The article is devoted to the development of a computer program with the help of which it is possible to simulate the number of flowing and non-flowing cultures of microorganisms for educational purposes. The Mono model is taken as the basic model of biomass growth. The apparatus of ordinary differential equations is used for the mathematical description of cell populations. As a result, the structure and functionality of the electronic learning module with its subsequent implementation in Python has been developed. As a result, the laboratory work "Modeling of flowing and non-flowing cultures of microorganisms" was developed, in the form of a computer program, performed within the framework of mastering the discipline "Biophysics" and consisting in studying the basic principles and methods of modeling the processes of development of microorganisms in flowing and non-flowing cultures. The developed program is implemented in the educational process.
Keywords: computer program, cell population, biophysics, microorganisms, computer modeling, Mono model, Python, biomass, flow conditions, non-flow conditions, system of equations
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
This paper considers the vectorization and parallelization of the "particle-particle" method used to take into account interactions between objects in the mathematical modeling of physical processes, using the example of taking into account the space charge when calculating the dynamics of charged particles. Comparison and estimation of time costs are carried out (as a test problem, the expansion of a multicomponent ion beam during one nanosecond with a step of Δt = 10-12 s was considered), taking into account the acceleration due to vectorization and parallelization between processor cores. It is concluded that the results of the work clearly demonstrate that the vectorization of computations can significantly speed up the computation time, and the explicit replacement of scalar operations with vector ones makes it possible to obtain additional speed-up in comparison with the use of automatic optimization of the program code. Key words: parallel computations, "particle-particle" method, vectorization of computations, numerical modeling, Coulomb interactions, dynamics of charged particles, ion beam, program code, equation of motion, mathematical model.
Keywords: parallel computations, particle-particle method, vectorization of computations, numerical simulation, Coulomb interactions, dynamics of charged particles, ion beam, program code, equation of motion, mathematical model
In the article we have considered the actual problem of determining the error in visualization of generalized control criteria. It is indicated that the most common nonlinear interaction of parameters in technical systems is the multiplicative interaction of measured physical quantities. Based on the fact that the physical elements of the processor measuring channel have linear dynamic characteristics, it is concluded that the application of nonlinear transformations for quantitative estimates of the properties of monitoring systems requires linearization, the errors of which undoubtedly affect the accuracy of the final mathematical model and its magnitude may be is estimated and attributed to the methodological error of visualization. The process of linearization is considered for the example of the multiplicative interaction P of measured physical quantities. As a result of the analysis of the properties of many industrial control objects under the conditions of steady-state technological processes, it was found that they are characterized by small fluctuations with respect to the mathematical expectation (no more than 10%), which makes it possible to apply the obtained mathematical models of errors arising in the process of linearizing the measurement equations for control criteria, for design and research works.
Keywords: control objects, measuring system, programmable logic controllers, visualization error, mathematical expectation, adaptive control, linearized measurement equation, measurement error