Extended self-similarity in two-dimensional complex plasmas

Self-similarity is a property of an object or process wherein a part is similar to the whole. Mathematically, it can often be expressed as a power-law scaling of the quantity of interest. Extended self-similarity is a concept widely used in the field of turbulence and refers to the power-law scaling of the longitudinal structure functions of the velocity field expressed through the structure functions of different orders, rather than distance. Originally discovered by [R. Benzi et al., Phys. Rev. E 48, R29 (1993)] in fully developed turbulence, it was later found to hold in other situations and systems as well. In this paper, we show that in an active-matter system, extended self-similarity is possible even without the presence of respective power-law scaling in the underlying structure functions of distance. The active-matter system used in this study was a single-layer suspension of active Janus particles in a plasma. Janus particles are polymer microspheres with hemispherical metal coating. When dispersed in a plasma, they acquire self-propulsion and act as microswimmers. Extended self-similarity was also observed in the velocity field of a single-layer suspension of laser-heated regular (passive) particles, where the underlying structure functions displayed a hint of the power-law scaling near the mean interparticle distance. Therefore, it appears to be an inherent characteristic of complex plasmas.