Universal Unfolding of Pitchfork Bifurcations and Shear-Band Formation in Rapid Granular Couette Flow

Simple item page
dc.creatorAlam, Meheboob
dc.date2004-11-23
dc.date.accessioned2026-07-07T03:02:17Z
dc.date.available2026-07-07T03:02:17Z
dc.descriptionA numerical bifurcation analysis is carried out to understand the role of gravity on the shear-band formation in rapid granular Couette flow. At {\it low} shear rates, there is a unique solution with a {\it plug} near the bottom wall and a {\it shear-layer} near the top-wall; this solution mirrors typical shearbanding-type profiles in earth-bound shear-cell experiments. Interestingly, a {\it stable} plug near the top-wall is also a solution of these equations at {\it high} shear rates; there is a multitude of other plugged states, with the plugs being located in an ordered fashion within the Couette gap. The origin of such shearbanding solutions is tied to the spontaneous symmetry-breaking {\it shearbanding} instabilities of the gravity-free uniform shear flow, leading to both subcritical and supercritical pitchfork bifurcations. In the language of singularity theory, we have established that this bifurcation problem admits {\it universal unfolding} of pitchfork bifurcations.
dc.description11 pages and 6 figures; Proceedings of the Symposium on Trends in Applications of Mathematics to Mechanics, 22-28 August, 2004, Seeheim-Jugenheim, Germnay (Editors: K. Hutter and Y. Wang)
dc.identifierhttps://arxiv.org/abs/cond-mat/0411572
dc.identifierhttp://arxiv.org/abs/cond-mat/0411572
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/25340
dc.subjectSoft Condensed Matter
dc.subjectStatistical Mechanics
dc.titleUniversal Unfolding of Pitchfork Bifurcations and Shear-Band Formation in Rapid Granular Couette Flow
dc.typetext

Files

Collections

arXiv