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
The paper studies the issue of the influence of the quality of the computational triangular grid on the accuracy of calculations in various computational problems. There is a well-known example of Schwartz, which shows that the approximation of a smooth surface by a polyhedral surface can give very large errors for calculating the surface area. This is due to the quality of the constructed triangulation of the surface. Therefore, it is natural to expect that there is some connection between a certain triangulation characteristic and the accuracy of solving some computational problem. In the presented article, as such a characteristic, a value is chosen - the average value of the minimum sine of the angle of all triangles of the computational grid. In the course of numerical experiments, the Dirichlet problem for the Laplace equation in a circular ring was solved, in which the error of the approximate solution was calculated (the gradient descent method was used to find a solution to the corresponding variational problem.). For the ring, a series of triangulations was constructed with a uniform division along the angle and a non-uniform division along the radius in polar coordinates. In this example, a linear dependence of the error on was shown. The article presents both the results of the calculation with different values and the calculation of the correlation coefficient of the studied quantities.
Keywords: boundary value problem, Delaunay triangulation, calculation accuracy, Dirichlet problem, mathematical modeling, triangular mesh, minimum triangle angle, piecewise linear approximation, variational method, Laplace equation
The article discusses several equivalent circuits constructed by sequentially connecting circuits for the membrane and protoplasm. The solution was made using the Cardano formula for cubic equations. The roots in the expression for the determination of resonant frequencies determined the resonant frequencies for the given parameters for the membrane and intercellular fluid; to obtain numerical values, values were used within several permissible limits. In the course of the calculations, it was confirmed that most resonant frequencies are in the millimeter and submillimeter ranges. It is also shown that the cell vibration frequencies occupy the decimeter, centimeter, millimeter and submillimeter wavelengths. Obviously, it is the impact on biological systems of electromagnetic radiation in the indicated wavelength ranges that will be most effective and can lead to a maximum biological response (effect).
Keywords: equivalent equivalent circuit, biological structure, membrane, oscillatory circuit, Cardano formula, protoplasm, resonant frequencies, electrical processes, equivalent equivalent circuit, electromagnetic radiation
The paper presents a numerical study of the effect of external electromagnetic fields of various configurations on the computer model of a neuron; Briefly describes the created software product, allowing to conduct numerical simulation of nerve cells, the mechanism of conduction of the nerve impulse. In an alternating field, the ion flux behaves as follows: at frequencies below 1 kHz, 3 maxima of the function of the average ion velocity are observed: these are 82 Hz, 340 Hz and 801 Hz. Under the influence of fields of higher frequencies from 1 kHz to 900 kHz, strong changes in velocities and currents do not occur. It is possible that in this frequency range the field does not have time to change the velocity modulus, but at a frequency of 970 kHz there is a sharp increase in the average ion velocity, which is most likely related to the effect of the myelin sheath, since no maximum is observed from the myelin sheath.
Keywords: Neuron, axon, biological effect, modeling, microwave radiation, axon potential