unconditional stability of an…
We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a…
Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…
Atmospheric powered descent guidance can be solved by successive convexification; however, its onboard application is impeded by the sharp increase in computation caused by nonlinear aerodynamic forces. The problem has to be converted into…
We present a lightweight network that infers grouping and boundaries, including curves, corners and junctions. It operates in a bottom-up fashion, analogous to classical methods for sub-pixel edge localization and edge-linking, but with a…
Using computer simulations and a thermodynamically self consistent integral equation we investigate the phase behaviour and thermodynamic anomalies of a fluid composed of spherical particles interacting via a two-scale ramp potential (a…
A simple and reliable algorithm for collision avoidance maneuvers (CAMs), capable of computing impulsive, multi-impulsive, and low-thrust maneuvers, is proposed. The probability of collision (PoC) is approximated by a polynomial of…
Plasmas with varying collisionalities occur in many applications, such as tokamak edge regions, where the flows are characterized by significant variations in density and temperature. While a kinetic model is necessary for…
We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned…
Recent work has demonstrated real-time mapping and reconstruction from dense perception, while motion planning based on distance fields has been shown to achieve fast, collision-free motion synthesis with good convergence properties.…
We present a wavelet-based adaptive method for computing 3D multiscale flows in complex, time-dependent geometries, implemented on massively parallel computers. While our focus is on simulations of flapping insects, it can be used for other…
Due to critical environmental issues, the power systems have to accommodate a significant level of penetration of renewable generation which requires smart approaches to the power grid control. Associated optimal control problems are…
Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
We prove a discrete analog of a certain four-vertex theorem for space curves. The smooth case goes back to the work of Beniamino Segre and states that a closed and smooth curve whose tangent indicatrix has no self-intersections admits at…
Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…
An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles placed in $\mathbb{R}^d (d \geq 1)$. The particles perform random jumps with pair wise repulsion, in the…
When generalizing schemes for real-valued data approximation or decomposition to data living in Riemannian manifolds, tangent space-based schemes are very attractive for the simple reason that these spaces are linear. An open challenge is…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…