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VERSION:2.0
PRODID:-//Mathematics - ECPv4.9.3.1//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Mathematics
X-ORIGINAL-URL:https://math.ua.edu
X-WR-CALDESC:Events for Mathematics
BEGIN:VEVENT
DTSTART;TZID=America/Chicago:20190325T110000
DTEND;TZID=America/Chicago:20190325T120000
DTSTAMP:20190618T193631
CREATED:20190108T160151Z
LAST-MODIFIED:20190321T143423Z
UID:3685-1553511600-1553515200@math.ua.edu
SUMMARY:Colloquium - Xiaofeng Ren\, George Washington University
DESCRIPTION:Topic: Non-hexagonal lattices from a two species interacting system \nAbstract: A two species interacting system motivated by the density functional theory for triblock copolymers contains long range interaction that affects the two species differently. In a two species periodic assembly of discs\, the two species appear alternately on a lattice. A minimal two species periodic assembly is one with the least energy per lattice cell area. There is a parameter $b$ in $[0\,1]$ and the type of the lattice associated with a minimal assembly varies depending on $b$. There are several thresholds defined by a number $B=0.1867…$ If $b \in [0\, B)$\, a minimal assembly is associated with a rectangular lattice whose ratio of the longer side and the shorter side is in $[\sqrt{3}\, 1)$; if $b \in [B\, 1-B]$\, a minimal assembly is associated with a square lattice; if $b \in (1-B\, 1]$\, a minimal assembly is associated with a rhombic lattice with an acute angle in $[\frac{\pi}{3}\, \frac{\pi}{2})$. Only when $b=1$\, this rhombic lattice is a hexagonal lattice. None of the other values of $b$ yields a hexagonal lattice\, a sharp contrast to the situation for one species interacting systems\, where hexagonal lattices are ubiquitously observed. \n
URL:https://math.ua.edu/event/colloquium-xiaofeng-ren-george-washington-university/
CATEGORIES:Colloquium,Math Department
ORGANIZER;CN="Shibin%20Dai":MAILTO:sdai4@ua.edu
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