Related papers: Collision Course for Objects Moving on a Spherical…
Consider two balls with radius $r>0$ whose centers are at a distance $2$, positioned symmetrically with respect to the origin in ${\mathbb{R}}^d$. Suppose that the initial velocities are independent standard normal vectors. When $r\to0$,…
Robotic object rearrangement combines the skills of picking and placing objects. When object models are unavailable, typical collision-checking models may be unable to predict collisions in partial point clouds with occlusions, making…
We consider a bounded domain $\Omega\subset\mathbb R^3$ and a rigid body $\mathcal{S}(t)\subset\Omega$ moving inside a viscous compressible Newtonian fluid. We exploit the roughness of the body to show that the solid collides its container…
Scattering can rapidly degrade our ability to form an optical image, to the point where only speckle-like patterns can be measured. Truly non-invasive imaging through a strongly scattering obstacle is difficult, and usually reliant on a…
The risk of collision between resident space objects has significantly increased in recent years. As a result, spacecraft collision avoidance procedures have become an essential part of satellite operations. To ensure safe and effective…
We propose an approach to detect flying objects such as UAVs and aircrafts when they occupy a small portion of the field of view, possibly moving against complex backgrounds, and are filmed by a camera that itself moves. Solving such a…
We consider Deser-Sarioglu-Tekin (DST) black holes as background and we study such the motion of massive particles as the collision of two spinning particles in the vicinity of its horizon. New kinds of orbits are allowed for small…
Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The…
We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking…
In a recent article, we have shown that a variety of localized polynomial frames, including isotropic as well as directional systems, are suitable for detecting jump discontinuities along circles on the sphere. More precisely, such edges…
Bubble-particle collisions in turbulence are central to a variety of processes such as froth flotation. Despite their importance, details of the collision process have not received much attention yet. This is compounded by the sometimes…
I derive a set of canonical elements that are useful for collision orbits (perihelion distance approaching zero at fixed semimajor axis). The coordinates are the mean anomaly and the two spherical polar angles at aphelion.
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a…
An $\epsilon$-approximate incidence between a point and some geometric object (line, circle, plane, sphere) occurs when the point and the object lie at distance at most $\epsilon$ from each other. Given a set of points and a set of objects,…
Arrangement of interacting particles on a sphere is historically a well known problem, however, ordering of particles with anisotropic interaction, such as the dipole-dipole interaction, has remained unexplored. We solve the orientational…
We study the axisymmetric impact of a rigid sphere onto an elastic membrane theoretically and experimentally. We derive governing equations from first principles and impose natural kinematic and geometric constraints for the coupled motion…
We classify the singular loci of real surfaces in three-space that contain two circles through each point. We characterize how a circle in such a surface meets this loci as it moves in its pencil and as such provide insight into the…
We revisit the computation of a probability of collision in the context of automotive collision avoidance (also referred to as conflict detection in other contexts). After reviewing existing approaches to the definition and computation of a…
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…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…