{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:50:19Z","timestamp":1760237419469,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T00:00:00Z","timestamp":1589500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Government of Republic of Bulgaria","award":["BG05 M2OP001 - 1.001 - 0008"],"award-info":[{"award-number":["BG05 M2OP001 - 1.001 - 0008"]}]},{"name":"Ministry of Education and Science of Republic of Bulgaria","award":["D01205\/23.11.2018"],"award-info":[{"award-number":["D01205\/23.11.2018"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study flow of substance in a channel of network which consists of nodes of network and edges which connect these nodes and form ways for motion of substance. The channel can have arbitrary number of arms and each arm can contain arbitrary number of nodes. The flow of substance is modeled by a system of ordinary differential equations. We discuss first a model for a channel which arms contain infinite number of nodes each. For stationary regime of motion of substance in such a channel we obtain probability distributions connected to distribution of substance in any of channel\u2019s arms and in entire channel. Obtained distributions are not discussed by other authors and can be connected to Waring distribution. Next, we discuss a model for flow of substance in a channel which arms contain finite number of nodes each. We obtain probability distributions connected to distribution of substance in the nodes of the channel for stationary regime of flow of substance. These distributions are also new and we calculate corresponding information measure and Shannon information measure for studied kind of flow of substance.<\/jats:p>","DOI":"10.3390\/e22050553","type":"journal-article","created":{"date-parts":[[2020,5,15]],"date-time":"2020-05-15T10:53:59Z","timestamp":1589540039000},"page":"553","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Statistical Characteristics of Stationary Flow of Substance in a Network Channel Containing Arbitrary Number of Arms"],"prefix":"10.3390","volume":"22","author":[{"given":"Roumen","family":"Borisov","sequence":"first","affiliation":[{"name":"Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria"}]},{"given":"Zlatinka I.","family":"Dimitrova","sequence":"additional","affiliation":[{"name":"Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria"}]},{"given":"Nikolay K.","family":"Vitanov","sequence":"additional","affiliation":[{"name":"Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria"},{"name":"Max-Planck Institute for the Physics of Complex Systems, Noethnitzerstr. 38, 01187 Dresden, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2020,5,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Marsan, G.A., Bellomo, N., and Tosin, A. (2013). 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