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VERSION:2.0
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BEGIN:VEVENT
DTSTAMP:20260912T060451Z
LAST-MODIFIED:20210401T143134Z
DTSTART:20210416T160000Z
DTEND:20210416T170000Z
UID:event2423@bu.edu
URL:http://physics.bu.edu/internal/events/show/2423
SUMMARY:Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shoc
	k waves
DESCRIPTION:Featuring Maxim Olshanii\, UMass Boston \n\nPart of the Biophys
	ics/Condensed Matter Seminar Series.\n\nThe recently proposed map [arXiv:20
	11.01415] between the hydrodynamic equations governing the two-dimensional 
	triangular cold-bosonic breathers [Phys. Rev. X 9\, 021035 (2019)] and the 
	high-density zero-temperature triangular free-fermionic clouds\, both trapp
	ed harmonically\, perfectly explains the former phenomenon but leaves unint
	erpreted the nature of the initial (t=0) singularity. This singularity is a
	 density discontinuity that leads\, in the bosonic case\, to an infinite fo
	rce at the cloud edge. The map itself becomes invalid at times tT/4. Here\,
	 we first map -- using the scale invariance of the problem -- the trapped m
	otion to an untrapped one. Then we show that in the new representation\, th
	e solution [arXiv:2011.01415] becomes\, along a ray in the direction normal
	 to one of the three edges of the initial cloud\, a freely propagating one-
	dimensional shock wave of a class proposed by Damski in [Phys. Rev. A 69\, 
	043610 (2004)]. There\, for a broad class of initial conditions\, the one-d
	imensional hydrodynamic equations can be mapped to the inviscid Burgers' eq
	uation\, a nonlinear transport equation. More specifically\, under the Dams
	ki map\, the t=0 singularity of the original problem becomes\, verbatim\, t
	he initial condition for the wave catastrophe solution found by Chandrasekh
	ar in 1943 [Ballistic Research Laboratory Report No. 423 (1943)]. At t=T/8\
	, our interpretation ceases to exist: at this instance\, all three effectiv
	ely one-dimensional shock waves emanating from each of the three sides of t
	he initial triangle collide at the origin\, and the 2D-1D correspondence be
	tween the solution of [arXiv:2011.01415] and the Damski-Chandrasekhar shock
	 wave becomes invalid.
LOCATION: \, \, 
STATUS:CONFIRMED
CLASS:PUBLIC
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