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The Viscous Nonlinear Dynamics of Twist and Writhe

Raymond E. Goldstein·Thomas R. Powers·Chris H. Wiggins
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Abstract

Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density embodies the dynamic interplay of twist and writhe. These are used to illustrate a novel nonlinear phenomenon: ``geometric untwisting" of open filaments, whereby twisting strains relax through a transient writhing instability without performing axial rotation. This may explain certain experimentally observed motions of fibers of the bacterium B. subtilis [N.H. Mendelson, et al., J. Bacteriol. 177, 7060 (1995)].

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Raymond E. Goldstein, Thomas R. Powers, Chris H. Wiggins. 1998-02-08. The Viscous Nonlinear Dynamics of Twist and Writhe. https://doi.org/10.1103/physrevlett.80.5232

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