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Subdiffusive transport of fluctuating elastic filaments in cellular flows
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Image of FIG. 1.
FIG. 1.

Snapshots from a simulation with 80 000, ℓ/ = 1000, and = 1, showing the buckling instability at the stagnation points at cell corners.

Image of FIG. 2.
FIG. 2.

Center-of-mass trajectories of polymers: (a)–(d) correspond to four different cell sizes at the same 20 000 and ℓ/ = 1000, each showing four different trajectories; (e) shows the case of a single polymer with = π and 20 000, but ℓ/ = 10 (enhanced online). [URL: http://dx.doi.org/10.1063/1.4812794.1]doi: 10.1063/1.4812794.1.

Image of FIG. 3.
FIG. 3.

(a) Mean square displacement () of the filament center-of-mass as a function of time at 20 000 for three values of ℓ/, where the long-time behavior follows an approximate power law () ∝  . (b) Dependence of the exponent α on the reduced persistence length ℓ/. (c) Distribution of waiting times, defined as periods of time spent by a filament inside a given cell, in simulations with 20 000 and ℓ/ = 10.

Image of FIG. 4.
FIG. 4.

(a) Frequency distribution of the magnitude of the center-of-mass velocity for various values of ℓ/ at 20 000. (b) Contours of the fluid velocity magnitude inside a given cell, indicating that the value of corresponds approximately to the largest ring of uniform velocity within the cell.

Image of FIG. 5.
FIG. 5.

Probability distributions of mass of the polymer in a unit cell at 20 000 for different values of ℓ/. Probabilities are normalized to be unity for a uniform distribution.

Image of FIG. 6.
FIG. 6.

Steady-state solution of the Fokker-Planck equation (13) at Pe = 10 000 for rigid rods of aspect ratio ε = 0.01.

Image of FIG. 7.
FIG. 7.

Characteristic distributions of filament configurations in a unit cell with (a) and ℓ/ = 1000 and (b) 10 000 and ℓ/ = 100.



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Scitation: Subdiffusive transport of fluctuating elastic filaments in cellular flows