Mathematics Colloquia and Seminars

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Talk 1:

Many different microswimmers propel themselves using flagella that beat periodically. The shape of the flagellar beat and swimming speed have been observed to change with fluid rheology. We quantify changes in the flagellar waveforms of Chlamydomonas reinhardtii in response to changes in fluid viscosity using (1) shape mode analysis and (2) a full swimmer simulation to analyze how shape changes affect the swimming speed. By decomposing the gait into the time-independent mean shape and the time-varying stroke, we find that the flagellar mean shape substantially changes in response to viscosity, while the changes in the time-varying stroke are more subtle. Using the swimmer simulation, we show that the observed change in swimming speed with viscosity is explained by the variations in mean flagellar shape and beat frequency, while the changes in swimming speed from the different time-varying strokes are on the scale of variation between cells.

Talk 2:

Metachronal paddling is a swimming strategy in which an aquatic creature oscillates sets of adjacent limbs with a constant phase lag, propagating a metachronal wave through its limbs and propelling it forward. This limb coordination strategy is utilized by swimmers across a wide range of Reynolds numbers, and due to its prevalence, we conjecture that this metachronal rhythm is biologically selected for its optimality of swimming performance. In this study, we apply reinforcement learning to a swimmer at zero Reynolds number and investigate whether the learning algorithm selects this metachronal rhythm, or if other coordination patterns emerge. To this end, we define a zero Reynolds number fluid environment and allow a swimmer agent to self-learn the optimal stroke. We design the swimmer agent with an elongated body and pairs of straight, inflexible paddles placed along the body for various fixed paddle spacings. Based on paddle spacing, the swimmer agent learns qualitatively different coordination patterns. At tight spacings, a back-to-front metachronal wave-like stroke emerges which resembles the commonly observed biological rhythm, but at wide spacings, different limb coordinations are selected. The stroke that results in the highest swimming speed varies depending on the number of paddle sets, however, the most efficient stroke is the back-to-front wave-like stroke in every case.

Also available on Zoom: https://ucdavis.zoom.us/j/98969645841