Eur. Phys. J. Plus (2021) 136: 523
https://doi.org/10.1140/epjp/s13360-021-01531-8

Regular Article

Density fluctuation analysis very near above and below critical point using morphological and spatiotemporal information

¹ Department of Physics and Astronomy, College of Charleston, 66 George Street, 29424, Charleston, SC, USA
² CNRS, Université de Bordeaux, Bordeaux INP, ICMCB, UMR 5026, F-33600, Pessac, France
³ Physique et Mécanique des Milieux Hétérogènes, CNRS, ESPCI, PSL Research University, Sorbonne Université, Sorbonne Paris Cité, Paris, France

^a oprisana@cofc.edu

Received: 8 March 2021
Accepted: 4 May 2021
Published online: 12 May 2021

Abstract

We investigate the fractal nature of critical fluctuations in sulfur hexafluoride (SF${}_6$) under microgravity conditions. For this purpose, we use the Bidimensional Empiric Mode Decomposition (BEMD) approach to separate the spatial scales of fluctuations in orthogonal Independent Mode Functions (IMFs). Statistical analysis of three morphology measures (area, eccentricity, and orientation of convex objects in recorded images) across different IMFs shows that critical fluctuations obey power-laws across multiple spatial scales. We also perform a spatiotemporal analysis of fluctuations by extracting one line of pixels from each image and creating a temporal stack from successive images, or “waterfalls.” The spatiotemporal section analysis along the spatial direction reveals multiple spatial scales present in the original fluctuating image. The analysis of the “waterfalls” along the temporal direction identifies a common power-law temporal behavior across all spatial scales. Our results show that critical fluctuations very near critical temperature ($T_c$) have a fractal structure captured by power-laws with multiple critical exponents. The morphology analysis shows that very near $T_c$, the fluctuating domains are mostly spherical with some anisotropy.