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UID:71ec12be21d5e8ff102b10b4a42a232b
CATEGORIES:Experimental Mathematics Seminar
CREATED:20231126T153452
SUMMARY:phere packings, singularities, and statistical mechanics
LOCATION:https://rutgers.zoom.us/j/94346444480 [password: The 20th Catalan number\, 
 alias (40)!/(20!*21!)
DESCRIPTION:<p>&nbsp;</p><p style="color: #000000; font-family: 'Times New Roman'; font
 -size: medium; font-weight: 400; letter-spacing: normal; orphans: 2; text-a
 lign: start; text-indent: 0px; text-transform: none; white-space: normal; w
 idows: 2; word-spacing: 0px;">What are all the ways to arrange N hard spher
 es into a rigid packing? And what can the solution tell us about how materi
 als crystallize? I will introduce an algorithm to enumerate rigid sphere pa
 ckings (clusters) and describe some of the data it produces, which include 
 many clusters with geometrically unusual properties. Among these are an abu
 ndance of “singular” clusters, those that are linearly flexible but non
 linearly rigid, so called because they correspond to singular solutions to 
 a set of algebraic equations. These are also the clusters one sees with unu
 sually high probability, in experiments which consider colloidal particles 
 interacting with a short-ranged potential. I will explain why these cluster
 s are so prevalent, drawing links between statistical mechanics and the vol
 umes of semialgebraic sets, and show how these calculations applied to our 
 sphere packing data bring insight into the pathways to crystallization of s
 ticky spheres.</p>
CONTACT: Miranda Holmes-Cerfon, University of British Columbia
DTSTAMP:20260827T173012
DTSTART;TZID=America/New_York:20231130T170000
DTEND;TZID=America/New_York:20231130T180000
SEQUENCE:0
TRANSP:OPAQUE
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