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Recent years have seen a surge of interest in active materials, in which energy injected at the microscale gives rise to larger-scale coherent motion. One prominent example is an active 2D liquid crystal composed of microtubules in the nematic phase. The activity is generated by molecular motors that consume ATP to generate local shearing between the microtubules. The resulting 2D fluid flow exhibits self-generated mesoscale chaotic dynamics with a characteristic folding and stretching pattern. We analyse this dynamics in the context of chaotic advection, in which the fluid can be viewed as "stirred" by the topological defects in the nematic order parameter. We compute the topological entropy from the braiding of these defects and show that all of the entropy arises from the positive one-half defects. We also show that the topological entropy generated by this stirring can be understood as a direct consequence of the micro-scale stretching quantified by the Lyapunov exponent. Finally, we describe a novel mechanism for the generation of persistent fractal structure seen in experiments. Though these fractal patterns are reminiscent of passively advected dye in 2D chaotic flows at low Reynolds number, the underlying mechanism for fractal generation is more subtle in active nematics.
Dr. Mitchell's research addresses fundamental questions in nonlinear dynamics and their application to classical, semiclassical and quantum physics, with an emphasis on chaotic transport. His current work can be classified into three main focus areas: (i) Theory of phase space transport and symbolic dynamics; (ii) Applications of nonlinear dynamics to AMO (atomic, molecular, and optical) physics; (iii) Geometry of front propagation in fluid flows. His work is highly interdisciplinary, bridging areas of physics, engineering, and mathematics. He has been at UC Merced since 2004.