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Theory of self-organized swimming with odd elasticity discovered ― Paves way to the development and realization of autonomous micromachines

2022.11.04

Swimming in water is a dynamic interaction between a body and a fluid, and the swimming of microscopic microorganisms is no exception. In particular, when the object is soft and elastic, deformation and swimming are inseparable, but the swimming formula for general elastic materials has long remained a mystery.

Associate Professor Kenta Ishimoto and his research group at the Research Institute for Mathematical Sciences, Kyoto University, have focused on the concept of "odd elasticity" as an extension of elasticity. Odd elasticity is the scientific description of a state in which the law of conservation of energy does not hold due to spontaneous deformation of living organisms or objects, which was previously considered impossible according to elastic body theory.

In their study, the research group introduced odd elasticity to Purcell's three-link swimmer, the most basic mathematical model of swimming, and calculated the fluid flow. They discovered that the internal fluctuation of an elastic body acts like a switch and produces autonomous and flexible swimming motions. They also found that the existing swimming laws and the law of force and deformation in malleable bodies, which had been considered completely different concepts, can both be expressed as stochastic currents in shape space, and succeeded in deriving a swimming formula.

In the future, the group anticipates contributing to the development and realization of autonomous micromachines that can move within the body and blood vessels, as well as to the investigation of the size of actual microorganisms with odd elasticity, both in terms of fundamental and applied research.

Diagram of Purcell's swimmer (left) and stochastic current in shape space (right)
Hydrodynamic numerical simulation that incorporates odd elasticity into the Purcell's swimmer, a mathematical model of micro-swimming. The object swims by itself without any external input or control.

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