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DTSTART;TZID=America/Los_Angeles:20181015T161500
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SUMMARY:Agent-Based and Continuous Models of Locust Hopper Bands: The Role of Intermittent Motion\, Alignment\, Attraction and Repulsion (Andrew J. Bernoff\, HMC)
DESCRIPTION:Locust swarms pose a major threat to agriculture\, notably in northern Africa and the Middle East. In the early stages of aggregation\, locusts form hopper bands. These are coordinated groups that march in columnar structures that are often kilometers long and may contain millions of individuals. We propose a model for the formation of locust hopper bands that incorporates intermittent motion\, alignment with neighbors\, and social attraction\, all behaviors that have been validated in experiments. Using a particle-in-cell computational method\, we simulate swarms of up to a million individuals\, which is several orders of magnitude larger than what has previously appeared in the locust modeling literature. We observe hopper bands in this model forming as a fingering instability. Our model also allows homogenization to yield a system of partial integro-differential evolution equations. We identify a bifurcation from a uniform marching state to columnar structures\, suggestive of the formation of hopper bands.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-prof-andrew-j-bernoff-hmc/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
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DTSTART;TZID=America/Los_Angeles:20181029T161500
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CREATED:20180910T073543Z
LAST-MODIFIED:20181016T222630Z
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SUMMARY:Minimal Gaussian Partitions\, Clustering Hardness and Voting (Steven Heilman\, USC)
DESCRIPTION:A single soap bubble has a spherical shape since it minimizes its surface area subject to a fixed enclosed volume of air.  When two soap bubbles collide\, they form a “double-bubble” composed of three spherical caps.  The double-bubble minimizes total surface area among all sets enclosing two fixed volumes.  This was proven mathematically in a landmark result by Hutchings-Morgan-Ritore-Ros and Reichardt using the calculus of variations in the early 2000s.  The analogous case of three or more Euclidean sets is considered difficult if not impossible.  However\, if we replace Lebesgue measure in these problems with the Gaussian measure\, then recent work of myself (for 3 sets) and of Milman-Neeman (for any number of sets) can actually solve these problems.  We also use the calculus of variations.  We will discuss applications of this Gaussian “multi-bubble” problem to optimal clustering of data and to designing elections that are resilient to hacking.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-given-by-prof-steven-heilman/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
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