Polymer Flying Carpet: Growth and Bending Set It in Motion ✛ ✦

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In a world where Reynolds numbers are minuscule, water turns into thick syrup, and the swimming tricks we know stop working. Here reigns the insidious scallop theorem: reciprocal motions produce no net displacement. Microorganisms found a way out: they grow polymer tails. But what if you cover an entire particle's surface with such growing filaments — like a molecular 'flying carpet'? That's exactly the scenario researchers explored, building a new theory of polymerization-driven motility.

To capture this effect, physicists derived a stability criterion: the dimensionless activity σ̄ must exceed the sum of elastic resistance χ and the catastrophe rate divided by filament density: σ̄ > χ + (λ̄+1)/ρ̄. When this threshold is crossed, the uniform carpet loses stability: on a microscopic sphere, two mighty vortices spontaneously form, resembling a swirling accretion disk around an active galactic nucleus. These vortices set the sphere spinning — as if the flying carpet began to twirl in a dance.

But the real magic unfolds when we control the growth pattern. Distribute polymerization centers along the equator — the sphere will only spin in place, like a top. Gather them into a polar patch — and it starts tracing circles. Symmetrically placed four points yield straight swimming: the vortices cancel the torque, and the carpet glides straight. Finally, a chiral pattern, akin to a spiral staircase, makes the sphere corkscrew through the fluid, simultaneously rotating and advancing.

These findings are not just elegant hydrodynamics. They provide a key to building swarms of autonomous microrobots whose behavior is 'hardwired' into their shell's nanostructure. Moreover, analyzing swimming trajectories could become a novel type of biosignature in the search for life on exoplanets: if we spot distinctive spiral tracks, perhaps they are the imprint of invisible polymerization swimmers. It's fascinating that similar mathematics governs cell movement in our own bodies: keratocytes that heal wounds, and even motile cancer cells, grow actin tails using the same polymerization mechanisms. This idea traces back to the profound connection between symmetries and conservation laws, discovered by Emmy Noether. In nonequilibrium systems, entropy production dictates the direction of processes, and our active carpet, continuously dissipating growth energy, is a vivid example of this. Remarkably, the described phenomena — from the reconnection of topological defects to collective flows — have parallels across vastly different scales, from turbulent streams to magnetic reconnection in astrophysical objects. This hints at the universality of active matter physics, and numerical simulations of such systems open the door to predictive design. The principle of superposition in the Stokes regime guarantees that each filament contributes its part to the overall dance, yet it is the collective bending that breaks symmetry and grants the carpet its freedom of motion.