Related papers: Rational Relativistic Collisions
For a triangle $\Delta$, let (P) denote the problem of the existence of points in the plane of $\Delta$, that are at rational distance to the 3 vertices of $\Delta$. Answer to (P) is known to be positive in the following situation: $\Delta$…
We aim to create deterministic collisions between orbiting bodies by applying a time-dependent external force to one or both bodies, whether the bodies are mutually repulsive, as in the two- or multi-electron atomic case or mutually…
We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…
Motivated by the problem of formation control for vehicles moving at unit speed in three-dimensional space, we are led to models of gyroscopically interacting particles, which require the machinery of curves and frames to describe and…
A consistent theory, which describes the incoherent scattering of classically moving relativistic particles by the nuclei of crystal planes without any phenomenological parameter is presented. The basic notions of quantum mechanics are…
We reinvestigate the problem of the appearance of relativistic jets when geometrical opening is taken into account. We propose a new criterion to define apparent velocities and Doppler factors, which we think being determined by the…
We experimentally examine the dynamics of two-particle collisions occuring on a surface. We find that in two-particle collisions a standard coefficient of restitution model may not capture crucial dynamics of this system. Instead, for a…
Given a projective intersection of two quadrics X in at least 9 variables, the quantitative behaviour of the rational points on X is investigated under the assumption that X contains a pair of conjugate singular points defined over the…
According to Newton's law of gravitation the force between two particles depends upon their inertial, as well as their active and passive gravitational masses. For ordinary matter all three of these are equal and positive. We consider here…
I show that particle collider experiments on relativistic nuclear collisions can serve as direct probes of the deformation of the colliding nuclear species. I argue that collision events presenting very large multiplicities of particles and…
Recursion formulae are derived for the calculation of two centre matrix elements of a radial function in relativistic quantum mechanics. The recursions are obtained between not necessarily diagonal radial eigensates using arbitrary radial…
Since some experiments have found superluminality, we assume that the particles in the universe are divided into three classes: the subluminal, luminal and superluminal particles by the speed of light, their energy-momenum relations are E2…
We perform direct numerical simulations of a bi-disperse suspension of heavy spherical particles in forced, homogeneous, and isotropic three-dimensional turbulence. We compute the joint distribution of relative particle distances and…
Forces parallel to particle trajectories occur in physically meaningful situations, including relativistic cosmology and Einstein frame scalar-tensor gravity. These situations have Newtonian analogues that we discuss to provide intuition…
We consider the one-dimensional scattering of two identical blocks of mass $M$ that exchange energy and momentum via elastic collisions with an intermediary ball of mass $m=\alpha M$. Initially, one block is incident upon the ball with the…
Lagrangian and Hamiltonian formulations of a free spinning particle in 2+1-dimensions or {\it anyon} are established, following closely the analysis of Hanson and Regge. Two viable (and inequivalent) Lagrangians are derived. It is also…
We consider the evolution of a parton system which is formed at the central rapidity region just after an ultrarelativistic heavy ion collision. The evolution of the system, which is composed of gluons, quarks and antiquarks, is described…
If gamma ray bursts are highly collimated, the energy requirements of each event may be reduced by several (~ 4-6) orders of magnitude, and the event rate increased correspondingly. Extreme conditions in gamma ray bursters lead to highly…
Two particle collisions close to the horizon of the rotating nonextremal Kerr's and Schwarzschild black holes are analyzed. For the case of multiple collisions it is shown that high energy in the centre of mass frame occurs due to a great…
We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system's center of mass is at rest. In the second…