On the motion of substance in a channel and growth of random networks

Nikolay K. Vitanov, Roumen Borisov and Kaloyan N. Vitanov

Physica A: Statistical Mechanics and its Applications, 2021, vol. 581, issue C

Abstract: We discuss the connection between the theory of motion of substance in a channel and the theory of growth of large random networks. The channel contains nodes connected by edges. The substance is located in the nodes of the channel. It can move between the nodes of the channel through the edges which connect the nodes. We study probability distributions connected to distribution of substance for selected cases of stationary motion of substance in a channel. The corresponding model equations contain as specific cases the model equations for the degree distributions of several classes of growing random networks. We consider two scenarios for stationary motion of substance in the channel. Scenario 1 is connected to stationary motion of substance in direction to nodes labeled by larger numbers. Scenario 2 is connected to stationary motion of substance in the opposite direction. Probability distributions are obtained for different cases connected to the two scenarios. The results for the Scenario 1 are connected to the theory of degree distributions of nodes of a random network growing in presence of preferential attachment (as specific case we obtain also the degree distribution for the Barabasi–Albert case). Corresponding results for Scenario 2 can be connected to the theory of growing random networks too. The kind of attachment for these results can be classified as negative preferential attachment or preferential attachment with preference of attachment to nodes of smaller degree.

Keywords: Motion of substance in a channel; Probability distributions for stationary motion of substance in a channel; Random networks; Network growth; Preferential attachment; Barabasi–Albert growth; Negative preferential attachment; Preferential attachment to nodes of smaller degree (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437121004805
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:581:y:2021:i:c:s0378437121004805

DOI: 10.1016/j.physa.2021.126207

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().