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SUMMARY:Topological states in collective dynamics
DTSTART;VALUE=DATE-TIME:20210504T131500Z
DTEND;VALUE=DATE-TIME:20210504T141500Z
DTSTAMP;VALUE=DATE-TIME:20210513T192848Z
UID:indico-event-6019@indico.math.cnrs.fr
DESCRIPTION:\n\n\nStates of matter (such as solid\, liquid\, etc) are char
acterized\nby different types of order associated with local invariances u
nder\ndifferent transformation groups. Recently\, a new notion of topologi
cal\norder\, popularized by the 2016 physics nobel prize awarded to Haldan
e\,\nKosterlitz and Thouless\, has emerged. It refers to the global rigidi
ty of\nthe system arising in some circumstances from topological constrain
ts.\nTopologically ordered states are extremely robust i.e. « topological
ly\nprotected » against localized perturbations. Collective dynamics occu
rs when\na system of self-propelled particles organizes itself into a cohe
rent\nmotion\, such as a flock\, a vortex\, etc. Recently\, the question o
f realizing\ntopologically protected collective states has been raised. In
this work\, we\nconsider a system of self-propelled solid bodies interact
ing through local\nfull body alignment up to some noise. In the large-scal
e limit\, this system\ncan be described by hydrodynamic equations with top
ologically non-trivial\nexplicit solutions. At the particle level\, these
solutions persist for a\ncertain time but eventually\, for some of them\,
decay towards a topologically\ntrivial state\, due to the noise induced by
the stochastic nature of the\nparticle system. We numerically analyse the
se topological phase transitions\nand investigate to what extent topologic
ally non-trivial states are\n‘protected’ against perturbations. To our
knowledge\, it is the first time\nthat a hydrodynamic model guides the de
sign of topologically non-trivial\nstates of a particle system and allows
for their quantitative analysis and\nunderstanding. In passing\, we will r
aise interesting mathematical questions\nunderpinning the analysis of coll
ective dynamics systems. \n\n\n\nhttps://indico.math.cnrs.fr/event/6019/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6019/
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