Related papers: Mechanical Snell's Law
We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a…
We study the hydrodynamic coupling between particles and solid, rough boundaries characterized by random surface textures. Using the Lorentz reciprocal theorem, we derive analytical expressions for the grand mobility tensor of a spherical…
Based on quantum mechanical approach the polarization transport of photons which propagate in a medium with slow varying refractive index is studied. The photon polarizations are separated in opposite directions normal to the ray which is…
We consider the periodic Manhattan lattice with alternating orientations going north-south and east-west. Place obstructions on vertices independently with probability $0<p<1$. A particle is moving on the edges with unit speed following the…
We study the problem of the existence, uniqueness and stability of solutions of reflected stochastic differential equations (SDEs) with a minimality condition depending on the law of the solution (and not on the paths). We require that some…
Direct numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding…
We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and…
The goal of this paper is to determine the laws of observed trajectories assuming that there is a mechanical system in the background and using these laws to continue the observed motion in a plausible way. The laws are represented by…
We consider a macroscopic body propagating in a one-dimensional resistive medium, consisting of an ideal gas at temperature $T$. For a whole family of collisions with varying degree of inelasticity, we find an exact expression for the…
We study a recently derived fully relativistic kinetic model for spin-1/2 particles. Firstly, the full set of conservation laws for energy, momentum and angular momentum are given, together with an expression for the (non-symmetric)…
The properties of light in the presence of electromagnetic and gravitational fields are compared. Once one takes account of the fact that clock rates vary with distance from a massive object, it is argued that in an absolute sense light…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…
From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations…
This work summarizes a series of studies on two-dimensional granular impact, where an intruding object strikes a granular material at high speed. Many previous studies on granular impact have used a macroscopic force law, which is dominated…
Although special relativity limits the actual velocity of a particle to $c$, the velocity of light, the observed velocity need not be the same as the actual velocity as the observer is only aware of the position of a particle at the time in…
This paper describes a path integral formulation of the free energy principle. The ensuing account expresses the paths or trajectories that a particle takes as it evolves over time. The main results are a method or principle of least action…
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…
We study the phenomena associated with the low-velocity impact of two solid discs of equal size using a cell model of brittle solids. The fragment ejection exhibits a jet-like structure the direction of which depends on the impact…
The continuous limit of large systems of particles of finite size on the line is described. The particles are assumed to move freely and stick under collision, to form compound particles whose mass and size is the sum of the masses and…
The motion of a magnetic spin particle in electromagnetic fields is considered on the basis of general principles of the classical relativistic theory. Alternative approaches in derivation of the equations of charge motion and spin…