Critical speed-up vs critical slow-down: a new kind of relaxation oscillation with application to stick-slip phenomena

Details Critical speed-up vs critical slow-down: a new kind of relaxation oscillation with application to stick-slip phenomena Critical speed-up vs critical slow-down: a new kind of relaxation oscillation with application to stick-slip phenomena

2011-07-17

arxiv.org/abs/1107.3331v1

Physics

Geophysics

Scientific paper

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 analysis of the solutions explains well the two sharply different steps of the stick-slip dynamics. The stick (slow) part takes place along a slow manifold in the phase space. But, in contrast with standard relaxation dynamics (of van der Pol type), the slow manifold is always formally attracting and the transition from slow to fast dynamics occurs because the slow dynamics has a finite time singularity breaking the assumption of slowness. This makes a new kind of relaxation oscillation. We show that the response of the stick-slip system to an external noise displays a progressive speed-up before the transition, in contrast with the well known critical slowing-down observed in the standard case.

Affiliated with

Also associated with

No associations

Rating

Critical speed-up vs critical slow-down: a new kind of relaxation oscillation with application to stick-slip phenomena does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Critical speed-up vs critical slow-down: a new kind of relaxation oscillation with application to stick-slip phenomena, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical speed-up vs critical slow-down: a new kind of relaxation oscillation with application to stick-slip phenomena will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-270764