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<\/p>\nSwimmers and fish move through the water following much the same
\nprinciple of “action-reaction” (for every action, an equal and opposite
\naction applies). By the coordinated movement of their limbs, they
\ndisplace the water and, in reaction, their bodies move forward despite
\nthe resistance of the water. But if they tried to swim in molasses,
\nthey’d never make it, as the resistance of the molasses would absorb all
\n their energy and they’d never make it forward. The Scallop Theorem
\nclearly demonstrates what happens in such fluids with high Reynolds
\ncoefficients. Newton’s third law applies.<\/p>\n
Yet, on another scale,
\nsingle-celled algae and spermatozoa manage to advance rapidly and with
\nease in highly viscous fluids and over very large distances in
\nproportion to their size. How do they get around Newton’s implacable
\nthird law?<\/p>\n
Symmetries and reciprocity<\/p>\n
Mathematician Kenta
\nIshimoto’s team set out to understand how these single-celled creatures
\nsnake their way through environments that, in principle, should paralyze
\n their movement. When the third law applies, it does so symmetrically
\nand reciprocally in environments in equilibrium; the solution to the
\nproblem posed lies in what are called “non-reciprocal and
\nnon-symmetrical interactions”, which characterize chaotic systems and
\nwhose elements participate dynamically in the system, like birds in a
\nmurmuration or pedestrians on a sidewalk. By establishing relationships
\nwith their environment, they alter the conditions of equilibrium.<\/p>\n
In
\n the case of unicellular algae and spermatozoa, researchers have modeled
\n the movement of cells and their flagella. In principle, a viscous fluid
\n would dissipate the flagella’s energy, preventing them from moving and
\nexhausting them within minutes. And yet, somehow, the flagella manage to
\n propel these cells without provoking any reaction from their
\nenvironment.<\/p>\n
The researchers discovered that flagella have
\ndeveloped an elasticity and flexibility on a microscopic scale that
\nenables them to move without losing much energy in the surrounding
\ncolloid-like fluid, which are complex plasmas where interactions are
\nnon-reciprocal. As quantum physics researchers have named stealth
\nparticles with names like “charming” or “strange”, the researchers
\ncalled this property “strange elasticity”. <\/p>\n
“Using
\nsimple, solutionable models and biological flagellar waveforms for
\nchlamydomonas algae and spermatozoa, we studied the strange flexural
\nmodulus to decipher non-local and non-reciprocal internal interactions
\nwithin the material.”<\/p>\n
But this strange elasticity
\nproperty does not fully explain the propulsion generated by the
\nundulatory motion of the flagella. The researchers have therefore also
\nderived a strange modulus of elasticity to describe the internal
\nmechanics of flagella. Their investigations include “transverse
\nresponses”, modified dislocation dynamics and topological waves. What is
\n certain is that the greater the strange modulus of elasticity, the
\nbetter the mobility in such fluids.<\/p>\n
<\/p>\n
While
\n these results may eventually help in the design of small micro-robots
\nmimicking living materials, modeling methods can already be used to
\nbetter understand the underlying principles of collective behavior.<\/p>\n
To see the research – Odd Elastohydrodynamics: Non-Reciprocal Living Material in a Viscous Fluid<\/a> – Kenta Ishimoto, Cl\u00e9ment Moreau, Kento Yasuda – Physical Review Journal<\/p>\n Illustration – 610820594<\/a> Scallop Theorem – https:\/\/en.wikipedia.org\/wiki\/Scallop_theorem<\/a><\/p>\n Reynolds number – https:\/\/en.wikipedia.org\/wiki\/Reynolds_number<\/a><\/p>\n Murmuration – Dossier Thot Cursus – https:\/\/cursus.edu\/en\/files\/13523\/murmuration<\/a><\/p>\n Kenta Ishimoto – Professor of Applied Mathematics – Department of Mathematics, Kyoto University Odd Elastohydrodynamics: Non-Reciprocal Living Material in a Viscous Fluid – Physical Review Journal Odd Viscosity and Odd Elasticity Experimental study of the nonreciprocal effective interactions between microparticles in anisotropic plasma
References<\/p>\n
https:\/\/www.math.kyoto-u.ac.jp\/~kenta.ishimoto\/<\/a><\/p>\n
https:\/\/journals.aps.org\/prxlife\/abstract\/10.1103\/PRXLife.1.023002<\/a><\/p>\n
https:\/\/www.annualreviews.org\/content\/journals\/10.1146\/annurev-conmatphys-040821-125506<\/a><\/p>\n
https:\/\/www.nature.com\/articles\/s41598-020-70441-z<\/a><\/p>\n