Bubble break-off in Hele-Shaw flows : Singularities and integrable structures
可精确求解与可积系统
2007-05-23 v2 软凝聚态物质
高能物理 - 理论
斑图形成与孤子
摘要
Bubbles of inviscid fluid surrounded by a viscous fluid in a Hele-Shaw cell can merge and break-off. During the process of break-off, a thinning neck pinches off to a universal self-similar singularity. We describe this process and reveal its integrable structure: it is a solution of the dispersionless limit of the AKNS hierarchy. The singular break-off patterns are universal, not sensitive to details of the process and can be seen experimentally. We briefly discuss the dispersive regularization of the Hele-Shaw problem and the emergence of the Painlev\'e II equation at the break-off.
关键词
引用
@article{arxiv.nlin/0604054,
title = {Bubble break-off in Hele-Shaw flows : Singularities and integrable structures},
author = {Seung-Yeop Lee and Eldad Bettelheim and Paul Wiegmann},
journal= {arXiv preprint arXiv:nlin/0604054},
year = {2007}
}
备注
27 pages, 9 figures; typo corrected