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On the motion of substance in a channel of a network and human migration

Nikolay K. Vitanov and Kaloyan N. Vitanov

Physica A: Statistical Mechanics and its Applications, 2018, vol. 490, issue C, 1277-1294

Abstract: We model the motion of a substance in a channel of a network that consists of chain of (i) nodes of the network and (ii) edges that connect the nodes and form the way for motion of the substance. The nodes of the channel can have different “leakage”, i.e., some amount of the substance can leave the channel at a node and the rate of leaving can be different for the different nodes of the channel. The nodes close to the end of the channel for some (design or other) reason may be more “attractive” for the substance in comparison to the nodes around the incoming node of the channel. We discuss channels containing infinite or finite number of nodes. The main outcome of the model is the distribution of the substance along the nodes. Two regimes of functioning of the channels are studied: stationary regime and non-stationary regime. The distribution of the substance along the nodes of the channel for the case of stationary regime is a distribution with a very long tail that contains as particular case the Waring distribution (for channel with infinite number of nodes) or the truncated Waring distribution (for channel with finite number of nodes). In the non-stationary regime of functioning of the channel one observes an exponential increase or exponential decrease of the amount of substance in the nodes. However the asymptotic distribution of the substance among the nodes of the channel in this regime remains stationary.

Keywords: Network channels; Network flows; Waring distribution; Social networks; Human migration (search for similar items in EconPapers)
Date: 2018
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