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DTSTART;TZID=America/Los_Angeles:20191125T161500
DTEND;TZID=America/Los_Angeles:20191125T171500
DTSTAMP:20201128T084944
CREATED:20190909T232742Z
LAST-MODIFIED:20191112T033822Z
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SUMMARY:Applied Math Talk: Patterns deformed by spatial inhomogeneity give by Prof. Jasper Weinburd (HMC)
DESCRIPTION:At the turn of the twentieth century\, physicist Henri Bénard heated a shallow plate of fluid from below. For temperatures above a critical value\, the fluid’s evenly heated state became unstable as thermal convection took hold; heated fluid rose in localized areas while cooler fluid fell nearby. The rising and falling fluid created hexagonal convection cells\, squares\, and stripes.\nSuppose that we modify Bénard’s experiment by heating only the left half plate. We expect the fluid on the right to remain stationary and only the the fluid on the left to form patterns. We confirm this intuition mathematically and\, more surprisingly\, find that the step-type inhomogeneity restricts the spatial period of the resulting patterns on the left. We examine this phenomenon using a universal partial differential equation model. The main difficulty arrises at the location of the discontinuous inhomogeneity because results on either side cannot be directly compared. We construct a transformation of variables that bridges this jump and allows a heteroclinic glueing argument from left to right. The explicit form of this transformation determines the widths of patterns that may occur in the inhomogeneous environment.\n
URL:https://colleges.claremont.edu/ccms/event/jasper-weinburd-pomona-college/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
GEO:34.099908;-117.7142522
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