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Here, we study the fluid dynamics of a pair of rigid helices rotating at a constant velocity, tethered at their bases, in a viscous fluid. Our computations use a regularized Stokeslet framework, both with and without a bounding plane, so we are able to discern precisely what flow features are unaccounted for in studies that ignore the surface from which the helices emanate. We examine how the spacing and phase difference between identical rotating helices affects their pumping ability, axial thrust, and power requirements. We also find that optimal mixing of the fluid around two helices is achieved when they rotate in opposite phase, and that the mixing is enhanced as the distance between the helices decreases.

In this paper we utilize the method of regularized Stokeslets to explore flow fields induced by 'carpets' of rotating flagella. We model each flagellum as a rigid, rotating helix attached to a wall, and study flows around both a single helix and a small patch of multiple helices. To test our numerical method and gain intuition about flows induced by a single rotating helix, we first perform a numerical timereversibility experiment. Next, we investigate the hypothesis put forth in (Darnton et al., Biophys J 86, 1863-1870) that a small number of rotating flagella could produce "whirlpools" and "rivers" a small distance above them. Using our model system, we are able to produce "whirlpools" and "rivers" when the helices are rotating out of phase. Finally, to better understand the transport of microscale loads by flagellated microorganisms, we model a fully coupled helix-vesicle system by placing a finite-sized vesicle held together by elastic springs in fluid near one or two rotating helices. We compare the trajectories of the vesicle and a tracer particle initially placed at the centroid of vesicle and find that the two trajectories can diverge significantly within a short amount of time. Interestingly, the divergent behavior is extremely sensitive to the initial position within the fluid.

Swarming groups of bacteria coordinate their behavior by self-organizing as a population to move over surfaces in search of nutrients and optimal niches for colonization. Many open questions remain about the cues used by swarming bacteria to achieve this self-organization. While chemical cue signaling known as quorum sensing is well described, swarming bacteria often act and coordinate on time scales that could not be achieved via these extracellular quorum sensing cues. Here, cell-cell contact-dependent protein exchange is explored as a mechanism of intercellular signaling for the bacterium Myxococcus xanthus. Detailed biologically calibrated computational model is used to study how M. xanthus optimizes the connection rate between cells and maximizes spread of an extracellular protein within the population. The maximum rate of protein spreading is observed for cells that reverse direction optimally for swarming. Cells that reverse too slowly or too fast fail to spread extracellular protein efficiently. In particular, a specific range of cell reversal frequencies was observed to maximize the cell-cell connection rate and minimize the time of protein spreading. Furthermore, our findings suggest that pre-designed motion reversal can be employed to enhance the collective behavior of biological synthetic active systems.

Focusing on the groundbreaking work of women in mathematics past, present, and future, Springer's Association for Women in Mathematics Series presents the latest research and proceedings of conferences worldwide organized by the Association for Women in Mathematics (AWM). All works are peer-reviewed to meet the highest standards of scientific literature, while presenting topics at the cutting edge of pure and applied mathematics, as well as in the areas of mathematical education and history. Since its inception in 1971, The Association for Women in Mathematics has been a non-profit organization designed to help encourage women and girls to study and pursue active careers in mathematics and the mathematical sciences and to promote equal opportunity and equal treatment of women and girls in the mathematical sciences. Currently, the organization represents more than 3000 members and 200 institutions constituting a broad spectrum of the mathematical community in the United States and around the world.