Microswimming by odd elasticity*

Microswimmers such as bacteria, sperm cells, and microalgae often generate a traveling wave to propel themselves at low Reynolds number. This non-reciprocal deformation is created by internal actuation within an elastic filament. In this talk, we introduce the concept of odd elasticity, which is a relatively new framework for describing the non-equilibrium state of matter and an extension of linear elasticity, to the field of microswimmer elastohydrodynamics. This provides a unified description of living materials in viscous fluids. We begin by presenting a minimal mathematical model known as Purcell's swimmer, being consisted of three rods connected by two hinges, and demonstrate that hinges with odd-elastic properties enable the swimmer to exhibit stable periodic locomotion without any controlled actuation. Furthermore, we formulate a general swimmer subjected to periodic deformations by extending the concept of odd elasticity into a non-linear regime. Through analyses of various simple mathematical models and experimental data, we introduce an extension of the elastic modulus to capture non-local, non-reciprocal interactions within the active filament.