On Propagation of Excitation Waves in Moving Media: The FitzHugh-Nagumo Model

BACKGROUND: Existence of flows and convection is an essential and integral feature of many excitable media with wave propagation modes, such as blood coagulation or bioreactors. METHODS/RESULTS: Here, propagation of two-dimensional waves is studied in parabolic channel flow of excitable medium of the FitzHugh-Nagumo type. Even if the stream velocity is hundreds of times higher that the wave velocity in motionless medium (), steady propagation of an excitation wave is eventually established. At high stream velocities, the wave does not span the channel from wall to wall, forming isolated excited regions, which we called "restrictons". They are especially easy to observe when the model parameters are close to critical ones, at which waves disappear in still medium. In the subcritical region of parameters, a sufficiently fast stream can result in the survival of excitation moving, as a rule, in the form of "restrictons". For downstream excitation waves, the axial portion of the channel is the most important one in determining their behavior. For upstream waves, the most important region of the channel is the near-wall boundary layers. The roles of transversal diffusion, and of approximate similarity with respect to stream velocity are discussed. CONCLUSIONS: These findings clarify mechanisms of wave propagation and survival in flow

Modeling of Information Processes in Social Networks

In order to model information dissemination in social networks, a special methodology of sampling statistical data formation has been implemented. The probability distribution laws of various characteristics of personal and group accounts in four social networks are investigated. Stochastic aspects of interrelations between these indicators were analyzed. The classification of groups of social network users is proposed, and their characteristic features and main empirical regularities of mutual transitions are marked. Regression models of forecasting changes in the number of users of the selected groups have been obtained

Weak Field Limit for Embedding Gravity

We study a perturbation theory for embedding gravity equations in a background for which corrections to the embedding function are linear with respect to corrections to the flat metric. The remaining arbitrariness after solving the linearized field equations is fixed by an assumption that the solution is static in the second order. A nonlinear differential equation is obtained, which allows for finding the gravitational potential for a spherically symmetric case if a background embedding is given. An explicit form of a spherically symmetric background parameterized by one function of radius is proposed. It is shown that this function can be chosen in such a way that the gravitational potential is in a good agreement with the observed distribution of dark matter in a galactic halo

Application of Circuit Modeling in the Study of Spark Formation During Electroerosion Treatment

Electrical discharge machining (EDM) of a workpiece is a complex, fast-flowing process characterized by alternating (intermittent) states: short circuit, idle and spark formation. The discontinuity of the EDM process means that the processing is carried out in single pulses, which are formed by a special pulse generator. The parameters of the generator pulses can be divided into time and electrical. The time period and duration of the pulses, as well as the difference between these two parameters (the “silence” interval), are considered temporary. The electric ones include the amplitude value of the voltage, the maximum permissible current, and the polarity of the pulses. in addition, depending on the device of the generator, the pulses can be composite, for example, have an igniting pulse with a higher voltage and a lower current than the main (working) pulse. In this work, we have developed a interelectrode gap model that allows not only to obtain values of electrical parameters, but also to evaluate and to optimize the electrical parameters of materials being processed with known electrical properties. The key advantage of this model is its modularity, which allows to add new functional blocks, which describe external and internal influences, for example, the concentration of erosion products, uneven electrical conductivity of the workpiece, and others, without changing its structure

Application of Circuit Modeling in the Study of Spark Formation During Electroerosion Treatment

Electrical discharge machining (EDM) of a workpiece is a complex, fast-flowing process characterized by alternating (intermittent) states: short circuit, idle and spark formation. The discontinuity of the EDM process means that the processing is carried out in single pulses, which are formed by a special pulse generator. The parameters of the generator pulses can be divided into time and electrical. The time period and duration of the pulses, as well as the difference between these two parameters (the “silence” interval), are considered temporary. The electric ones include the amplitude value of the voltage, the maximum permissible current, and the polarity of the pulses. in addition, depending on the device of the generator, the pulses can be composite, for example, have an igniting pulse with a higher voltage and a lower current than the main (working) pulse. In this work, we have developed a interelectrode gap model that allows not only to obtain values of electrical parameters, but also to evaluate and to optimize the electrical parameters of materials being processed with known electrical properties. The key advantage of this model is its modularity, which allows to add new functional blocks, which describe external and internal influences, for example, the concentration of erosion products, uneven electrical conductivity of the workpiece, and others, without changing its structure