The article presents an overview of the work on modeling the behavior of a double electric layer in membranes under influences of various nature, including the example of various surface phenomena (adsorption, surfactants, adhesion, wedging pressure, electroosmosis, etc.). It was noted that the size and distribution of the charge over the surface near which it is formed has an effect on the structure of the DES; to obtain the potential distribution, it is necessary to know the structure of the membrane-electrolyte solution interface; it is intermediate to be able to calculate the charge distribution, and, accordingly, to calculate the potential distribution itself. It was pointed out that when choosing a mathematical interpretation of the process, the Poisson equation is often used, taking into account the self-consistent field, or the Navier-Stokes equations are solved together with the Nernst-Planck equation and the electroneutrality condition; the Gui-Chapman model is used to describe processes with low accuracy by molecular dynamics methods, supplemented by the ion adsorption condition according to the Langmuir isotherm; when modeling the electrolyte current, the description of the surface current of ions is used, taking into account the viscous properties of the medium.

Keywords: double electric layer, zeta potential, membrane, primembrane layer, spatial charge density, Navier-Stokes equation, surface current, Poisson equation, capacitor, fluid flow potential

It is indicated in the article that the study of the electron bunching process in the drift space of a transit klystron is an urgent task that allows one to establish general laws applicable to more complex models. In this connection, the behavior of the pre-modulated electron beam in the drift space of the transit klystron has been investigated. A numerical model has been implemented that takes into account the effect of space charge fields and the interaction of charged particles with elements of an electrodynamic system. A series of numerical experiments with different values ​​of the current and initial velocities of electrons, as well as their comparison with theoretical data, have been carried out. As a result of numerical experiments, data were obtained that characterize the dynamics of the electron flux in the drift space of the transit klystron at different values ​​of the initial velocity (0.5 s, 0.9 s) and cathode current (10 mA, 1A, 10A).

Keywords: flyby klystron, mathematical model, numerical simulation, large particle method, particle-particle method, drift space, convection current distribution, electron flow, multithreaded calculations, system of differential equations

The article presents a detailed analysis of the structure of the model of management of the hematopoietic functional system of the body in various physiological situations, which activates the activity of a certain adaptive circuit that characterizes the functional state. The first state and adaptation to the contour of the functional hematopoietic system of the body included in the work are considered in detail. The structural equation of adaptation of the first contour is made. It is concluded that the equation of adaptation compiled for a hypothetical control model adaptation, in the actual state of Affairs raises a number of inconsistencies with the hypothetical implementation-related deviations from the ideal parameters of functioning: autonomic nervous system, internal environment, metabolic state, the processes of transmitting the control actions. All these deviations affect the observed realization of the set of blood form elements (RSBE).

Keywords: physiological model of functional hematopoietic system, the adaptive circuit, the space of external influences, categorical diagram, adaptation processes, gemondo-nuclear level, functino mapping, homomorphic mapping, the equation of adaptation