Multiple timescales in a strongly coupled dusty plasma revealed by survival-function analysis

Under liquidlike conditions, particles are found to rearrange on multiple timescales in a two-dimensional dusty plasma experiment. Our analysis is based on survival functions, which are time-series graphs of the probability that a particle's number of nearest neighbors remains unchanged. Nondefects are found to exhibit two distinct timescales, revealed by an elbow in their survival function. Defects have survival functions that are more nearly exponential, with decay rates that offer insight at a microscopic level into the viscoelastic relaxation in a liquid.

Figure 1

Illustrative example of our analysis method. (a) Images of consecutive video frames, which allow measurements of particle positions. (b) Delaunay triangulation is applied to identify nearest neighbors, which are joined by the drawn line segments. The number of line segments originating at the location of a particle is its coordination. (c) Particle coordination maps are obtained by recording the coordination value of each particle at its position. Next, we track particles and their coordinations from frame to frame and identify the event when its coordination first changes. Until this event, that coordination is considered to be a survivor, as identified by the outlining boxes. In each frame, we count the number of fivefold coordinations (likewise for six- and sevenfold coordination) that have survived since the initial frame. The resulting table of data (d) is plotted in (e) as a time series, which are the survival functions. The images here were cropped for brevity; their area is $1\%$ of the camera's full field of view.

Figure 2

Particle-coordination survival functions, obtained with our structural analysis. For nondefects, the curves in (a) have two exponential timescales, revealing a complexity in the microscopic rearrangements. For defects, on the other hand, the survival-function curves in (b) are more nearly exponential. The defect survival function diminishes about three times faster than the survival function for nondefects. Plotting survival functions separately for the common fivefold and sevenfold defects in (c) reveals that they survive differently. Representative error bars due to counting statistics are shown for survivor function data points. Separately, the decay times had uncertainties of $<1\%$ from the exponential fits.