Ph.D Student | Berman Rotem Sara |
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Subject | Swimming and Alignment in Low-Reynolds-Number Medium |

Department | Department of Physics |

Supervisors | Professor Emeritus Joseph Avron |

Professor Alexander Leshansky | |

Full Thesis text |

This work presents mathematical modeling of two problems from fields governed by low Reynolds hydrodynamics, which are the motion of macromolecules inside biological cells and the swimming of microorganisms.

Inspired by the experimental problem of microtubules arrangement arising from molecular motors connections, we solved the problem of flow-driven re-orientation of connected sticks moving in low Reynolds number medium. The molecular motors were modeled by moving connection points and two connection possibilities were considered. Contrary to former works, we showed that in our modeling, the interaction of a motor which advances on two sticks is highly symmetrical and does not lead to sticks arrangement. However, we found that the alignment of sticks can arise from an interaction which was not considered before, of one motor advancing on one stick and carrying the other. In order to induce alignment, the required properties of the motor are random detachment and a velocity which depends on the angle between the sticks or the sign of the angle change. Going to more complex assemblages, we solved the problem of regular polygons made of connected sticks.

The second part
of this thesis is devoted to swimming of short undulating filaments, motivated
by the propulsion of *C. elegans*. We calculated the distance per stroke
and efficiency for a sinusoidal swimmer with wide range of wave numbers and
amplitudes, employing particle-based algorithm and resistive force theory
(RFT). The comparison between the approaches revealed the limit of the RFT
applicability, above which inter-filament hydrodynamic interactions become
important and the RFT overestimates the advancement of the swimmer and its
swimming efficiency. It was found that for the finite sinusoidal swimmer, there
are global maxima of distance per stroke and swimming efficiency. The
parameters of biological swimmers were compared with the best sine wave gaits,
and most of the swimmers proved to be in the range of parameters appropriate
for maximizing the efficiency of swimming, but also showing relatively high
distance covered per stroke. Concentrating on *C. elegans*, we calculated
its propulsion from the experimental deformation function using the
particle-based algorithm, and reached a good agreement with the experimental
results. Using this calculation, we were able to compute the propulsion
efficiency of the nematode. Compared to the sine wave, both the distance per
stroke and the swimming efficiency of *C. elegans* proved to be much
higher, demonstrating the importance of geometric optimization of the spatial
beating stroke.