{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T04:40:00Z","timestamp":1784090400356,"version":"3.55.0"},"reference-count":44,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,30]],"date-time":"2024-10-30T00:00:00Z","timestamp":1730246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Commission through project STORM","award":["31038"],"award-info":[{"award-number":["31038"]}]},{"name":"European Commission through project STORM","award":["30N\/2023"],"award-info":[{"award-number":["30N\/2023"]}]},{"name":"European Commission through project STORM","award":["4000134960"],"award-info":[{"award-number":["4000134960"]}]},{"name":"Romanian Ministry of Research, Innovation, and Digitalization under the Romanian National Core Program LAPLAS VII","award":["31038"],"award-info":[{"award-number":["31038"]}]},{"name":"Romanian Ministry of Research, Innovation, and Digitalization under the Romanian National Core Program LAPLAS VII","award":["30N\/2023"],"award-info":[{"award-number":["30N\/2023"]}]},{"name":"Romanian Ministry of Research, Innovation, and Digitalization under the Romanian National Core Program LAPLAS VII","award":["4000134960"],"award-info":[{"award-number":["4000134960"]}]},{"name":"Belgian Office for Science (BELSPO)","award":["31038"],"award-info":[{"award-number":["31038"]}]},{"name":"Belgian Office for Science (BELSPO)","award":["30N\/2023"],"award-info":[{"award-number":["30N\/2023"]}]},{"name":"Belgian Office for Science (BELSPO)","award":["4000134960"],"award-info":[{"award-number":["4000134960"]}]},{"name":"European Space Agency PRODEX project MISION PEA","award":["31038"],"award-info":[{"award-number":["31038"]}]},{"name":"European Space Agency PRODEX project MISION PEA","award":["30N\/2023"],"award-info":[{"award-number":["30N\/2023"]}]},{"name":"European Space Agency PRODEX project MISION PEA","award":["4000134960"],"award-info":[{"award-number":["4000134960"]}]},{"name":"Romanian Ministry of Research, Innovation, and Digitalization","award":["31038"],"award-info":[{"award-number":["31038"]}]},{"name":"Romanian Ministry of Research, Innovation, and Digitalization","award":["30N\/2023"],"award-info":[{"award-number":["30N\/2023"]}]},{"name":"Romanian Ministry of Research, Innovation, and Digitalization","award":["4000134960"],"award-info":[{"award-number":["4000134960"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The Rank-Ordered Multifractal Analysis (ROMA) is a tool designed to characterize scale (in)variance and multifractality based on rank ordering the fluctuations in \u201cgroups\u201d characterized by the same mono-fractal behavior (Hurst exponent). A range-limited structure-function analysis provides the mono-fractal index for each rank-ordered range of fluctuations. We discuss here two examples of multi-scale solar wind turbulence and complexity where ROMA is applied on the following: (a) data collected by Ulysses spacecraft in the fast solar wind, outside the ecliptic, between 25 and 31 January 2007, at roughly 2.5 Astronomical Units (AU) from the Sun, in the Southern heliosphere, at latitudes between \u221276.5 and \u221277.3 degrees, and (b) slow solar wind data collected in the ecliptic plane by Venus Express spacecraft, at 0.72 AU, on 28 January 2007. The ROMA spectrum of fast solar wind derived from ULYSSES data shows a scale-dependent structure of fluctuations: (1) at the smallest\/kinetic range of scales (800 to 3200 km), persistent fluctuations are dominant, and (2) at the inertial range of scales (104 to 2 \u00d7 105 km), anti-persistent fluctuations are dominant, but less clearly developed and possibly indicative for the development of instabilities with cross-over behavior. The ROMA spectrum of the slow solar wind derived from Venus Express data, suggests a different structure of turbulence: (1) fully developed multifractal turbulence across scales between 5 \u00d7 104 and 4 \u00d7 105 km, with the Hurst index changing from anti-persistent to persistent values for the larger amplitude magnetic fluctuations; (2) at the smallest scales (400 to 6400 km), fluctuations are mainly anti-persistent, and the ROMA spectrum indicates a tendency towards mono-fractal behavior.<\/jats:p>","DOI":"10.3390\/e26110929","type":"journal-article","created":{"date-parts":[[2024,11,1]],"date-time":"2024-11-01T13:09:27Z","timestamp":1730466567000},"page":"929","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Solar Wind Turbulence and Complexity Probed with Rank-Ordered Multifractal Analysis (ROMA)"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7038-9494","authenticated-orcid":false,"given":"Marius","family":"Echim","sequence":"first","affiliation":[{"name":"Royal Belgian Institute for Space Aeronomy, Avenue Circulaire 3, 1180 Bruxelles, Belgium"},{"name":"Institute of Space Science INFLPR Subsidiary, Atomi\u0219tilor 409, 077125 M\u0103gurele, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3604-2352","authenticated-orcid":false,"given":"Costel","family":"Munteanu","sequence":"additional","affiliation":[{"name":"Institute of Space Science INFLPR Subsidiary, Atomi\u0219tilor 409, 077125 M\u0103gurele, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9474-7468","authenticated-orcid":false,"given":"Gabriel","family":"Voitcu","sequence":"additional","affiliation":[{"name":"Institute of Space Science INFLPR Subsidiary, Atomi\u0219tilor 409, 077125 M\u0103gurele, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5294-0075","authenticated-orcid":false,"given":"Eliza","family":"Teodorescu","sequence":"additional","affiliation":[{"name":"Institute of Space Science INFLPR Subsidiary, Atomi\u0219tilor 409, 077125 M\u0103gurele, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chang, T. 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