Applied and Computational Mathematics Seminar

Seminar Details

Speaker:
Alan Newell
Affiliation:
University of Arizona
Title:
Elastic sheets, phase surfaces and pattern universes
Time:
2PM Tuesday, 5 June, 2018
Location:
SCN 2.31, O'Brien Centre for Science (North)

Abstract

There is a lovely result for elastic surfaces that says that the first two terms of the energy functional, expressed as an asymptotic expansion in the sheet thickness, can be written respectively as coordinate invariant combinations of the metric and curvature two forms of that surface. We have recently shown that the same result holds for instability driven patterns arising from gradient flows in that the averaged free energy can be expanded in terms of the inverse aspect ratio (the ratio of pattern wavelength to box size) and the first two terms reflect the metric and curvature two forms of the pattern phase surface. I will then show you how these surfaces have point and loop defects which have natural topological indices of integer multiples of 1/3,1 and 1/2. We call such objects pattern quarks and leptons. We then ask if there are further parallels between fundamental particle physics and cosmology and pattern forming systems and suggest that there are indeed intriguing parallels for both dark matter and dark energy, the former giving rise to galactic star orbital speeds consistent with Rubin's observations.

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