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Complexity Phenomena and ROMA of the Magnetospheric Cusp, Hydrodynamic Turbulence, and the Cosmic Web

Dynamic Complexity is a phenomenon exhibited by a nonlinearly interacting system within which multitudes of different sizes of large scale coherent structures emerge, resulting in a globally nonlinear stochastic behavior vastly different from that could be surmised from the underlying equations of interaction. The hallmark of such nonlinear, complex phenomena is the appearance of intermittent fluctuating events with the mixing and distributions of correlated structures at all scales. We briefly review here a relatively recent method, ROMA (rank-ordered multifractal analysis), explicitly constructed to analyze the intricate details of the distribution and scaling of such types of intermittent structures. This method is then applied to the analyses of selected examples related to the dynamical plasmas of the cusp region of the magnetosphere, velocity fluctuations of classical hydrodynamic turbulence, and the distribution of the structures of the cosmic gas obtained through large scale, moving mesh simulations. Differences and similarities of the analyzed results among these complex systems will be contrasted and highlighted. The first two examples have direct relevance to the geospace environment and are summaries of previously reported findings. The third example on the cosmic gas, though involving phenomena much larger in spatiotemporal scales, with its highly compressible turbulent behavior and the unique simulation technique employed in generating the data, provides direct motivations of applying such analysis to studies of similar multifractal processes in various extreme environments. These new results are both exciting and intriguing.