Giant density fluctuations and other out-of-equilibrium properties of active matter. Francesco Ginelli

Transcription

1 G desy flucuos d ohe ou-of-equlum popees of cve me Fcesco Gell Isu des Sysèmes Complees, Ps-Ile-de-Fce d SPEC, CEA/Scly Wh: H. Ché S. Rmswmy S. Msh R. Moge

2 Acve pcles possess el degees of feedom whch llow hem o self popel hemselves y ecg eegy fom he evome d dsspe o move wh pefeed deco. Self popelled pcles hus cy pefeed deco of moo whch c e oeed y ecos wh ey pcles. (A) (B) Vecl sheckg (C) (D) Lel moveme Euope slg Dsspo y fco Dve gul ods o suse

3 Esemles of ecg cve pcles: spoeous symmey ekg d collecve moo Slgs flock - Pedo emp Rome hks o Cludo Cee Isuo Supeoe d Sà - Rom - Ily STARFLAG

4 Collecve moo s chcezed y spoeous symmey ekg pheomeo. Symmey ekg my hppe wh locl ecos oly, o glol odeg feld(s) d whou y ovous lede. The symmey oke odeed phse s chcezed y emkle ou-of equlum popees Smple mcoscopc models ppoch Smple mcoscopc dymcs. Pcles e desced y he off-lce poso d deco They hve oly locl ecos.,, N Dve-ovedmped ppomo: hey evolve wh sychoous dscee me sochsc dymcs (whose me sep s of he ode of he elo me) wh cos modulo velocy v 0. No eel felds e pese.

5 Vcsek model ( movg sps ) Vcsek e l, PRL (995) Scly locl eco ge: Algme ccodg o locl ode pmee eghohood (vege deco of he eghos) Dsplceme wh cos modulo velocy, oke Glle vce v 0 R ( η)o ~ ~ ~ f < v 0 R R ( η) s oo y dom, del coeled gle(s) ( η)o v ufomly dsued (sold) gle lyg oud v wh mplude η

6 Compeo ewee desy d ose leds o ode Sog ose: dsodeed se Low ose: log ge ode (Mem-Wge heoem does o hold) Low desy ccl le: l η c ~ d d ~ l η pes uech o odeed phse (cose-ged desy feld) L6384, /8 (3M pcles)

7 G ume flucuos chceze he odeed phse he low ose egme Defe volumes of cesg le sze l Mesue he vege ( me) ume of pcles he volume d s ms flucuos l d A equlum ~ / Vcsek model (d, d3) 0.8 d d3 (veclly escled)

8 A hydodymc ppoch Toe & Tu, PRL (995), PRE (998) We hydodymc-lke Lgev equos fo desy c(, ) d v(, ) velocy felds (slow vles). Allow fo volo of Glle vce Solve y lezo oud desy homogeeous, odeed se c(,) c 0 δc, v(,) v 0 δv, Check ole ems y DRG lyss ( ) ( ) Compue ume desy sucue fco ( dveges lge wvelegh!!!) S ( q 0) d ( DRG esul) ~ 4 5 d3 (coecue) ~

9 Iclude emc symmey Dve ovedmped dymcs: sychoous lgohm Fe eco ge, o eel felds ( ) ( ) T R R κ η η ~ ~ Acve emc o suse, d [ ] [ ] [ ] δ ~ f < κ ±D 0 Scl ode pmee: lges egevlue of he glol emc eso N

10 Some umecl esuls: d uech o odeed phse Sog ose: dsode Low ose: qus log ge ode (Mem-Wge heoem holds)

11 Eve lge g ume flucuos he odeed phse ~ V. Ny, S. Rmswmy & N. Meo, Scece (007)

12 Nemc coseg Devos fom ege Pood s lw: sho dsce cusp L ~ C() g ( ) c L ( ) ep L() ( ) ( ) ( ) S k kl 0.4

13 ( ) ( ) N f s, Devg mesoscopc descpo y dec cose gg ( ) ( ) ( ) N f s,, ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( )( ) ( ) ,, T N s T N s N s s f v f f f κ (y Io clculus) [ ] ( ) v v T κ Defe ememeg Desy evoluo

14 Mulplcve ose eme ( ) ( ) ( ) N s f, κ ω ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) [ ] δ δ δ δ δ ω ω ' ' ' ',, y y y y v f f v f f v N s s N s s ζ 0 ~ v T T s ose em Wh coelos ove he cose gg scle s I hs he sme coelos s (see D.S. De, J. Phys A (996))

15 0 0 A A I R θ θ θ Cose ged emc eso evoluo Epd oo m fo smll ose Gde epso s fo desy Epd he omlzo em up o secod ode (fo suffcly lge ol desy) ( ) ( ) T η η θ θ R R ~ ~ ( ) ( ) ( ) N f s,,

16 Cose ged Lgev equos [ ] ( ) [ ] ( ) ξ ( ) Ξ 3 4 g Γ [ ] [ ] [ ] δ wh: Γ [ ] Γ [ ] Γ [ ] Γ [ ] ( ) Ξ 3 4 g Γ ( ) ( ) K, η σ g

17 [ ] ( ) [ ] ( ) ξ [ ] ( ) [ ] ( ) ξ ( ) Ξ 3 4 g Γ Mulplcve Nose Ou of equlum cue em (co e deved fom coec symmey Fck fee eegy em) Voles flucuo dsspo Algme Cose ged Lgev equos

18 A pedgogcl check: ck o Bow pcles - p p κ w w w.p. w.p. p - p Sce [ ] [ ] [ ] ( ) q ( p ) [ ] wh δ [ q(, ) ] [ (, )] ( ') ( ) ( )[ ] q v0δ δ y p p / Bow pcles!! δ

19 Compso wh mcoscopc ehvo: Coseg Mcoscopc cve emcs Lgev equos Deemsc veso of mesoscopc dymcs

20 Compso wh mcoscopc ehvo: Segego Mcoscopc dymcs Lgev dymcs mulplcve ose Lgev dymcs ddve ose

21 Segego ohe self popelled pcles models Vcsek model, s ose s sed owds he odedsodeed so Odeed, splly homogeeous Bd egme Dsodeed phse Wekly ecg soly oecs

22 Pol pcles wh emc ecos (wh F. Peu, M. Be)

23 Coclusos Esemles of cve pcle hve geue o-equlum feues Cpued y smple models G ume desy flucuos, supedffuso, Segego pheome wh o-shp efces Coec ose coelos e eeded Lgev descpo