Related papers: Exactly quantized dynamics of classical incommensu…
A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of $n$ rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by…
The nonequilibrium steady state of a granular fluid, driven by a random external force, is demonstrated to exhibit long range correlations, which behave as $\sim 1/r$ in three and $\sim \ln(L/r)$ in two dimensions. We calculate the…
The quantum motion of nuclei, generally ignored in sliding friction, can become important for an atom, ion, or light molecule sliding in an optical lattice. The density-matrix-calculated evolution of a quantum Prandtl-Tomlinson model,…
A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm ``quantum system is measured by a classical apparatus" is untenable, while a quantum matter can be…
The quantization of the forced harmonic oscillator is studied with the quantum variable ($x,\hat v$), with the commutation relation $[x,\hat v]=i\hbar/m$, and using a Shr\"odinger's like equation on these variable, and associating a linear…
We numerically study the flow of dense granular materials between parallel plates driven by an external force. The granular materials form a jammed solid-like state when the external force is below a critical force, while they flow like…
The equations of electrostatic drift kinetics are observed to possess a symmetry associated with their intrinsic scale invariance. Under the assumptions of spatial periodicity, stationarity, and locality, this symmetry implies a particular…
A simple example of one particle moving in a (1+1) space-time is considered. As an example we take the harmonic oscillator. We confirm the statement that the classical Equations of Motion do not determine at all the quantization scheme. To…
Exact solutions for symmetric discrete breathers (DBs) are obtained in forced-damped linear chain with on-site vibro-impact constraints. The damping is related to inelastic impacts; the forcing may be chosen from broad class of periodic…
We review the mechanism for transport in strongly anharmonic chains of oscillators near the atomic limit where all oscillators are decoupled. In this regime, the motion of most oscillators remains close to integrable, i.e. quasi-periodic,…
We study the clustering properties of particles sliding downwards on a fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo simulations on a…
The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure…
We study the short-time dynamics of a liquid ligament, held between two solid cylinders, when one is impulsively accelerated along its axis. A set of one-dimensional equations in the slender-slope approximation is used to describe the…
We derive a novel and rigorous correction to the classical Reynolds lubrication approximation for fluids with viscosity depending upon the pressure. Our analysis shows that the pressure dependence of viscosity leads to additional nonlinear…
New method of quantization is presented. It is based on classical Newton-Lagrange equations of motion (representing the fundamental physical law of mechanics) rather than on their traditional Lagrangian and/or Hamiltonian precursors. It is…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
The equations for the sliding of a single block driven by an elastic force show numerically a fast and a slow step in their dynamics when a dimensionless parameter is very large, a limit pertinent for many applications. An asymptotic…
Classical simulations of high-temperature nuclear spin dynamics in solids are known to accurately predict relaxation for spin 1/2 lattices with a large number of interacting neighbors. Once the number of interacting neighbors becomes four…
It has long been recognized that the key to understand kinetic friction force $F_k$ is the analysis of microscopic instabilities that lead to sudden irreversible "pops" of certain degrees of freedom. In this Letter, the nature of such…
The dynamics of fluid particles on cylindrical manifolds is investigated. The velocity field is obtained by generalizing the isotropic Kraichnan ensemble, and is therefore Gaussian and decorrelated in time. The degree of compressibility is…