Spatially Localized Models of Extended Systems |
| |
| Authors: | Wittenberg Ralf W Holmes Philip |
| |
| Institution: | (1) Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, 207 Church Street SE, Minneapolis, MN, 55455, U.S.A;(2) Program in Applied and Computational Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08544, U.S.A |
| |
| Abstract: | We investigate the construction of low-dimensional spatiallylocalized models of extended systems. Specifically, theKuramoto–Sivashinsky (KS) equation on large one-dimensional domainsdisplays spatiotemporally complex dynamics that are remarkablywell-localized in both real and Fourier space, as demonstrated by a(spline) wavelet representation. We show how wavelet projectionsmay be used to construct various localized, relativelylow-dimensional models of KS spatiotemporal chaos. There ispersuasive evidence that short, periodized systems, internally forcedat their largest scales, form minimal models for chaotic dynamics inarbitrarily large domains. Such models assist in the understandingof extended systems. |
| |
| Keywords: | spatiotemporal chaos low-dimensional models wavelets Kuramoto– Sivashinsky equation |
| 本文献已被 SpringerLink 等数据库收录！ |
|
