Nonlinear evolution wave equation for an artery with an aneurysm: an exact solution obtained by the modified method of simplest equation

We study propagation of traveling waves in a blood filled elastic artery with an axially symmetric dilatation (an idealized aneurysm) in long-wave approximation.The processes in the injured artery are modelled by equations for the motion of the wall of the artery and by equation for the motion of the fluid (the blood). For the case when balance of nonlinearity, dispersion and dissipation in such a medium holds the model equations are reduced to a version of the Korteweg-deVries-Burgers equation with variable coefficients. Exact travelling-wave solution of this equation is obtained by the modified method of simplest equation where the differential equation of Riccati is used as a simplest equation. Effects of the dilatation geometry on the travelling-wave profile are considered.Comment: 17 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1701.0237

Model of a motion of substance in a channel of a network consisting of two arms

We study the problem of the motion of substance in a channel of a network for the case of channel having two arms. Stationary regime of the flow of the substance is considered. Analytical relationships for the distribution of the substance in the nodes of the arms of the channel are obtained. The obtained results are discussed from the point of view of technological applications of the model (e.g., motion of substances such as water in complex technological facilities).Comment: 14 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1709.0183

Mathematical model of a flow of reacting substances in a channel of network

Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and social processes [3, 4]. In our previous research we have discussed the flow of a single substance in a channel of network. It may happen however that two substances flow in the same channel of network. In addition the substances may react and then the question arises about the distribution of the amounts of the substances in the segments of the channel. A study of the dynamics of the flow of the substances as well as a study of the distribution of the substances is presented in this paper on the base of a discrete - time model of flow of substances in the nodes of a channel of a network.Comment: 15 pages, 1 figure. arXiv admin note: text overlap with arXiv:1807.0877

Discrete-time model for a substance motion in a channel of a network. Application to a human migration channel

We discuss a discrete-time model for motion of substance in a channel of a network. For the case of stationary motion of the substance and for the case of time-independent values of the parameters of the model we obtain a new class of statistical distributions that describe the distribution of the substance along the nodes of the channel. The case of interaction between a kind of substance specific for a node of the network and another kind of substance that is leaked from the channel is studied in presence of possibility for conversion between the two substances. Several scenarios connected to the dynamics of the two kinds of substances are described. The studied models: (i) model of motion of substance through a channel of a network, and (ii) model of interaction between two kinds of substances in a network node connected to the channel, are discussed from the point of view of human migration dynamics and interaction between the population of migrants and the native population of a country.Comment: 33 pages, 11 figure