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Interactions between active particles and dynamical structures in chaotic flow
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10.1063/1.4754873
/content/aip/journal/pof2/24/9/10.1063/1.4754873
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/9/10.1063/1.4754873
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(a) Snapshot of one unit cell of the flow field at zero phase (that is, for t such that sin Ωt = 0). Arrows show the local fluid velocity, and the shading shows the vorticity. As time progresses, the flow field oscillates sinusoidally in the horizontal direction. (b) Poincare section (at zero phase) for a fluid element initially in the chaotic sea, for B = 0.12 and Ω = 6.28. Only one quarter of the unit cell is shown (corresponding to the lower-left vortex in (a)); the rest of the unit cell is related by symmetry. The central empty region is a period-1 elliptic island; the surrounding empty regions are a period-3 island chain. (c) Finite-time Lyapunov exponent (FTLE) field at zero phase. Again, only one quarter of the unit cell is shown.

Image of FIG. 2.
FIG. 2.

Chaotic diffusion coefficient D normalized by D 0, the diffusion coefficient for fluid elements, as a function of the swimming speed v s , for spherical swimmers with σ s = σ r = 0. Error bars are computed from the statistical fluctuations between many sets of simulations. Two distinct regions of suppressed long-time transport are seen, corresponding to trapping by the period-3 islands and by the period-1 islands.20

Image of FIG. 3.
FIG. 3.

Chaotic diffusion coefficient D normalized by D 0 as a function of σ s , for v s = 0, σ r = 0, and α = 0. When compared with Fig. 2, transport is more strongly suppressed, but the distinct signatures of each type of elliptic island are no longer present.

Image of FIG. 4.
FIG. 4.

Average time for a swimmer to cross a cell boundary as a function of its spatial location for (a) v s = 0.004 and σ s = σ r = 0 and (b) σ s = 0.15 and v s = σ r = 0. Only one quarter of the flow domain is shown. The shade/color bar gives the cell-crossing time in flow cycles. For the deterministic swimmer in (a), trapping is strong in the period-3 islands and on a small ring just inside the period-1 island. The purely stochastic swimmer can wander into the core of the period-1 island, where trapping is strongest.

Image of FIG. 5.
FIG. 5.

Chaotic diffusion coefficients D in the two-dimensional parameter space spanned by v s and σ s for σ r = 0. The shade/color bar shows D relative to D 0. The black line separates the regions of suppressed transport (D/D 0 < 1) from those of enhanced transport (D/D 0 > 1).

Image of FIG. 6.
FIG. 6.

Chaotic diffusion coefficients D in the two-dimensional parameter space spanned by v s and σ r for σ s = 0. The shade/color bar shows D relative to D 0. The black line separates the regions of suppressed transport (D/D 0 < 1) from those of enhanced transport (D/D 0 > 1). Transport is suppressed in larger region of parameter space than it was for purely translational stochasticity case in Fig. 5.

Image of FIG. 7.
FIG. 7.

Spatially resolved maps of the average time to cross a cell boundary for v s = 0.004, and σ r = (a) 0.1, (b) 1.0, (c) 3.0, and (d) 6.0. σ s = 0 for all panels. The shade/color bar gives the cell-crossing times in flow cycles. The times are much longer than the comparable v s = 0.004, σ r = 0 case shown in Fig. 4(a).

Image of FIG. 8.
FIG. 8.

(a) Chaotic diffusion coefficient D normalized by D 0 as a function of eccentricity α for deterministic swimmers with v s = 0.002. Transport is much more strongly suppressed for ellipsoids of intermediate eccentricities than it is for spheres. (b)–(d) Probability density functions of swimmer position for (b) α = 0, (c) α = 0.5, and (d) α = 1. The strong suppression of transport for ellipsoidal particles is due to the formation of attractors.

Image of FIG. 9.
FIG. 9.

(a) Chaotic diffusion coefficient D normalized by D 0 as a function of eccentricity α for deterministic swimmers with v s = 0.08. For this speed, transport of ellipsoidal particles is strongly enhanced relative to spheres. (b)–(d) Probability density functions of swimmer position for (b) α = 0, (c) α = 0.5, and (d) α = 1. The strong enhancement of transport is due to the clustering of ellipsoids on the stable manifolds of the hyperbolic fixed points.

Image of FIG. 10.
FIG. 10.

Mean nearest neighbor distance δ NN scaled by the value for passive particles δ0 as a function of eccentricity for (a) v s = 0.002 and (b) v s = 0.08. High aspect ratio swimmers tend to be closer to each than spherical swimmers are, leading to enhanced encounter rates.

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/content/aip/journal/pof2/24/9/10.1063/1.4754873
2012-09-26
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Interactions between active particles and dynamical structures in chaotic flow
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/9/10.1063/1.4754873
10.1063/1.4754873
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