Lab Home | Phone | Search
Center for Nonlinear Studies  Center for Nonlinear Studies
 Colloquia Archive 
 Postdoc Seminars Archive 
 Quantum Lunch 
 CMS Colloquia 
 Q-Mat Seminars 
 Q-Mat Seminars Archive 
 Kac Lectures 
 Dist. Quant. Lecture 
 Ulam Scholar 
 Summer Research 
 Past Visitors 
 History of CNLS 
 Maps, Directions 
 CNLS Office 
Thursday, June 18, 2009
3:30 PM - 4:30 PM
CNLS Conference Room (TA-3, Bldg 1690)


Selection Rules in Laplacian Growth

John Widloski
University of Texas at Austin

Selection rules (length-scale selection) in natural phenomena are often observed, but little understood. Often, this selection can be attributed to the dynamics of some unstable interface, a particularly simple class of which is Laplacian Growth, where the velocity V of an interface is proportional to the gradient of a harmonic function. The most well known case is viscous fingering in Hele-Shaw cells, a phenomenon that emerges when a less viscous fluid (air) is forced into a more viscous fluid (oil) and contained to a narrow region between two glass plates. Because of interfacial instabilities, fingers emerge from the initially featureless interface that creep down the channel and, further, exhibit selection rules that beg to be explained. This has led to a mathematical reformulation of the viscous fingering problem as the more general free-boundary problem, revealing a rich structure that profoundly interconnects various branches of mathematical physics.

Host: Mark Mineev, LANL