What’s true for jealous lovers and frustrated parents also applies to nanoscale cogs and wheels and environmental regulations: Cutting some slack sometimes gives better results than being too strict.
Giovanni Volpe, a physicist at the Institute for Photonic Sciences in Barcelona, and his colleagues took a fresh look at the mathematics of constraints — specifically, of “noisy” constraints. That’s when both the constrained object and the stuff that’s constraining it experience small, random fluctuations, or noise.
An example, Volpe explains, is the atomic force microscope, a tool that can sense and impart tiny forces on objects as small as single atoms, but has limited accuracy because of thermal vibrations. Other examples include molecular machines that transport stuff within living cells while attached to microscopic strings — again a situation where thermal shaking is relentless.
Volpe’s team calculated what happens when constraints become tighter. Initially, an object becomes more stable, as expected. But only to an extent. “Beyond a certain threshold…things start to get worse,” Volpe says.
Staying right at that threshold provides just the right amount of slack to get the best possible results. It’s similar to how a child will remain calm when allowed to move around but will get more fidgety when asked to stay still. And it’s a happy medium that evolution may have found eons of years ago for cellular machines, Volpe says. (But one that possessive lovers still struggle with.)
To corroborate their theory, the researchers tried applying their reverse psychology to microscopic beads suspended in water. A tool called an optical tweezer can keep a bead more or less in place using laser pulses. But the bead will keep jostling a bit, due to random collisions with the water molecules that surround it.
To some extent, the bead can be stabilized, says Volpe’s collaborator Sandro Perrone. “As you increase the power of the laser, the particle becomes more and more still.” But when the researchers kept cranking up the power of their optical tweezer, they obtained the opposite result. Past a certain threshold, a 200-nanometer bead became more restless, not less, the researchers describe in an upcoming Physical Review E.
The result could have applications in the design of nanoscale machines, Volpe says. For example, it shows that making an atomic force microscope stiffer won’t necessarily help.
Yaneer Bar-Yam of the New England Complex Systems Institute in Cambridge, Mass., says the newly discovered principle could find applications to ecosystems and to social and economic sciences — all of which involve random, unpredictable fluctuations — assuming that those phenomena obey the same mathematical rules.
A possible case in point, Bar-Yam says, is the chronic food shortages in the state-run economy of the old Soviet Union. “The effectiveness of food delivery is much better in a free market,” he says, though a complete lack of regulation can lead to chaos.