{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:59:06Z","timestamp":1760241546260,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2018,4,29]],"date-time":"2018-04-29T00:00:00Z","timestamp":1524960000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>The aim of this work is to construct an algorithm for visualizing a polydisperse phase of solid particles (dust) in an inhomogeneous flow of a two-phase gas-dust mixture that would allow us to see, within one plot, the degree of polydispersity of the dust phase and the difference in the spatial distributions of individual fractions of dust particles in the computational domain. The developed technique allows us to reproduce concentrations from one to three fractions of dust particles in each cell in the computational domain. Each of the three fractions of dust particles is mapped to one of the main channels of the RGB palette. The intensity of the color shade is set to be proportional to the relative concentration of dust particles in this fraction. The final image for a polydisperse mixture is obtained by adding images in each of the three color channels. To visualize the degree of polydispersity, we propose depicting the spatial distribution of the entropy of the dust mixture. The definition of the entropy of a mixture is generalized to take into account the states of a mixture with zero number of particles in the mixture. They correspond to dust-free sections of the computational domain (voids). The proposed method for visualizing the polydispersity of a mixture of particles is demonstrated using the example of dynamic numerical modeling of the spatial features of dust structures formed in turbulent gas-dust flows and in flows with shock waves.<\/jats:p>","DOI":"10.3390\/jimaging4050061","type":"journal-article","created":{"date-parts":[[2018,4,30]],"date-time":"2018-04-30T03:45:49Z","timestamp":1525059949000},"page":"61","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Tricolor Technique for Visualization of Spatial Variations of Polydisperse Dust in Gas-Dust Flows"],"prefix":"10.3390","volume":"4","author":[{"given":"Vitaly V.","family":"Korolev","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikhail A.","family":"Bezborodov","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1565-8940","authenticated-orcid":false,"given":"Ilya G.","family":"Kovalenko","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrey M.","family":"Zankovich","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikhail A.","family":"Eremin","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Information Technology, Volgograd State University, Universitetskij Prospekt, 100, 400062 Volgograd, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1086\/510117","article-title":"Image-processing techniques for the creation of presentation-quality astronomical images","volume":"133","author":"Rector","year":"2007","journal-title":"Astron. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/2945.773807","article-title":"Large datasets at a glance: Combining textures and colors in scientific visualization","volume":"5","author":"Healey","year":"1999","journal-title":"Trans. Vis. Comput. Graph."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1109\/TVCG.2007.70623","article-title":"Weaving versus Blending: A quantitative assessment of the information carrying capacities of two alternative methods for conveying multivariate data with color","volume":"13","author":"Kim","year":"2007","journal-title":"Trans. Vis. Comput. Graph."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1080\/01621459.1973.10482434","article-title":"The use of faces to represent points in k-dimensional space graphically","volume":"68","author":"Chernoff","year":"1973","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1109\/TVCG.2010.199","article-title":"Superquadric glyphs for symmetric second-order tensors","volume":"16","author":"Schultz","year":"2010","journal-title":"Trans. Vis. Comput. Graph."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4920","DOI":"10.1016\/j.polymer.2014.07.047","article-title":"Dispersity and spinnability: Why highly polydisperse polymers are desirable for electrospinning","volume":"55","author":"Palangetic","year":"2014","journal-title":"Polymer"},{"key":"ref_7","unstructured":"Grabbe, C. (2006). Dusty plasmas and applications in space and industry. Plasma Physics Applied, Transworld Research Network."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1063\/1.3047679","article-title":"Environmental consequences of nuclear war","volume":"61","author":"Toon","year":"2008","journal-title":"Phys. Today"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Draine, B.T. (2004). Astrophysics of Dust in Cold Clouds. The Cold Universe, Springer-Verlag.","DOI":"10.1002\/chin.200335262"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"102106","DOI":"10.1063\/1.4824452","article-title":"Electromagnetic waves in a polydisperse dusty plasma","volume":"20","author":"Shchekinov","year":"2013","journal-title":"Phys. Plasmas"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Fortov, V.E., and Morfill, G.E. (2010). Types of Experimental Complex Plasmas. Complex and Dusty Plasmas: From Laboratory to Space, CRC Press, Taylor & Fransis Group.","DOI":"10.1201\/9780367802882"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1086\/157165","article-title":"On the physics of dust grains in hot gas","volume":"231","author":"Draine","year":"1979","journal-title":"Astrophys. J."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Marchisio, D.L., and Fox, R.O. (2013). Computational Models for Polydisperse Particulate and Multiphase Systems, Cambridge University Press.","DOI":"10.1017\/CBO9781139016599"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1002\/ctpp.201500099","article-title":"Voids in dusty plasma of a stratified DC glow discharge in noble gases","volume":"56","author":"Fedoseev","year":"2016","journal-title":"Contrib. Plasma Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1111\/j.1365-2966.2004.07869.x","article-title":"Synthetic infrared images and spectral energy distributions of a young low-mass stellar cluster","volume":"351","author":"Kurosawa","year":"2004","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1111\/j.1365-2966.2004.07216.x","article-title":"Maximum-entropy image reconstruction using wavelets","volume":"347","author":"Maisinger","year":"2004","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2097","DOI":"10.1088\/0004-6256\/139\/6\/2097","article-title":"Detailed decomposition of galaxy images. II. Beyond axisymmetric models","volume":"139","author":"Peng","year":"2010","journal-title":"Astron. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1088\/0004-637X\/707\/1\/510","article-title":"Lifting the dusty veil with near- and mid-infrared photometry. II. A large-scale study of the galactic infrared extinction law","volume":"707","author":"Zasowski","year":"2009","journal-title":"Astron. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1086\/150177","article-title":"Large-scale shock formation in spiral galaxies and its implications on star formation","volume":"158","author":"Roberts","year":"1969","journal-title":"Astrophys. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1134\/S1063773713020047","article-title":"Spatial variations of the extinction law in the galactic disk from Infrared observations","volume":"39","author":"Gontcharov","year":"2013","journal-title":"Astron. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1134\/S1063773711120048","article-title":"Variations of the interstellar extinction law within the nearest kiloparsec","volume":"38","author":"Gontcharov","year":"2012","journal-title":"Astron. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1134\/S1063773713070025","article-title":"Some properties of dust outside the galactic disk","volume":"39","author":"Gontcharov","year":"2013","journal-title":"Astron. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1086\/155591","article-title":"The size distribution of interstellar grains","volume":"217","author":"Mathis","year":"1977","journal-title":"Astrophys. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"296","DOI":"10.1086\/318651","article-title":"Dust grain-size distributions and extinction in the milky way, large magellanic cloud, and small magellanic cloud","volume":"548","author":"Weingartner","year":"2001","journal-title":"Astrophys. J."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1093\/mnras\/stu1290","article-title":"Dense molecular cloud cores as a source of micrometer-sized grains in galaxies","volume":"443","author":"Hirashita","year":"2014","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1111\/j.1365-2966.2009.14405.x","article-title":"Shattering and coagulation of dust grains in interstellar turbulence","volume":"394","author":"Hirashita","year":"2009","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kr\u00fcgel, E. (2003). The Physics of Interstellar Dust, Institute of Physics Publishing.","DOI":"10.1887\/0750308613"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s12650-013-0157-2","article-title":"A rate-of-strain-based method of hydrodynamic flow analysis: Identification of discontinuities, Compression\u2013Rarefaction and Shear Waves","volume":"16","author":"Korolev","year":"2013","journal-title":"J. Vis."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1111\/j.1365-2966.2005.08762.x","article-title":"Intergalactic medium metal enrichment through dust sputtering","volume":"358","author":"Bianchi","year":"2005","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1134\/S1990341315040100","article-title":"Hydrodynamic model of a self-gravitating optically thick gas and dust cloud","volume":"70","author":"Zhukova","year":"2015","journal-title":"Astrophys. Bull."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Toro, E.F. (1999). Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer.","DOI":"10.1007\/978-3-662-03915-1"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"L45","DOI":"10.1086\/425978","article-title":"The universality of turbulence in galactic molecular clouds","volume":"615","author":"Heyer","year":"2004","journal-title":"Astrophys. J."},{"key":"ref_33","first-page":"715","article-title":"The small-scale density and velocity structure of quiescent molecular clouds","volume":"257","author":"Falgarone","year":"1992","journal-title":"Astron. Astrophys."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1086\/175954","article-title":"Turbulence in molecular clouds","volume":"448","author":"Dubinski","year":"1995","journal-title":"Astrophys. J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1086\/307784","article-title":"The energy dissipation rate of supersonic, magnetohydrodynamic turbulence in molecular clouds","volume":"524","year":"1999","journal-title":"Astrophys. J."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Federrath, C., Roman-Duval, J., Klessen, R.S., Schmidt, W., and Mac Low, M.-M. (2010). Comparing the statistics of interstellar turbulence in simulations and observations. Solenoidal versus compressive turbulence forcing. Astron. Astrophys., 512.","DOI":"10.1051\/0004-6361\/200912437"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1146\/annurev.astro.41.011802.094859","article-title":"Interstellar turbulence I: Observations and processes","volume":"42","author":"Elmegreen","year":"2004","journal-title":"Annu. Rev. Astron. Astrophys."},{"key":"ref_38","first-page":"406","article-title":"On a steady gas flow with a shock wave in a potential well","volume":"264","author":"Kovalenko","year":"1992","journal-title":"Astron. Astrophys."},{"key":"ref_39","unstructured":"Jones, A.P. (2004, January 27\u201329). Dust formation, propagation and survival in the ISM. Proceedings of the Dusty and Molecular Universe: A Prelude to Herschel and ALMA, Paris, France."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1093\/mnras\/259.2.345","article-title":"The existence and shapes of dust lanes in galactic bars","volume":"259","author":"Athanassoula","year":"1992","journal-title":"Mon. Not. R. Astron. Soc."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1038\/16861","article-title":"Magnetic field as a tracer of sheared gas flow in barred galaxies","volume":"397","author":"Beck","year":"1999","journal-title":"Nature"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1111\/j.1365-2966.2008.13327.x","article-title":"Tracing spiral density waves in M81","volume":"387","author":"Kendall","year":"2008","journal-title":"Mon. Not. R. Astron. Soc."}],"container-title":["Journal of Imaging"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-433X\/4\/5\/61\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:02:39Z","timestamp":1760194959000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-433X\/4\/5\/61"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,29]]},"references-count":42,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2018,5]]}},"alternative-id":["jimaging4050061"],"URL":"https:\/\/doi.org\/10.3390\/jimaging4050061","relation":{},"ISSN":["2313-433X"],"issn-type":[{"type":"electronic","value":"2313-433X"}],"subject":[],"published":{"date-parts":[[2018,4,29]]}}}