Local-heterogeneous responses and transient dynamics of cage breaking and formation in colloidal fluids

W. K.

 

Kegel

and

A.

 

van Blaaderen

,  , ().

B.

 

Cui

,

B.

 

Lin

, and

S. A.

 

Rice

,  , ().

O.

 

Pouliquen

,

M.

 

Belzons

, and

M.

 

Nicolas

,  , ().

O.

 

Dauchot

,

G.

 

Marty

, and

G.

 

Biroli

,  , ().

M. D.

 

Ediger

,  , ().

L.

 

Berthier

,  , ().

C. A.

 

Angell

,  , ().

G.

 

Marty

and

O.

 

Dauchot

,  , ().

C.

 

Donati

,

J. F.

 

Douglas

,

W.

 

Kob

,

S. J.

 

Plimpton

,

P. H.

 

Poole

, and

S. C.

 

Glotzer

,  , ().

C.

 

Donati

,

S. C.

 

Glotzer

,

P. H.

 

Poole

,

W.

 

Kob

, and

S. J.

 

Plimpton

,  , ().

N.

 

Lačević

,

F. W.

 

Starr

,

T. B.

 

Schrøder

, and

S. C.

 

Glotzer

,  , ().

A. R.

 

Abate

and

D. J.

 

Durian

,  , ().

M. E.

 

Cates

,

J. P.

 

Wittmer

,

J.-P.

 

Bouchaud

, and

P.

 

Claudin

,  , ().

M. L.

 

Falk

and

J. S.

 

Langer

,  , ().

A. R.

 

Abate

and

D. J.

 

Durian

,  , ().

A. S.

 

Keys

,

A. R.

 

Abate

,

S. C.

 

Glotzer

, and

D. J.

 

Durian

,  , ().

F.

 

Lechenault

,

O.

 

Dauchot

,

G.

 

Biroli

, and

J. P.

 

Bouchaud

,  , ().

K. A.

 

Lorincz

and

P.

 

Schall

,  , ().

R.

 

Candelier

and

O.

 

Dauchot

,  , ().

R.

 

Candelier

and

O.

 

Dauchot

,  , ().

Y.

 

Takehara

,

S.

 

Fujimoto

, and

K.

 

Okumura

,  , ().

P.

 

Habdas

and

E. R.

 

Weeks

,  , ().

P.

 

Habdas

,

D.

 

Schaar

,

A. C.

 

Levitt

, and

E. R.

 

Weeks

,  , ().

L. G.

 

Wilson

,

A. W.

 

Harrison

,

A. B.

 

Schofield

,

J.

 

Arlt

, and

W. C. K.

 

Poon

,  , ().

I.

 

Sriram

,

A.

 

Meyer

, and

E. M.

 

Furst

,  , ().

J.

 

Pesic

,

J. Z.

 

Terdik

,

X.

 

Xu

,

Y.

 

Tian

,

A.

 

Lopez

,

S. A.

 

Rice

,

A. R.

 

Dinner

, and

N. F.

 

Scherer

,  , ().

E.

 

Kolb

,

J.

 

Cviklinski

,

J.

 

Lanuza

,

P.

 

Claudin

, and

E.

 

Clément

,  , ().

D. R.

 

Nelson

and

B. I.

 

Halperin

,  , ().

D. R.

 

Nelson

and

B. I.

 

Halperin

,  , ().

A.

 

Jaster

,  , ().

P. M.

 

Reis

,

R. A.

 

Ingale

, and

M. D.

 

Shattuck

,  , ().

C. R.

 

Berardi

,

K.

 

Barros

,

J. F.

 

Douglas

, and

W.

 

Losert

,  , ().

K.

 

Watanabe

and

H.

 

Tanaka

,  , ().

G.

 

Haller

and

G.

 

Yuan

,  , ().

G.

 

Haller

,  , ().

S. C.

 

Shadden

,

M.

 

Astorino

, and

J.-F.

 

Gerbeau

,  , ().

S.

 

Raben

,

S.

 

Ross

, and

P.

 

Vlachos

,  , ().

J. S.

 

Olafsen

and

J. S.

 

Urbach

,  , ().

B.

 

Aldridge

,

G.

 

Haller

,

P.

 

Sorger

, and

D.

 

Lauffenburger

,  , ().

M.

 

Astorino

,

J.

 

Hamers

,

S. C.

 

Shadden

, and

J.-F.

 

Gerbeau

,  , ().

J.

 

Peng

and

J. O.

 

Dabiri

,  , ().

T.

 

Peacock

and

J.

 

Dabiri

,  , ().

S. C.

 

Shadden

,

F.

 

Lekien

, and

J. E.

 

Marsden

,  , ().

G.

 

Haller

and

T.

 

Sapsis

,  , ().

Recently,

G.

 

Haller

[ , ()] has defined LCSs rigorously in terms of hyperbolic material surfaces with extreme finite time repulsion and extraction, to avoid spurious identification of LCSs that appear due to shear or stretching.

See supplementary material at http://dx.doi.org/10.1063/1.4894866 for the time evolution of

$\bar{\psi }_{6}$

$ψ¯6$ (Video 1), the power of particles (Video 2), and the FTLE field with the superposition of the power of particles (Video 3). All movies are created for a few hundred frames. In addition, Figs. 1 and 2 are shown for the maximal stretching directions along the FTLE ridges, and the time averaged spatial correlation of

$\bar{\psi }_{6}(t)$

$ψ¯6(t)$⁠, respectively.

P. S.

 

Addison

, (, ).

D.

 

Gabor

,  , ().

The Fourier transform of the Gabor wavelet is given by

$\Phi (f)=\frac{\nu }{f_{b}} \exp [-\pi (\frac{ \nu (f-f_{b})}{f_{b}} )^{2}]$

$Φ(f)=νfbexp[−π(ν(f−fb)fb)2]$ that is a Gaussian form of frequency f with mean f_b and the standard deviation

$\sigma _{f_b}=\frac{1}{\sqrt{2\pi }}\frac{f_{b}}{\nu }$

$σfb=12πfbν$⁠. Here

$\sigma _{f_b}$

$σfb$ provides the amount uncertainty to the identification of f_b in the frequency plane. As ν is smaller (larger), the uncertainty becomes larger (smaller) in frequency (while the uncertainty in time (scale) becomes smaller (larger) in the wavelet transform). In our analysis, the time scale of perturbation is about 14 frames. In our study, we set two conditions to decide the value of ν: to have time resolution at least 14 frames which can be captured by choosing ν ⩽ 1, and to distinguish the base frequency f_b to the other frequency components. In this sense, The value of ν less than 1 will increase the uncertainty in frequency which makes it difficult to differentiate the b.

J. R.

 

Melrose

and

R. C.

 

Ball

,  , ().

X.

 

Cheng

,

J. H.

 

McCoy

,

J. N.

 

Israelachvili

, and

I.

 

Cohen

,  , ().