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This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.
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Tumasz, S. E., and J.-L. Thiffeault, 2013, “Estimating topological entropy from the motion of stirring rods,” Procedia IUTAM 7
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Blancher, S., Y. Le Guer, and K. El Omari, 2014, “Spatio-temporal structure of the fully developed transitional flow in a symmetric wavy channel. part. 1: Linear and weakly nonlinear stability analysis,” J. Fluid Mech. 764
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Blazevski, D., and G. Haller, 2014, “Hyperbolic and elliptic transport barriers in three-dimensional unsteady flows,” Physica D 273
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Foures, D. P. G., C. P. Caulfield, and P. J. Schmid, 2014, “Optimal mixing in two-dimensional plane Poiseuille flow at finite Péclet number,” J. Fluid Mech. 748
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Nagai, M., Y. Hayasaka, T. Kawashima, and T. Shibata, 2014, “Active mixing in microchamber using cilia of Vorticella convallaria,” IEEJ Trans. Elect. Electron. Eng. 9
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Pratt, L. J., I. I. Rypina, T. M. Özgökmen, P. Wang, H. Childs, and Y. Bebieva, 2014, “Chaotic advection in a steady, three-dimensional, ekman-driven eddy,” J. Fluid Mech. 738
2014
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Shapiro, O. H., V. I. Fernandez, M. Garren, J. S. Guasto, F. P. Debaillon-Vesque, E. Kramarsky-Winter, A. Vardi, and R. Stocker, 2014, “Vortical ciliary flows actively enhance mass transport in reef corals,” Proc. Natl Acad. Sci. USA 111
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Springham, J., and R. Sturman, 2014, “Polynomial decay of correlations in linked–twist maps,” Ergod. Theory Dyn. Sys. 34
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2014
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Wang, S., G. Metcalfe, R. L. Stewart, J. Wu, N. Ohmura, X. Feng, and C. Yang, 2014, “Solid-liquid separation by particle-flow-instability,” Energy & Environmental Sci. 7
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Wu, F., M. F. M. Speetjens, D. L. Vainchtein, R. R. Trieling, and H. J. H. Clercx, 2014, “Comparative numerical-experimental analysis of the universal impact of arbitrary perturbations on transport in three-dimensional unsteady flows,” Phys. Rev. E 90
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Arrieta, J., J. H. E. Cartwright, E. Gouillart, N. Piro, O. Piro, and I. Tuval, 2015, “Geometric mixing, peristalsis, and the geometric phase of the stomach,” PlosOne 10
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Baskan, Ö., M. F. M. Speetjens, G. Metcalfe, and H. J. H. Clercx, 2015, “Experimental and computational study of scalar modes in a periodic laminar flow,” Int. J. Thermal Sci. 96
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Brumley, D. R., M. Polin, T. J. Pedley, and R. E. Goldstein, 2015, “Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin,” J. Roy. Soc. Interface 12
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Domingos, M. G., and S. S. S Cardoso, 2015, “Turbulent thermals with chemical reaction,” J. Fluid Mech 784
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El Omari, K., Y. Le Guer, D. Perugini, and M. Petrelli, 2015, “Cooling of a magmatic system under thermal chaotic mixing,” Pure Appl. Geophys. 172
2015
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Haller, G., 2015, “Lagrangian coherent structures,” Annu. Rev. Fluid Mech. 47
2015
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Budišić, M., S. Siegmund, D. Thai Son, and I. Mezić, 2016, “Mesochronic classification of trajectories in incompressible 3D vector fields over finite times,” Discrete and Continuous Dyn. Sys. — Series S 9
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Faubel, R., C. Westendorf, E. Bodenschatz, and G. Eichele, 2016, “Cilia-based flow network in the brain ventricles,” Science 353
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Petrelli, M., K. El Omari, Y. Le Guer, and D. Perugini, 2016, “Effects of chaotic advection on the timescales of cooling and crystallization of magma bodies at mid crustal levels,” Geochem. Geophys, Geosys. 17
2016
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Smith, L. D., M. Rudman, D. R. Lester, and G. Metcalfe, 2016, “Mixing of discontinuously deforming media,” Chaos 26
2016
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Wang, S., R. Stewart, and G. Metcalfe, 2016, “Visualization of the trapping of inertial particles in a laminar mixing tank,” Chem. Eng. Sci. 143
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Yang, D., B. Batista, O. Steinbock, J .H. E. Cartwright, and S. S. S. Cardoso, 2016, “Wavy membranes and the growth rate of a planar chemical garden: Enhanced diffusion and bioenergetics,” Proc. Natl Acad. Sci. USA 113
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Wang, S., X. Huang, and C. Yang, 2011, “Mixing enhancement for high viscous fluids in a microfluidic chamber,” Lab on a chip 11
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