Related papers: Collision Course for Objects Moving on a Spherical…
Avoiding collisions between obstacles and vehicles such as cars, robots or aircraft is essential to the development of automation and autonomy. To simplify the problem, many collision avoidance algorithms and proofs consider vehicles to be…
This Engineering Note addresses the challenge of estimating the probability of collision for tethered spacecraft during close encounters with other space objects. Standard probability of collision methods, based on spherical hard-body…
We analyse the dynamics of the collision of two spherical massive shells in a generally spherically symmetric background, obtaining an expression from the conservation law that imposes a constraint between the different parameters involved.…
We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analysed by decomposing…
Let $C$ be a smooth projective curve defined over $\Qbar$, let $\pi:\mathcal{E}\lra C$ be an elliptic surface and let $\sigma_{P_1},\sigma_{P_2},\sigma_{Q}$ be sections of $\pi$ (corresponding to points $P_1,P_2, Q$ of the generic fiber $E$…
Particle-particle and particle-wall collisions occur in many natural and industrial applications such as sedimentation, agglomeration, and granular flows. To accurately predict the behavior of particulate flows, fundamental knowledge of the…
We lay out the phenomenological behavior of event-shape observables evaluated by solving optimal transport problems between collider events and reference geometries -- which we name 'manifold distances' -- to provide guidance regarding…
As we move through the world, the pattern of light projected on our eyes is complex and dynamic, yet we are still able to distinguish between moving and stationary objects. We propose that humans accomplish this by exploiting constraints…
In this work, we provide a solution to the problem of computing collision stress in particle-tracking simulations. First, a formulation for the collision stress between particles is derived as an extension of the virial stress formula to…
We investigate classical scattering off a harmonically oscillating target in two spatial dimensions. The shape of the scatterer is assumed to have a boundary which is locally convex at any point and does not support the presence of any…
We examine the behavior of $n$ Brownian particles diffusing on the real line with bounded, measurable drift and bounded, piecewise continuous diffusion coefficients that depend on the current configuration of particles. Sufficient…
Planetary-scale collisions are common during the last stages of formation of solid planets, including the Solar system terrestrial planets. The problem of growing planets has been divided into studying the gravitational interaction of…
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…
Motions of a material point along a set of parabolas are studied, taking into account the forces of Coulomb friction. The obtained results are compared with similar motions along the cycloid. The analysis is carried out using numerical…
We give a straightforward and divergence free derivation of the equation of motion for a small but finite object in an arbitrary background using strong field point particle limit. The resulting equation becomes a generalized geodesic for a…
Computing the relative motion of objects is an important navigation task that we routinely perform by relying on inherently unreliable biological cells in the retina. The non-linear and adaptive response of memristive devices make them…
This paper introduces a novel benchmark to study the impact and relationship of built environment elements on pedestrian collision prediction, intending to enhance environmental awareness in autonomous driving systems to prevent pedestrian…
We present the first triangle mesh-based technique for tracking the evolution of general three-dimensional multimaterial interfaces undergoing complex topology changes induced by deformations and collisions. Our core representation is a…
The motion of three interacting point vortices in the plane can be thought of as the motion of three geometrical points endowed with a dynamics. This motion can therefore be re-formulated in terms of dynamically evolving geometric…
We prove a symmetric version of B\'ezout's theorem. More precisely, we show that the symmetric orbit type of a transverse intersection of complex symmetric hypersurfaces in projective space is determined by the degrees. In the projective…