Estimation of parameters characterizing a steady-state synthesis process with nonlinear microorganism growth kinetics

The paper describes a theoretical basis developed for estimating the parameters of a steady-state biotechnological process characterized by nonlinear microorganism growth kinetics. This study aimed to obtain a common methodological basis for estimating input parameters that determine actual technology implementation, taking into account all possible restrictions on the concentration of incoming substrate Sf (g/l) and dilution rate D (h-1 ). The theory development was based on a mathematical model describing one of the most common processes of lactic acid production. This mathematical model includes three mass balance equations (for biomass, substrate, and product), as well as an equation of microorganism growth kinetics. The study established relations for calculating the ultimate value of the dilution rate D ult at a given Sf , relations for the maximum and minimum values of Sf , as well as Sf and D providing the maximum productivity value QP, g/(l·h), where QP = PD (P – product concentration, g/l). These relations were designed to calculate the parameters of possible process implementation for two options at the same value of QP: two values of D calculated for a given Sf and two values of Sf calculated for a given D. A numerical experiment is described using the constants of the mathematical model confirmed by foreign studies. This numerical experiment is illustrated using an Sf-D dependence pattern determining an acceptable value range for Sf and D, with the separate calculation of parameters according to Sf sections. For each of these sections, calculation formulas are provided. It is concluded that the developed theoretical basis is sufficiently general in nature to be applied to biotechnological processes that involve other kinetic relations, as well as microorganism strains creating by-products and using raw materials that are employed to reproduce the substrate in the process of synthesis.

Theoretical Study and Numerical Experiment on the Influence of Trend Changes on Correlation Coefficient

When one of two time series undergoes an obvious change in trend, the correlation coefficient between the two will be distorted. In the context of global warming, most meteorological time series have obvious linear trends, so how do variations in these trends affect the correlation coefficient? In this paper, the correlation between time series with trend changes is studied theoretically and numerically. Adopting the trend coefficient, which reflects the nature and size of the trend change, we derive a formula r = f(k, l) for the correlation coefficient of time series X and Y with respective trend coefficients k and l. Analysis of the function graph shows that the changes in correlation coefficient with respect to the trend coefficients produce a twisted saddle surface, and the saddle point coordinates are given by the trend coefficients of time series X and Y with the opposite signs. The curve f(k, l) = f(0, 0) divides the coordinate planes into regions where f(k, l) > f(0, 0) and f(k, l) < f(0, 0). When the trend coefficients k and l are very small and the correlation coefficient is also very small, then k > 0 and l > 0 (or k < 0 and l < 0) amplifies a positive correlation, whereas k > 0 and l < 0 (or k < 0 and l > 0) amplifies a negative correlation, as found in previous research. Finally, experiments using meteorological data verify the reliability and effectiveness of the theory.

Reducing the hydrodynamic force in the hydraulic distributor by modernizing the spool coupe parts

Due to a sharp change in the direction and velocity of the fluid flow in the hydraulic distributor, hydrodynamic forces arise. When positioning and holding the spool, the magnitude of the above forces determines the required control power. The aim of the article was to find an optimal constructive solution that would reduce the influence of hydrodynamic forces. In the article we have considered the theoretical foundations laid in the analytical solution of the problem of calculating the magnitude of the hydrodynamic force acting on the plunger of the spool. In addition, a numerical experiment was carried out using CAD Solidworks and the Flow Simulation application package and a comparison of the results obtained with the analytical solution of the problem. During the numerical experiment, it was found that by upgrading the spool sleeve, it is possible to reduce the value of the hydrodynamic force by 4.5 times, compared with the original design. At the same time, it was found that the modernization of the plunger does not further reduce the maximum hydrodynamic forces. The article highlights the economic benefits of reducing the required power to control the hydraulic distributor. The article may be of interest to both researchers whose research interests lie in the field of hydrodynamics, and manufacturers of hydraulics.

DEVELOPMENT OF BEHAVIORAL MODEL FOR SWITCHING VOLTAGE REGULATOR MICROCIRCUIT 1290EF1

The issue of developing a behavioral model of pulse voltage converter IC is considered on the example of a microcircuit of domestic production 1290EF1. In order to verify the adequacy of the model, taking into account its frequency characteristics, recommendations and basic requirements are given when performing a full-scale and numerical experiment to determine the frequency characteristics of such type of nonlinear dynamic objects.

ELIMINATION OF IMPACT WHEN CLOSING THE DISC VALVE ON THE DRAINAGE OF HORIZONTAL SEDIMENTS

The reasons for the occurrence of an impact when closing a butt erfl y valve installed on pipelines that discharge sludge water from horizontal sedimentation tanks of treatment facilities are considered. The assumption about the possibility of water hammer was experimentally refuted. It is hypothesized that the cause of the impact is the disruption of the fl uid fl ow when fl owing around a fl at plate at critical angles of att ack. A numerical experiment was carried out, which consists in modeling the movement of a water fl ow in a completely fi lled, closed space of a pipe. As a result of the experiment, it was revealed that the fl ow stall was caused by the formation of zones of high and low pressure, respectively, before and after the valve. This provides additional energy to increase the closing torque, comparable to the force of a pneumatic actuator, and results in an impact.

REGULATION OF STRESS-DEFORMED STATE IN COMPRESSED ELEMENTS OF STEEL FRAMES

The article is devoted to the regulation of the stress-strain state in the compressed elements of steel frames under full operating load. It is proposed to perform reinforcement of such elements with different end eccentricities of load application by rational regulation of the stress-strain state in the reinforcement elements. It is shown that the use of SDS adjustment for frame racks increases their bearing capacity and reduces deformability and welds. The new proposed technology of SDS regulation and possible constructive decisions are offered. Numerical experiment revealed high efficiency of application of the proposed solutions during the reconstruction and reinforcement of the metal frame system. The implementation of the proposed method of SDS regulation confirmed its effectiveness.

Classification of Chaotic Squeak and Rattle Vibrations by CNN Using Recurrence Pattern

The chaotic squeak and rattle (S&R) vibrations in mechanical systems were classified by deep learning. The rattle, single-mode, and multi-mode squeak models were constructed to generate chaotic S&R signals. The repetition of nonlinear signals generated by them was visualized using an unthresholded recurrence plot and learned using a convolutional neural network (CNN). The results showed that even if the signal of the S&R model is chaos, it could be classified. The accuracy of the classification was verified by calculating the Lyapunov exponent of the vibration signal. The numerical experiment confirmed that the CNN classification using nonlinear vibration images as the proposed procedure has more than 90% accuracy. The chaotic status and each model can be classified into six classes.

Vertical turbulent exchange structure and parametrization for 3D shallow water hydrodynamics models

The work describes research of vertical turbulent exchange structure and parametrization for 3D shallow water hydrodynamics models. In this paper, the coefficients of horizontal turbulent exchange are calculated using a whole set of averaging periods of turbulent velocity pulsations. Using experimental data on the pulsations of the velocity components, the coefficient of vertical turbulent exchange was calculated on the basis of various approaches to its parameterization, based on the analysis of the obtained coefficient distributions, the most adequate parameterization of the coefficient was selected, which is used in the software package. The distribution of the vertical turbulent exchange coefficient obtained in a numerical experiment was compared with the results of full-scale measurements, and the calculation results obtained using the mathematical statistics apparatus were analysed.

Convergence of a distributed method for minimizing sum of convex functions with fixed point constraints

In this paper, we consider a distributed optimization problem of minimizing sum of convex functions over the intersection of fixed-point constraints. We propose a distributed method for solving the problem. We prove the convergence of the generated sequence to the solution of the problem under certain assumption. We further discuss the convergence rate with an appropriate positive stepsize. A numerical experiment is given to show the effectiveness of the obtained theoretical result.