Resonance in slow passage problem

Slow passage through resonance.

The slow passage problem through a resonance is considered. As a model problem, we consider a damped harmonically forced oscillator whose forcing frequency is slowly ramped linearly in time. The setup is similar to the familiar slow passage through a Hopf bifurcation problem, where for slow variations of the control parameter, oscillations are delayed until the parameter has exceeded the critic...

Resonance-induced Surfatron Acceleration of a Relativistic Particle

We study motion of a relativistic charged particle in a plane slow electromagnetic wave and background uniform magnetic field. The wave propagates normally to the background field. The motion of the particle can be described by a Hamiltonian system with two degrees of freedom. Parameters of the problem are such that in this system one can identify slow and fast variables: three variables are ch...

Slow Passage through Resonance for a Weakly Nonlinear Dispersive Wave

ASME International Mechanical Engineering Congress & Exposition November 17 22 , 2002 , New Orleans , Louisiana IMECE 2002 - 3 9139

We investigate slow passage through the 2:1 resonance tongue in Mathieu's equation. Using numerical integration, we find that amplification or de-amplification can occur. The amount of amplitication (or de-amplification) depends on the speed travelling through the tongue and the initial conditions. We use the method of multiple scales to obtain a slow flow approximatiou. The WKB method is then ...

The Stretch to Stray on Time: Resonant Length of Random Walks in a Transien

First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time, or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under a transient describing relax...