Related papers: Rough Collisions
Astute variations in the geometry of mathematical billiard tables have been and continue to be a source of understanding their wide range of dynamical behaviors, from regular to chaotic. Viewing standard specular billiards in the broader…
Recent studies show interest in materials with asymmetric friction forces. We investigate terminal motion of a solid body with circular contact area. We assume that friction forces are asymmetric orthotropic. Two cases of pressure…
A class of Hamiltonian impact systems exhibiting smooth near integrable behavior is presented. The underlying unperturbed model investigated is an integrable, separable, 2 degrees of freedom mechanical impact system with effectively bounded…
In a Hamiltonian system with impacts (or "billiard with potential"), a point particle moves about the interior of a bounded domain according to a background potential, and undergoes elastic collisions at the boundaries. When the background…
We introduce the notion of a "rigid" quantum system as a system with constant relative positions of its nuclei and constant relative distribution of the electrons with respect to the nuclei. In accordance with this definition, a molecule…
We introduce a model of friction between two contacting (stationary or co-sliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact…
A body moves in a medium composed of noninteracting point particles; interaction of particles with the body is absolutely elastic. It is required to find the body's shape minimizing or maximizing resistance of the medium to its motion. This…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
Although rare, collisions of two or more bodies in the N-body problem are apparent obstacles at which Newton's Law of Gravity ceases to make sense. Without understanding the nature of collisions, a complete understanding of the N-body…
The laws of friction are reasonably well understood for the case of blocks in contact with rough plane surfaces. However, as far as bodies with circular sections are concerned, the physics of friction becomes more involving and it is not…
The general concern of this paper is the effect of rough boundaries on fluids. We consider a stationary flow, governed by incompressible Navier-Stokes equations, in an infinite domain bounded by two horizontal rough plates. The roughness is…
We study the collision between the cue and the ball in the game of billiards. After studying the collision process in detail, we write the (rotational) velocities of the ball and the cue after the collision. We also find the squirt angle of…
We generalize the Persson contact mechanics and rubber friction theory to the case where both surfaces have surface roughness. The solids can be rigid, elastic or viscoelastic, and can be homogeneous or layered. We calculate the contact…
We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. We give new results on periodicity and boundedness of orbits which suggest…
The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially…
When a rigid rough solid slides on a rigid rough surface, it experiences a random motion in the direction normal to the average contact plane. Here, through simulations of the separation at single-point contact between self-affine…
Mathematical billiards is much like the real game: a point mass, representing the ball, rolls in a straight line on a (perfectly friction-less) table, striking the sides according to the law of reflection. A billiard trajectory is then…
The point at which two random rough surfaces make contact takes place at the contact of the highest asperities. The distance upon contact d_0 in the limit of zero load has crucial importance for determination of dispersive forces. Using…
By means of Molecular Dynamics simulations, we investigate the elementary process of avalanches and size segregation by surface flow in 2 dimensions: a single ball confined to moving along an inclined line consisting of balls. The global…
We consider the motion of a finite though large number $N$ of hard spheres in the whole space $\mathbb{R}^n$. Particles move freely until they experience elastic collisions. We use our recent theory of Compensated Integrability in order to…