Related papers: Exactly solvable dynamical models with a minimal l…

We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…

Recent model simulations discovered unexpected non-monotonic features in the wear-free dry phononic friction as a function of the sliding speed. Here we demonstrate that a rather straight- forward application of linear-response theory,…

In many interacting particle systems, relaxation to equilibrium is thought to occur via the growth of 'droplets', and it is a question of fundamental importance to determine the critical length at which such droplets appear. In this paper…

We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions.…

We obtain some existence theorems for periodic solutions to several linear equations involving fractional Laplacian. We also prove that the lower bound of all periods for semilinear elliptic equations involving fractional Laplacian is not…

Dynamical behaviors of a dissipative particle in a periodic potential subject to chaotic noise are reported. We discovered a macroscopic symmetry breaking effect of chaotic noise on a dissipative particle in a multi-stable systems emerging,…

We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly…

A free particle coupled to a heat bath can exhibit a number of thermodynamic anomalies like a negative specific heat or reentrant classicality. These low-temperature phenomena are expected to be modified at very low temperatures where…

We study the dynamics of a mechanical oscillator with linear and cubic forces -the Duffing oscillator- subject to a feedback mechanism that allows the system to sustain autonomous periodic motion with well-defined amplitude and frequency.…

We calculate the first order maximal acceleration corrections to the classical electrodynamics of a particle in external electromagnetic fields. These include additional dissipation terms, the presence of a critical electric field, a…

For the classical N-body problem, an approach is proposed based on the introduction of some natural in the physical sense optimization problems of mathematical programming for finding a conditional minimum for the characteristics of the…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach…

Subharmonic response is a well known phenomena in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics…

A variation of fundamental constants of physics is proposed in a frame of static universe. It is shown when the velocity of light increases (decreases) the Planck's constant increases (decreases) and mass of bodies decreases (increases).…

A classical particle in a harmonic potential gives rise to a continuous energy spectra, whereas the corresponding quantum particle exhibits countably infinite quantized energy levels. In recent years, classical non-Markovian wave-particle…

We investigate the structure of discontinuities in clearance (or minimum time) functions for nonlinear control systems with general, closed obstacles (or targets). We establish general results regarding interactions between admissible…

We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces. Our approach is based on choosing a suitable trial…

Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…

One cannot pull an open, curved string along itself. This fact is clearly reflected in the unwrapping motion of a string or chain as it is dragged around an object, and implies strong consequences for slender structures in passive…