!"#$%&'#()*+#,*-.! +/010#+)+!*)-0! 2-((#*$3 ! - PowerPoint PPT Presentation

!"#$%&'#()*+#,*-.! +/010#+)+!*)-0! 2-((#*$3 ! 4,**)45*$!+1#*! $.-++)+!6#7%!0)-.#78 ! Patrick Charbonneau

9#()*+#,*-.!4,..-:,0-7,0+ ! Carolina Brito (Porto Alegre) Benoit Charbonneau (Waterloo) Eric Corwin (Oregon) Daan Frenkel (Cambridge) Andrea Fortini (Bayreuth) Atsushi Ikeda (Montpellier) Jorge Kurchan (ENS Paris) Kunimasa Miyazaki (Nagoya) Koos van Meel (Vienna) Giorgio Parisi (La Sapienza) Gilles Tarjus (UPMC) Pierfrancesco Urbani (CEA) Francesco Zamponi (ENS Paris)

;0)%#+7,083!"<!408+7-..#=-5,* ! ϕ FCC ϕ th ϕ GCP Pressure, β P ϕ K ϕ d ϕ f ϕ m Packing fraction, ϕ

",(,$)*),/+!408+7-.!*/4.)-5,*! >-'#/+! Auer and Frenkel, Nature (2002)

?),()70#4-.!@0/+70-5,*! 70#-*$/.-0!.-C4)! ABB!.-C4) !!!!D+E! !#4,+-%)'0,*! F&+#(1.)G!H70#-*$.)I! J&+#(1.)G!H7)70-%)'0,*I! Pfender and Ziegler, Notices FK&4)..!&L!9 K !.-C4)! D+E!!!!!K&+#(1.)G! AMS (2004)

K9!*/4.)-5,*!:-00#)0! R Freezing Melting D 4 0.288 0.337 0.617 4D surface free energy is 2-3 times larger than 3D at similar supersaturations! B./+7)0!<#=)! van Meel, Frenkel, Charbonneau, PRE (2009)

Q#S/#'!,0')0!-*'!'#()*+#,* ! M,*'!,0')0!1-0-()7)0+ !! "!#$ !<7)#*%-0'7!-*'!T).+,*! • Liquid/crystal structure resemblance vanishes with dimension. • In high-dimensions, glasses are more easily accessible than crystal. van Meel, Charbonneau, Fortini, Charbonneau, PRE (2009)

“[T]here were almost as many versions of the phlogiston theory as there were pneumatic chemists. That proliferation of versions of a theory is a very usual symptom of crisis.” -- Kuhn, The Structure of Scientific Revolutions (1962) K. Chang, NYT, 29/07/2008

"-0'!+1%)0)!2-((#*$ ! U/7&,@&)S/#.#:0#/(!40#54-.! 70-*+#5,*P!%)*4)!')+40#:#*$!#7! 0)S/#0)+!-!$,,'!(#40,+4,1#4!$.-++! 7%),08E!! ! &L<70#*$)*7!7)+7!,@!$.-++!7%),0#)+E!

V-((#*$!1%-+)!'#-$0-(! H%#*'+#$%7!#+!FWOFWI ! e e Temperature 0.1 0.2 0.3 0.4 0.5 0.6 al w (b) φ =0.635 free vol u me theory st Carnahan-Starlin g 150 Liquid d φ =0.6465 free vol u me theory φ =0.640 free vol u me theory a R u t g ers, et a l. 100 Rinto u l and Torq u ato o s s Speedy a y l Jammed Load G grains etc. d 50 . Loose grains, a bubbles, droplets etc. i- - 0.55 0.6 1/Density f Figure 1 A possible phase diagram for jamming. 0.5 0.5 Σ equilibrium liquid φ 0.4 0.4 j 0.3 0.3 Pressure, P d/p 0.2 0.2 stable glass 0.1 0.1 marginal glass Volume fraction, φ φ φ φ φ 0.0 0.0 d th K GCP 4 4 5 5 6 6 7 7 8 8 9 9 J-line 2 d ϕ /d Liu and Nagel Nature (1998), Liu and Kamien PRL (2007); PZ RMP (2010); CKUPZ Nat. Comm. (2014)

XD,.D#*$!9)*+#78 ! 26 Consistent with d =3 results 0.15 25 Chaudhuri, Berthier, Sastry PRL (2010) 24 0.1 0.1 23 d ϕ j 2 0.05 f 22 1/p 21 0 20 0 0.1 0.2 0.3 0.4 γ 1/2 0.05 ϕ d fluid EOS (fit) threshold glass (extr.) ϕ K ideal glass (RT) Decreasing γ 0.1, 0.03, ... , 0.00003 ϕ th ϕ GCP 0 10 15 20 25 30 d ϕ 2 CIPZ PRL (2011); CCPZ PRL (2012)

B-$)!B,..-1+) ! Between the liquid and jamming, something must happen, because How determined are the force ϕ < ϕ g !"# !%# !&# contacts (and the rattlers)? Low ϕ > ϕ g High ϕ > ϕ g Low ϕ > ϕ g High ϕ > ϕ g 1 1 5 5 1 − < f ij > 2 2 !$# d =4,6,8 ϕ > ϕ g 10 − 1 10 − 1 α 5 5 !'# Vibrations 2 2 10 − 2 10 − 2 10 2 10 2 10 3 10 3 10 4 10 4 10 5 10 5 10 6 10 6 10 7 10 7 CKUPZ Nature Comm. (2014) p

V-((#*$!H(-0$#*-..8!+7-:.)I!4-$) ! r/ σ − 1 10 − 12 10 − 9 10 − 6 10 − 3 As proposed by Wyart PRL (2012), (a) two critical regimes can be identified. 20 20 1RSB solution does not: critical exponents are 0. 15 15 Z ( r ) Z ( r ) 10 10 ∼ ∆ φ 0 ∼ ∆ φ ∼ ∆ φ µ (b) Ib IIb IIIb 5 5 d =3–10 0 0 ¯ z r σ σ + O ( p − µ ) CCPZ PRL (2012)

N +7 !1,6)0!.-63!*)-0!4,*7-47+ ! SS HS ! =0.5 ! =0.4 Eqs. The near-contact Z b l FIG. 8. Color online for a nearly Silbert, Liu, Nagel, PRE (2005) Donev, Stillinger, Torquato, PRE (2005) Skoge et al., PRE (2006)

T)-0!4,*7-47+3!0)(,D)!0-Y.)0+ ! r/ σ − 1 r/ σ − 1 10 − 7 10 − 5 10 − 3 10 − 1 10 1 10 − 5 10 − 3 10 − 1 10 1 (e) HS (f) SS Z ( r ) − Z ( σ + σ 10 − 7 ) 10 3 10 3 ! =0.42(1) 10 1 10 1 ∼ ( r/ σ − 1)1 − α ∼ ( r/ σ − 1)1 − α 10 − 1 10 − 1 d =3–10 d =3–10 ! =0.38(3) 10 − 3 10 − 3 10 − 1 10 − 1 (a) 5 5 A/..><M! ! =0.41269 2 2 Suggest that upper and lower critical fraction rattlers 10 − 2 10 − 2 dimension d =2 (?) 5 5 Agrees with finite-size scaling arguments 2 2 of Goodrich and Liu PRL (2012). 10 − 3 10 − 3 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 d CCPZ PRL (2012); Lerner, Duering, Wyart Soft Matter (2013)

F *' !1,6)0!.-63!@,04)!4,*7-47+ ! will in- HS models. SS infinite-system- recent that . diffi- ideal O’Hern et al. PRE (2003) Donev, Stillinger, Torquato, PRE (2005) 10 0 10 0 10 0 (a) (b) 5 5 5 HS SS 2 2 2 Embarrasingly ∼ f 1+ θ ∼ f 1+ θ G ( f ) G ( f ) different… 10 − 1 10 − 1 10 − 1 x 10 − 210 − 1 100 101 102 1.0 1.0 5 5 5 Z − ( x ) " =0.28(3) 0.5 0.5 " =0.42(2) 2 2 2 0.0 0.0 10 − 2 10 − 2 10 − 2 5 10 − 1 5 10 − 1 10 0 10 0 10 1 10 1 5 10 − 1 5 10 − 1 10 0 10 0 10 1 10 1 2 2 2 2 5 5 2 2 5 5 2 2 2 2 5 5 2 2 5 5 f/ ¯ f/ ¯ f f CCPZ PRL (2012)

A,04)!4,*7-47+3!0)(,D)!:/4Z.)0+ ! − 1 10 10 0 d =2 d =3 HS/SS 0.17 − 2 1 10 10 − 2 g ( f/ � f � ) N = 8000 N = 1000 HS SS f tot − 3 10 N = 124 f A f N 10 − 4 f 1 . 25 − 4 10 − 6 − 4 − 2 0 2 10 10 10 10 10 f 1 . 17462 f Lerner, Duering, Wyart Soft Matter f 1 . 42311 10 − 6 (2013); DeGiuli et al. arXiv:1402.3834 10 0 d =4 HS/SS 10 − 2 g ( f/ � f � ) 10 0 f tot f A f N 10 − 4 f 1 . 3 10 − 1 P ( Z buck . ) f 1 . 17462 f 1 . 42311 10 − 6 10 − 5 10 − 5 10 − 3 10 − 3 10 − 1 10 − 1 10 1 10 1 f/ � f � 10 − 2 CCPZ unpublished (2014) 10 − 3 2 2 4 4 6 6 8 8 10 10 12 12 d

B-$)!)D,./5,* ! 10 − 2 -1 10 dt 2 N = 1024 10 − 6 -2 10 N = 256 N = 256 ∆ ( t ) -3 10 2 > < δ R ! [NE\ 10 − 10 p = 10 2 –10 8 -4 10 -5 10 10 − 14 2 3 4 1 10 − 8 10 − 8 10 − 4 10 − 4 1 1 < f > 10 10 10 10 t Brito and Wyart J. Chem. Phys. (2009) 10 − 3 10 − 3 ! [NEKN\]K 10 − 6 10 − 6 High pressure challenges: d = 3 ∆ EA -eliminate rattlers d = 4 -network and thus rattlers d = 6 10 − 9 10 − 9 reorganize d = 8 ∼ p − κ ∼ p − 3 / 2 10 − 12 10 − 12 10 2 10 2 10 4 10 4 10 6 10 6 10 8 10 8 p CKUPZ Nat. Comm. (2014)

B,*4./+#,*+ ! • <,()!S/-.#7-5D)! $%&!'($%)*$)+,! @)-7/0)+!,@! 7%)!()-*&^).'!@/..!><M!+,./5,*!1)0+#+7!-..!7%)! 6-8!',6*!7,! & [FE! • >)^*)()*7!-*'!()-+/0)()*7!,@!40#54-.! )G1,*)*7+!-*'!,@!')D#-5,*+!#+!,*$,#*$E! • <,()!-+1)47+!,@!7%)!?-0'*)0!70-*+#5,*!(-8! :)!)G1)0#()*7-..8!7)+7-:.)E! • ;.)*78!,@!6,0Z!-:,/7!7%)!'8*-(#4-.!70-*+#5,*! %-+!-.+,!:))*!',*)!&L!+))!_/.#-*$!V#*`+!1,+7)0E!