Odd elastohydrodynamics: non-reciprocal living material in a viscous fluid

Abstract

Motility is a fundamental feature of living matter, encompassing single cells and collective behavior. Such living systems are characterized by non-conservativity of energy and a large diversity of spatio-temporal patterns. Thus, fundamental physical principles to formulate their behavior are not yet fully understood. This study explores a violation of Newton's third law in motile active agents, by considering non-reciprocal mechanical interactions known as odd elasticity. By extending the description of odd elasticity to a nonlinear regime, we present a general framework for the swimming dynamics of active elastic materials in low-Reynolds-number fluids, such as wave-like patterns observed in eukaryotic cilia and flagella. We investigate the non-local interactions within a swimmer using generalized material elasticity and apply these concepts to biological flagellar motion. Through simple solvable models and the analysis of {\it Chlamydomonas} flagella waveforms and experimental data for human sperm, we demonstrate the wide applicability of a non-local and non-reciprocal description of internal interactions within living materials in viscous fluids, offering a unified framework for active and living matter physics.

arXiv comment18 pages, 9 figures

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• Robust undulatory locomotion via neuromechanical adjustments in a dissipative medium
• Rigid flocks, undulatory gaits, and chiral foldamers in a chemically active polymer
• Irreversibility of stochastic state transitions in Langevin systems with odd elasticity
• Yielding in dense active matter
• Screw Symmetry, Chiral Hydrodynamics and Odd Instability in Active Cholesterics
• Bending-compression coupling in extensible slender microswimmers