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| Publications [#9832] of Thomas P. Witelski
search www.ams.org.Papers Published
- D. Vaynblat, J. R. Lister and Thomas P. Witelski, Symmetry and self-similarity in rupture and pinchoff:A geometric bifurcation,
European Journal of Applied Mathematics (2001) 12, 3, pp. 209-232.
(last updated on 2001/08/15)
Abstract:
Long-wavelength models for van der Waals driven
rupture of a free thin viscous sheet and for capillary
pinchoff of a
viscous fluid thread both give rise to families of
first-type
similarity solutions. The scaling exponents in these
solutions are
independent of the dimensionality of problem. However, the
structure of
the similarity solutions exhibits an intriguing geometric
dependence on the dimensionality of the system: van der
Waals driven sheet
rupture proceeds symmetrically whereas thread rupture is
inherently
asymmetric. To study the bifurcation of rupture
from symmetric to asymmetric forms,
we generalize the governing equations with the dimension
serving as a
control parameter. The bifurcation is governed by
leading-order inviscid
dynamics in which viscous effects are asymptotically small
but
nevertheless provide the selection mechanism.
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