Noise adds a twist to the story of a mysterious motion

The mysterious winding motion of a nanowire, trapped in an optical trap’s focused laser beams, prompted a deeper dive into the mathematical treatment for this kind of system by authors of a recent article in Chaos. Their simplified, computationally affordable model explains the winding behavior as created by the system’s inherent noise — once thought a mechanism for washing out an existing signal or motion, or in exceptional cases amplifying it.

“It had been proposed that the winding motion might be arising from the non-conservative nature of the trapping force,” said co-author Bruce Henry. “We developed a simple mathematical model that included this type of thinking and put it into a more general context. This opens the possibility of looking for the effect elsewhere.”

To mimic the trapped nanowire system, the team modeled a particle in a nonconservative force field with overdamped motion, symmetric in two dimensions. Their mathematical analysis depicted how noise can create a winding motion over longtime scales when you would otherwise expect a stationary particle. “Our mathematical result predicts the average frequency of the winding motion as a function of the strength of the attractive forces and the viscous damping,” Henry said.

The phase angle that accumulates in the form of this dynamic twist grows linearly, on average, over sufficiently long times, which indicates that a “periodicity” of the motion may exist that wasn’t detectable in the power spectrum analysis. The linearity, according to Henry, “is probably a consequence of having an average constant rate of energy balanced between the non-conservative force and the damping.”

As the group looks to apply their analytic treatment to more dynamical systems, such as those with hysteresis, they hope this work inspires experimentalists to look for signatures of winding behavior that can’t be detected by the often-used power spectrum analysis.

Source: “Noise induced aperiodic rotations of particles trapped by a non-conservative force,” by Ignacio Ortega-Piwonka, Christopher N. Angstmann, Bruce I. Henry, and Peter J Reece, Chaos: An Interdisciplinary Journal of Nonlinear Science (2018). The article can be accessed at https://doi.org/10.1063/1.5018443 .