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Open AccessArticle

# Statistical Characteristics of Stationary Flow of Substance in a Network Channel Containing Arbitrary Number of Arms

by 1,3,*
1
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
2
Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria
3
Max-Planck Institute for the Physics of Complex Systems, Noethnitzerstr. 38, 01187 Dresden, Germany
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(5), 553; https://doi.org/10.3390/e22050553
Received: 19 April 2020 / Revised: 11 May 2020 / Accepted: 12 May 2020 / Published: 15 May 2020
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’s 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. View Full-Text
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Borisov, R.; Dimitrova, Z.I.; Vitanov, N.K. Statistical Characteristics of Stationary Flow of Substance in a Network Channel Containing Arbitrary Number of Arms. Entropy 2020, 22, 553.