Abstract
Motivated by the observation of localized circular excitations ('oscillons') in vertically vibrated granular layers [P. Umbanhowar, F. Melo, H. Swinney, Nature 382 (1996) 793], we numerically investigate an extension of a Swift-Hohenberg model that exhibits a subcritical transition to square patterns. For sufficiently strong damping of the basic state, stable oscillon structures are found. The localization mechanism is quite general and is due to non-adiabatic effects. Bound structures of oscillons of equal and opposite polarity are found with bound states of like polarity being less robust. Much of the phenomena are consistent with the experimental observations and suggest that oscillons are not specific to patterns in granular media or to parametrically driven systems. Experimental tests are suggested that would determine whether this minimal framework is sufficient to describe the phenomena.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 83-92 |
| Number of pages | 10 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 129 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - May 1 1999 |
Funding
The authors gratefully acknowledge discussions with I. Aranson, C. Bizon, J. Fineberg, W.L. Kath, M. Shattuck, M. Silber, L. Tsimring, and P. Umbanhowar. The numerical simulations have been performed with an extension of a code by G.D. Granzow. This research has been supported by DOE under grant DE-FG02-92ER14303.
Keywords
- Fronts
- Granular media
- Localized states
- Parametric excitation
- Pattern formation
- Square patterns
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics