Swimming of Microorganism and the String- and Membrane- like Algebra

TL;DR

This paper models microorganism swimming using string and membrane algebraic frameworks, refining previous fluid dynamics analyses by incorporating inertia and exploring algebraic structures like the $W_{1+ abla}$ algebra to understand collective motion.

Contribution

It introduces a refined algebraic approach to microorganism swimming, incorporating fluid inertia and analyzing collective behaviors through advanced algebraic structures.

Findings

Incorporation of fluid inertia as a perturbation improves the model.

Identification of the central extension of the algebra controlling deformation.

Examination of N-point string- and membrane-like amplitudes for collective swimming.

Abstract

Swimming of microorganisms is further developed from a viewpoint of strings and membranes swimming in the incompressible fluid of low Reynolds number. In our previous paper the flagellated motion was analyzed in two dimensional fluid, by using the method developed in the ciliated motion with the Joukowski transformation. This method is further refined by incorporating the inertia term of fluid as the perturbation. Understanding of the algebra controlling the deformation of microorganisms in the fluid is further developed, obtaining the central extension of the algebra with the help of the recent progress on the $W_{1+\infty}$ algebra. Our previous suggestion on the usefulness of the $N$-point string- and membrane-like amplitudes for studying the collective swimming motion of $N-1$ microorganisms is also examined.