Investigation and improvement of three-dimensional plasma crystal analysis

In this work, existing methods for plasma crystal analysis are investigated using artificial and simulated calibration data, which reproduce a multiphase system consisting of fcc, hcp, and bcc crystal data. Disturbances of the artificial data including Gaussian noise, stretching, and randomly missing particles are used to investigate the methods thoroughly. A popular method, called bond order parameter, has been repeatedly criticized as a structure analysis tool and will be improved with the help of a recent development. The method is called the bcc-sensitive Minkowski structure metric. It enhances robustness and consistency, while remaining compatible with previous bond-order-based results. Also, a promising method rooted in the molecular dynamics community is tested, yielding detailed insight of bond-order-specific drawbacks. With this investigation, the state of three-dimensional plasma crystal analysis will be significantly improved.

Figure 1

Exemplary $(q_4,q_6)$ diagrams of both BOP using 12 nearest neighbors (top) and BCCMSM (bottom). Amounts of particles in a $(q_4,q_6)$ quadrant are shown using a gradient from black (high) to white (low). The analysis is done using artificial data with 5% of Gaussian noise (see Sec. 3). The drawn polygons represent regions used to distinguish the crystalline structures for every particle.

Figure 2

Relative structural trends with increasing Gaussian noise. The results are calculated for (a) BOP, (b) ACNA, and (c) BCCMSM. The false positives are calculated relative to the number of recognized particles.

Figure 3

Relative structural trends for increasingly stretched calibration data using (a) BOP, (b) ACNA, and (c) BCCMSM.

Figure 4

Relative structural trends for calibration data for an increasing amount of missing particles. The results for (a) BOP, (b) ACNA, and (c) BCCMSM are shown.

Figure 5

Relative structural trends for a Yukawa system, which is cooled down using a Langevin thermostat. The results for (a) BOP, (b) ACNA, and (c) BCCMSM are shown.