{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:55:48Z","timestamp":1760784948375,"version":"build-2065373602"},"reference-count":85,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T00:00:00Z","timestamp":1617148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The solar photosphere and the outer layer of the Sun\u2019s interior are characterized by convective motions, which display a chaotic and turbulent character. In this work, we evaluated the pseudo-Lyapunov exponents of the overshooting convective motions observed on the Sun\u2019s surface by using a method employed in the literature to estimate those exponents, as well as another technique deduced from their definition. We analyzed observations taken with state-of-the-art instruments at ground- and space-based telescopes, and we particularly benefited from the spectro-polarimetric data acquired with the Interferometric Bidimensional Spectrometer, the Crisp Imaging SpectroPolarimeter, and the Helioseismic and Magnetic Imager. Following previous studies in the literature, we computed maps of four quantities which were representative of the physical properties of solar plasma in each observation, and estimated the pseudo-Lyapunov exponents from the residuals between the values of the quantities computed at any point in the map and the mean of values over the whole map. In contrast to previous results reported in the literature, we found that the computed exponents hold negative values, which are typical of a dissipative regime, for all the quantities derived from our observations. The values of the estimated exponents increase with the spatial resolution of the data and are almost unaffected by small concentrations of magnetic field. Finally, we showed that similar results were also achieved by estimating the exponents from residuals between the values at each point in maps derived from observations taken at different times. The latter estimation technique better accounts for the definition of these exponents than the method employed in previous studies.<\/jats:p>","DOI":"10.3390\/e23040413","type":"journal-article","created":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T05:57:18Z","timestamp":1617170238000},"page":"413","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Analysis of Pseudo-Lyapunov Exponents of Solar Convection Using State-of-the-Art Observations"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0791-0352","authenticated-orcid":false,"given":"Giorgio","family":"Viavattene","sequence":"first","affiliation":[{"name":"INAF\u2014Osservatorio Astronomico di Roma, Via Frascati 33, I-00078 Monte Porzio Catone, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0144-2252","authenticated-orcid":false,"given":"Mariarita","family":"Murabito","sequence":"additional","affiliation":[{"name":"INAF\u2014Osservatorio Astronomico di Roma, Via Frascati 33, I-00078 Monte Porzio Catone, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1837-2262","authenticated-orcid":false,"given":"Salvatore L.","family":"Guglielmino","sequence":"additional","affiliation":[{"name":"INAF\u2014Osservatorio Astrofisico di Catania, Via S. Sofia 78, I-95123 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2596-9523","authenticated-orcid":false,"given":"Ilaria","family":"Ermolli","sequence":"additional","affiliation":[{"name":"INAF\u2014Osservatorio Astronomico di Roma, Via Frascati 33, I-00078 Monte Porzio Catone, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3403-647X","authenticated-orcid":false,"given":"Giuseppe","family":"Consolini","sequence":"additional","affiliation":[{"name":"INAF\u2014Istituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100, I-00133 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabrizio","family":"Giorgi","sequence":"additional","affiliation":[{"name":"INAF\u2014Osservatorio Astronomico di Roma, Via Frascati 33, I-00078 Monte Porzio Catone, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7711-5397","authenticated-orcid":false,"given":"Shahin","family":"Jafarzadeh","sequence":"additional","affiliation":[{"name":"Rosseland Centre for Solar Physics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway"},{"name":"Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1038\/35009036","article-title":"Turbulent convection at very high Rayleigh numbers","volume":"404","author":"Niemela","year":"2000","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2","DOI":"10.12942\/lrsp-2009-2","article-title":"Solar Surface Convection","volume":"6","author":"Nordlund","year":"2009","journal-title":"Living Rev. Sol. Phys."},{"key":"ref_3","first-page":"265","article-title":"Observations Tending to Investigate the Nature of the Sun, in Order to Find the Causes or Symptoms of Its Variable Emission of Light and Heat; With Remarks on the Use That May Possibly Be Drawn from Solar Observations","volume":"91","author":"Herschel","year":"1801","journal-title":"Philos. Trans. R. Soc. Lond. Ser. I"},{"key":"ref_4","unstructured":"Rimmele, T.R. (2019, January 9\u201313). Status of the Daniel K. Inouye Solar Telescope. Proceedings of the American Astronomical Society Meeting Abstracts #234, St. Louis, MO, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1088\/2058-7058\/33\/3\/13","article-title":"Convection cells the size of Texas dazzle with clarity on the Sun","volume":"33","author":"Johnston","year":"2020","journal-title":"Phys. World"},{"key":"ref_6","first-page":"146","article-title":"Multi-frame blind deconvolution with linear equality constraints","volume":"Volume 4792","author":"Bones","year":"2002","journal-title":"Image Reconstruction from Incomplete Data II"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1086\/303951","article-title":"Time Series of Solar Granulation Images. I. Differences between Small and Large Granules in Quiet Regions","volume":"480","author":"Hirzberger","year":"1997","journal-title":"Astrophys. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1086\/307018","article-title":"Time Series of Solar Granulation Images. II. Evolution of Individual Granules","volume":"515","author":"Hirzberger","year":"1999","journal-title":"Astrophys. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"A126","DOI":"10.1051\/0004-6361\/201528011","article-title":"Dynamics of small-scale convective motions","volume":"598","author":"Lemmerer","year":"2017","journal-title":"Astron. Astrophys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1038\/356322a0","article-title":"Evolution and advection of solar mesogranulation","volume":"356","author":"Muller","year":"1992","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"40","DOI":"10.3847\/1538-4357\/836\/1\/40","article-title":"Height-dependent Velocity Structure of Photospheric Convection in Granules and Intergranular Lanes with Hinode\/SOT","volume":"836","author":"Oba","year":"2017","journal-title":"Astrophys. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7","DOI":"10.3847\/1538-4357\/aa8e44","article-title":"The Small-scale Structure of Photospheric Convection Retrieved by a Deconvolution Technique Applied to Hinode\/SP Data","volume":"849","author":"Oba","year":"2017","journal-title":"Astrophys. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"L159","DOI":"10.1088\/2041-8205\/723\/2\/L159","article-title":"Where the Granular Flows Bend","volume":"723","author":"Khomenko","year":"2010","journal-title":"Astrophys. J. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"138","DOI":"10.3847\/1538-4357\/ab6bce","article-title":"Study of the Dynamics of Convective Turbulence in the Solar Granulation by Spectral Line Broadening and Asymmetry","volume":"890","author":"Ishikawa","year":"2020","journal-title":"Astrophys. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"L123","DOI":"10.1086\/183539","article-title":"The detection of mesogranulation on the sun","volume":"245","author":"November","year":"1981","journal-title":"Astrophys. J. Lett."},{"key":"ref_16","first-page":"219","article-title":"Variation of granulation properties on a mesogranular scale","volume":"241","author":"Brandt","year":"1991","journal-title":"Astron. Astrophys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"L65","DOI":"10.1051\/0004-6361:20034617","article-title":"Evidence of mesogranulation from magnetograms of the Sun","volume":"412","year":"2003","journal-title":"Astron. Astrophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1051\/0004-6361:20053152","article-title":"Dynamics of solar mesogranulation","volume":"444","author":"Leitzinger","year":"2005","journal-title":"Astron. Astrophys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1086\/381221","article-title":"The Scales of Granulation, Mesogranulation, and Supergranulation","volume":"597","author":"Rast","year":"2003","journal-title":"Astrophys. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1023\/B:SOLA.0000033368.00217.de","article-title":"Structure Properties of Supergranulation and Granulation","volume":"221","author":"Berrilli","year":"2004","journal-title":"Sol. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1023\/B:SOLA.0000033368.00217.de","article-title":"Dynamics and Structure of Supergranulation","volume":"221","author":"Berrilli","year":"2004","journal-title":"Sol. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/s41116-018-0013-5","article-title":"The Sun\u2019s supergranulation","volume":"15","author":"Rincon","year":"2018","journal-title":"Living Rev. Sol. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1038\/29245","article-title":"Long-lived giant cells detected at the surface of the Sun","volume":"394","author":"Beck","year":"1998","journal-title":"Nature"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1126\/science.1244682","article-title":"Giant Convection Cells Found on the Sun","volume":"342","author":"Hathaway","year":"2013","journal-title":"Science"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"L32","DOI":"10.1088\/2041-8205\/784\/2\/L32","article-title":"Identifying Potential Markers of the Sun\u2019s Giant Convective Scale","volume":"784","author":"McIntosh","year":"2014","journal-title":"Astrophys. J. Lett."},{"key":"ref_26","first-page":"1063","article-title":"On mesogranulation, network formation and supergranulation","volume":"357","author":"Rieutord","year":"2000","journal-title":"Astron. Astrophys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/s41116-020-00025-6","article-title":"Dynamo models of the solar cycle","volume":"17","author":"Charbonneau","year":"2020","journal-title":"Living Rev. Sol. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4","DOI":"10.12942\/lrsp-2012-4","article-title":"Solar Surface Magneto-Convection","volume":"9","author":"Stein","year":"2012","journal-title":"Living Rev. Sol. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41116-018-0017-1","article-title":"Quiet Sun magnetic fields: An observational view","volume":"16","year":"2019","journal-title":"Living Rev. Sol. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"L137","DOI":"10.1086\/521726","article-title":"Emergence of Small-Scale Magnetic Loops in the Quiet-Sun Internetwork","volume":"666","author":"Centeno","year":"2007","journal-title":"Astrophys. J. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"L33","DOI":"10.1051\/0004-6361:20079032","article-title":"Magnetic field emergence in quiet Sun granules","volume":"481","author":"Tsuneta","year":"2008","journal-title":"Astron. Astrophys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"L36","DOI":"10.1088\/2041-8205\/747\/2\/L36","article-title":"On the Polarimetric Signature of Emerging Magnetic Loops in the Quiet Sun","volume":"747","year":"2012","journal-title":"Astrophys. J. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"L36","DOI":"10.1088\/2041-8205\/770\/2\/L36","article-title":"Diffusion of Solar Magnetic Elements up to Supergranular Spatial and Temporal Scales","volume":"770","author":"Giannattasio","year":"2013","journal-title":"Astrophys. J. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1088\/0004-637X\/788\/2\/137","article-title":"Diffusion of Magnetic Elements in a Supergranular Cell","volume":"788","author":"Giannattasio","year":"2014","journal-title":"Astrophys. J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"8","DOI":"10.3847\/1538-4365\/229\/1\/8","article-title":"Kinematics of Magnetic Bright Features in the Solar Photosphere","volume":"229","author":"Jafarzadeh","year":"2017","journal-title":"Astrophys. J. Suppl. Ser."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1086\/177028","article-title":"Small-Scale Horizontal Magnetic Fields in the Solar Photosphere","volume":"460","author":"Lites","year":"1996","journal-title":"Astrophys. J."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1086\/522922","article-title":"The Horizontal Magnetic Flux of the Quiet-Sun Internetwork as Observed with the Hinode Spectro-Polarimeter","volume":"672","author":"Lites","year":"2008","journal-title":"Astrophys. J."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"L149","DOI":"10.1088\/2041-8205\/723\/2\/L149","article-title":"Transverse Component of the Magnetic Field in the Solar Photosphere Observed by SUNRISE","volume":"723","author":"Danilovic","year":"2010","journal-title":"Astrophys. J. Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s11207-018-1341-2","article-title":"Linear Polarization Features in the Quiet-Sun Photosphere: Structure and Dynamics","volume":"293","author":"Kianfar","year":"2018","journal-title":"Sol. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1088\/0004-637X\/700\/2\/1391","article-title":"Emergence of Small-scale Magnetic Loops Through the Quiet Solar Atmosphere","volume":"700","year":"2009","journal-title":"Astrophys. J."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1088\/0004-637X\/745\/2\/160","article-title":"The Frontier between Small-scale Bipoles and Ephemeral Regions in the Solar Photosphere: Emergence and Decay of an Intermediate-scale Bipole Observed with SUNRISE\/IMaX","volume":"745","author":"Guglielmino","year":"2012","journal-title":"Astrophys. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"L12","DOI":"10.1051\/0004-6361\/201834628","article-title":"Observations of solar small-scale magnetic flux-sheet emergence","volume":"622","author":"Fischer","year":"2019","journal-title":"Astron. Astrophys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"62","DOI":"10.3847\/1538-4357\/ab917b","article-title":"On the Magnetic Nature of an Exploding Granule as Revealed by Sunrise\/IMaX","volume":"896","author":"Guglielmino","year":"2020","journal-title":"Astrophys. J."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"A87","DOI":"10.1051\/0004-6361\/201629881","article-title":"Comparison of different populations of granular features in the solar photosphere","volume":"605","author":"Falco","year":"2017","journal-title":"Astron. Astrophys."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1051\/0004-6361:20010494","article-title":"Dynamics of the solar granulation. VII. A nonlinear approach","volume":"373","author":"Nesis","year":"2001","journal-title":"Astron. Astrophys."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Viavattene, G., Consolini, G., Giovannelli, L., Berrilli, F., Del Moro, D., Giannattasio, F., Penza, V., and Calchetti, D. (2020). Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection. Entropy, 22.","DOI":"10.3390\/e22070716"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"A154","DOI":"10.1051\/0004-6361\/201116520","article-title":"The stellar atmosphere simulation code Bifrost. Code description and validation","volume":"531","author":"Gudiksen","year":"2011","journal-title":"Astron. Astrophys."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"A121","DOI":"10.1051\/0004-6361\/201118252","article-title":"Simulations of the solar near-surface layers with the CO5BOLD, MURaM, and Stagger codes","volume":"539","author":"Beeck","year":"2012","journal-title":"Astron. Astrophys."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1016\/j.jcp.2011.09.026","article-title":"Simulations of stellar convection with CO5BOLD","volume":"231","author":"Freytag","year":"2012","journal-title":"J. Comput. Phys."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1086\/169376","article-title":"Wave Generation by Turbulent Convection","volume":"363","author":"Goldreich","year":"1990","journal-title":"Astrophys. J."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1146\/annurev-astro-081817-052044","article-title":"New View of the Solar Chromosphere","volume":"57","author":"Carlsson","year":"2019","journal-title":"Annu. Rev. Astron. Astrophys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s11207-012-9954-3","article-title":"Acoustic Events in the Solar Atmosphere from Hinode\/SOT NFI Observations","volume":"278","author":"Malherbe","year":"2012","journal-title":"Sol. Phys."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s11207-014-0630-7","article-title":"Families of Granules, Flows, and Acoustic Events in the Solar Atmosphere from Hinode Observations","volume":"290","author":"Malherbe","year":"2015","journal-title":"Sol. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"5512","DOI":"10.1093\/mnras\/sty1861","article-title":"Vertical propagation of acoustic waves in the solar internetworkas observed by IRIS","volume":"479","author":"Kayshap","year":"2018","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1088\/0004-637X\/784\/1\/29","article-title":"The Generation and Damping of Propagating MHD Kink Waves in the Solar Atmosphere","volume":"784","author":"Morton","year":"2014","journal-title":"Astrophys. J."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"A102","DOI":"10.1051\/0004-6361\/201424221","article-title":"Observational evidence for buffeting-induced kink waves in solar magnetic elements","volume":"569","author":"Stangalini","year":"2014","journal-title":"Astron. Astrophys."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"19","DOI":"10.3847\/1538-4357\/aa6c5e","article-title":"Polarized Kink Waves in Magnetic Elements: Evidence for Chromospheric Helical Waves","volume":"840","author":"Stangalini","year":"2017","journal-title":"Astrophys. J."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"R3427","DOI":"10.1103\/PhysRevA.44.R3427","article-title":"Lyapunov exponents for hydromagnetic convection","volume":"44","author":"Kurths","year":"1991","journal-title":"Phys. Rev. A"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1965","DOI":"10.1016\/0960-0779(94)00189-W","article-title":"Lyapunov exponents for solar surface convection","volume":"5","author":"Steffen","year":"1995","journal-title":"Chaos Solitons Fractals"},{"key":"ref_60","first-page":"263","article-title":"Non linear dynamics of the solar granulation: A first approach","volume":"286","author":"Hanslmeier","year":"1994","journal-title":"Astron. Astrophys."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"3457","DOI":"10.1007\/s11207-014-0543-5","article-title":"Interpreting the Helioseismic and Magnetic Imager (HMI) Multi-Height Velocity Measurements","volume":"289","author":"Nagashima","year":"2014","journal-title":"Sol. Phys."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1088\/0004-637X\/810\/1\/54","article-title":"Magnetic Upflow Events in the Quiet-Sun Photosphere. I. Observations","volume":"810","author":"Jafarzadeh","year":"2015","journal-title":"Astrophys. J."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1007\/s11207-006-0103-8","article-title":"IBIS: A New Post-Focus Instrument for Solar Imaging Spectroscopy","volume":"236","author":"Cavallini","year":"2006","journal-title":"Sol. Phys."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"A102","DOI":"10.1051\/0004-6361\/201526144","article-title":"Plasma flows and magnetic field interplay during the formation of a pore","volume":"600","author":"Ermolli","year":"2017","journal-title":"Astron. Astrophys."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"126","DOI":"10.3847\/1538-4357\/aaf727","article-title":"Height Dependence of the Penumbral Fine-scale Structure in the Inner Solar Atmosphere","volume":"873","author":"Murabito","year":"2019","journal-title":"Astrophys. J."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s11207-005-5782-z","article-title":"Solar Image Restoration By Use Of Multi-frame Blind De-convolution With Multiple Objects And Phase Diversity","volume":"228","year":"2005","journal-title":"Sol. Phys."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1051\/0004-6361\/202038360","article-title":"Unveiling the magnetic nature of chromospheric vortices","volume":"639","author":"Murabito","year":"2020","journal-title":"Astron. Astrophys."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1051\/0004-6361:20052981","article-title":"Comments on the optimization of high resolution Fabry-P\u00e9rot filtergraphs","volume":"447","author":"Scharmer","year":"2006","journal-title":"Astron. Astrophys."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"A40","DOI":"10.1051\/0004-6361\/201424319","article-title":"CRISPRED: A data pipeline for the CRISP imaging spectropolarimeter","volume":"573","author":"Hillberg","year":"2015","journal-title":"Astron. Astrophys."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"L5","DOI":"10.1051\/0004-6361\/201936617","article-title":"Characterization and formation of on-disk spicules in the Ca II K and Mg II k spectral lines","volume":"631","author":"Bose","year":"2019","journal-title":"Astron. Astrophys."},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Bose, S., Joshi, J., Henriques, V.M.J., and Rouppe van der Voort, L. (2021). Spicules and downflows in the solar chromosphere. arXiv.","DOI":"10.1051\/0004-6361\/202040014"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s11207-011-9834-2","article-title":"The Helioseismic and Magnetic Imager (HMI) Investigation for the Solar Dynamics Observatory (SDO)","volume":"275","author":"Scherrer","year":"2012","journal-title":"Sol. Phys."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s11207-011-9841-3","article-title":"The Solar Dynamics Observatory (SDO)","volume":"275","author":"Pesnell","year":"2012","journal-title":"Sol. Phys."},{"key":"ref_74","first-page":"354","article-title":"High spatial resolution observations of some solar photospheric line profiles","volume":"238","author":"Hanslmeier","year":"1990","journal-title":"Astron. Astrophys."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"76","DOI":"10.3847\/1538-4357\/834\/1\/76","article-title":"On the Formation of a Stable Penumbra in a Region of Flux Emergence in the Sun","volume":"834","author":"Murabito","year":"2017","journal-title":"Astrophys. J."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1088\/0004-637X\/755\/2\/175","article-title":"Dead Calm Areas in the Very Quiet Sun","volume":"755","author":"Hijano","year":"2012","journal-title":"Astrophys. J."},{"key":"ref_77","unstructured":"Baker, G.L., and Gollub, J.P. (1992). Chaotic Dynamics, Cambridge University Press."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s11207-012-9942-7","article-title":"A Comparative Analysis of Photospheric Bright Points in an Active Region and in the Quiet Sun","volume":"280","author":"Romano","year":"2012","journal-title":"Sol. Phys."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1051\/0004-6361\/200912394","article-title":"Magnetic flux emergence into the solar photosphere and chromosphere","volume":"507","year":"2009","journal-title":"Astron. Astrophys."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1088\/0004-637X\/724\/2\/1083","article-title":"Multiwavelength Observations of Small-scale Reconnection Events Triggered by Magnetic Flux Emergence in the Solar Atmosphere","volume":"724","author":"Guglielmino","year":"2010","journal-title":"Astrophys. J."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"127","DOI":"10.3847\/1538-4357\/aab2a8","article-title":"IRIS Observations of Magnetic Interactions in the Solar Atmosphere between Preexisting and Emerging Magnetic Fields. I. Overall Evolution","volume":"856","author":"Guglielmino","year":"2018","journal-title":"Astrophys. J."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s11207-008-9174-z","article-title":"The Solar Optical Telescope for the Hinode Mission: An Overview","volume":"249","author":"Tsuneta","year":"2008","journal-title":"Sol. Phys."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1002\/asna.201011386","article-title":"European Solar Telescope: Progress status","volume":"331","author":"Collados","year":"2010","journal-title":"Astron. Nachrichten"},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"A11","DOI":"10.1051\/0004-6361\/201935325","article-title":"The Polarimetric and Helioseismic Imager on Solar Orbiter","volume":"642","author":"Solanki","year":"2020","journal-title":"Astron. Astrophys."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"A1","DOI":"10.1051\/0004-6361\/202038467","article-title":"The Solar Orbiter mission. Science overview","volume":"642","author":"Zouganelis","year":"2020","journal-title":"Astron. Astrophys."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/4\/413\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:10:44Z","timestamp":1760364644000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/4\/413"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,31]]},"references-count":85,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,4]]}},"alternative-id":["e23040413"],"URL":"https:\/\/doi.org\/10.3390\/e23040413","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,3,31]]}}}