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Sep 3, 2005 Castel Gandolfo . Stretching and Tumbling of Polymers in a random flow with mean shear. M. Chertkov (Los Alamos NL) I. Kolokolov, V. Lebedev, K. Turitsyn (Landau Institute, Moscow). Jou r nal of Fluid Mechanics , 531 , pp. 251-260 (2005).
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Stretching and Tumbling of Polymers in a random
flow with mean shear
M. Chertkov (Los Alamos NL)
I. Kolokolov, V. Lebedev, K. Turitsyn (Landau Institute, Moscow)
Journal of Fluid Mechanics,531, pp. 251-260 (2005)
large scale velocity
(Groisman, Steinberg ’00-’04)
Polymer is much smaller than
any velocity related scale
theoretically in this study:
Fast (ballistic) motion
Slow (stochastic) one
Separation of trajectories
(auxiliary problem in the same velocity field)
Hinch & Leal 1972
Tumbling Time Statistics
of the noise
We studied polymer subjected to Strong permanent shear
+ Weak fluctuations in large scale velocity
K.S. Turitsyn, submitted to Phys. Rev. E (more to the theory)
A. Celani, A. Puliafito, K. Turitsyn, EurophysLett, 70 (4), pp. 439-445 (2005)
A. Puliafito, K.S. Turitsyn, to appear in Physica D (numerics+theory)
Gerashenko, Steinberg, submitted to PRL (experiment)
(non-equilibrium stat. mech)
(linear polymer in shear+ thermal fluctuations)
Probability of the given
trajectory (forward path)
Microscopic entropy produced
along the given path
(degree of the detailed balance violation)
grows with time
Related to work done by shear force over polymer
( independence !!)
The distribution of the angle is asymmetric, localized at the positive angles of order twith the asymptotic
P() sin-2 at large angles determined by the regular shear dynamics.
PDF of the angle is also localized at twith algebraic tails in intermediate region t<<||<<1. These tails come from the two regions: the regular one gives the asymptotic P() -2, and from the stochastic region, which gives a non-universal asymptotic P() -x, where x is some constant which depends on thestatistical properties of the
chaotic velocity component.
tTumbling time distribution
Gerashenko, Steinberg, submitted to PRL
The characteristic tumbling times are of order t=1/(st ), however due to stochastic nature of the tumbling process there are tails corresponding to the anomalous small or large tumbling times. The right tail always behaves like P(t) exp(-c t/t), while the left tail is non-universal depending on the statistics of random velocity field.