Borisov Roumen, Dimitrova Zlatinka I, Vitanov Nikolay K
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria.
Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, Blvd. Tzarigradsko Chaussee 72, 1784 Sofia, Bulgaria.
Entropy (Basel). 2020 May 15;22(5):553. doi: 10.3390/e22050553.
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.
我们研究网络通道中的物质流，该通道由网络节点和连接这些节点并形成物质运动路径的边组成。通道可以有任意数量的分支，每个分支可以包含任意数量的节点。物质流由常微分方程组建模。我们首先讨论一种通道模型，其每个分支都包含无限数量的节点。对于这种通道中物质的稳态运动，我们得到了与通道任何一个分支以及整个通道中物质分布相关的概率分布。其他作者未讨论过所得到的这些分布，并且它们可能与华林分布相关。接下来，我们讨论一种通道中物质流的模型，其每个分支都包含有限数量的节点。对于物质流的稳态，我们得到了与通道节点中物质分布相关联的概率分布。这些分布也是新的，并且我们计算了所研究的这种物质流的相应信息测度和香农信息测度。
