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Center for Nonlinear Studies |
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