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Register a new userPersistence of perfect packing in twisted bundles of elastic filaments
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It is generally understood that geometric frustration prevents maximal hexagonal packings in uniform filament bundles upon twist. We demonstrate that a hexagonal packed elastic filament bundle can preserve its order over a wide range of twist due to a subtle counteraction of geometric expansion with elastic contraction. Using x-ray scanning and by locating each filament in the bundle, we show the remarkable persistence of order even as the twist is increased well above 360 degrees, by measuring the spatial correlation function across the bundle crosssection. We introduce a model which analyzes the combined effects of elasticity including filament stretching, and radial and hoop compression necessary to explain this generic preservation of order observed with Hookean filaments.
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Although the free energy of a genome packing into a virus is dominated by DNA-DNA interactions, ordering of the DNA inside the capsid is elasticity-driven, suggesting general solutions with DNA organized into spool-like domains. Using analytical calculations and computer simulations of a long elastic filament confined to a spherical container, we show that the ground state is not a single spool as assumed hitherto, but an ordering mosaic of multiple homogeneously-ordered domains. At low densities, we observe concentric spools, while at higher densities, other morphologies emerge, which resemble topological links. We discuss our results in the context of metallic wires, viral DNA, and flexible polymers.
It is known from the wave-like motion of microtubules in motility assays that the piconewton forces that motors produce can be sufficient to bend the filaments. In cellular phenomena such as cytosplasmic streaming, molecular motors translocate along cytoskeletal filaments, carrying cargo which entrains fluid. When large numbers of such forced filaments interact through the surrounding fluid, as in particular stages of oocyte development in $Drosophila~melanogaster$, complex dynamics are observed, but the detailed mechanics underlying them has remained unclear. Motivated by these observations, we study here perhaps the simplest model for these phenomena: an elastic filament, pinned at one end, acted on by a molecular motor treated as a point force. Because the force acts tangential to the filament, no matter what its shape, this follower-force problem is intrinsically non-variational, and thereby differs fundamentally from Euler buckling, where the force has a fixed direction, and which, in the low Reynolds number regime, ultimately leads to a stationary, energy-minimizing shape. Through a combination of linear stability theory, analytical study of a solvable simplified two-link model, and numerical studies of the full elastohydrodynamic equations of motion we elucidate the Hopf bifurcation that occurs with increasing forcing of a filament, leading to flapping motion analogous to the high Reynolds number oscillations of a garden hose with a free end.
The buckling and twisting of slender, elastic fibers is a deep and well-studied field. A slender elastic rod that is twisted with respect to a fixed end will spontaneously form a loop, or hockle, to relieve the torsional stress that builds. Further twisting results in the formation of plectonemes -- a helical excursion in the fiber that extends with additional twisting. Here we use an idealized, micron-scale experiment to investigate the energy stored, and subsequently released, by hockles and plectonemes as they are pulled apart, in analogy with force spectroscopy studies of DNA and protein folding. Hysteresis loops in the snapping and unsnapping inform the stored energy in the twisted fiber structures.
We investigate with experiments the twist induced transverse buckling instabilities of an elastic sheet of length $L$, width $W$, and thickness $t$, that is clamped at two opposite ends while held under a tension $T$. Above a critical tension $T_lambda$ and critical twist angle $eta_{tr}$, we find that the sheet buckles with a mode number $n geq 1$ transverse to the axis of twist. Three distinct buckling regimes characterized as clamp-dominated, bendable, and stiff are identified, by introducing a bendability length $L_B$ and a clamp length $L_{C}(<L_B)$. In the stiff regime ($L>L_B$), we find that mode $n=1$ develops above $eta_{tr} equiv eta_S sim (t/W) T^{-1/2}$, independent of $L$. In the bendable regime $L_{C}<L<L_B$, $n=1$ as well as $n > 1$ occur above $eta_{tr} equiv eta_B sim sqrt{t/L}T^{-1/4}$. Here, we find the wavelength $lambda_B sim sqrt{Lt}T^{-1/4}$, when $n > 1$. These scalings agree with those derived from a covariant form of the Foppl-von Karman equations, however, we find that the $n=1$ mode also occurs over a surprisingly large range of $L$ in the bendable regime. Finally, in the clamp-dominated regime ($L < L_c$), we find that $eta_{tr}$ is higher compared to $eta_B$ due to additional stiffening induced by the clamped boundary conditions.
The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology. Here we provide a particularly surprising consequence of this confluence of geometry and physics in tubular structures: the anomalously large persistence of a localized pinch in an elastic pipe whose effect decays very slowly as an oscillatory exponential with a persistence length that diverges as the thickness of the tube vanishes, which we confirm experimentally. The result is more a consequence of geometry than material properties, and is thus equally applicable to carbon nanotubes as it is to oil pipelines.
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