Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

In this paper, three new models of fractal–fractional Michaelis–Menten enzymatic reaction (FFMMER) are studied. We present these models based on three different kernels, namely, power law, exponential decay, and Mittag-Leffler kernels. We construct three schema of successive approximations according to the theory of fractional calculus and with the help of Lagrange polynomials. The approximate solutions are compared with the resulting numerical solutions using the finite difference method (FDM). Because the approximate solutions in the classical case of the three models are very close to each other and almost matches, it is sufficient to compare one model, and the results were good. We investigate the effects of the fractal order and fractional order for all models. All calculations were performed using Mathematica software.

Hierarchical Approach to Identifying Fluid Flow Models in a Heterogeneous Porous Medium

A three-dimensional numerical hydrodynamic model fairly accurately describes the processes of developing oil and gas fields, and has good predictive properties only if there are high-quality input data and comprehensive information about the reservoir. However, under conditions of high uncertainty of the input data, measurement errors, significant time and resource costs for processing and analyzing large amounts of data, the use of such models may be unreasonable and can lead to ill-posed problems: either the uniqueness of the solution or its stability is violated. A well-known method for dealing with these problems is regularization or the method of adding some additional a priori information. In contrast to full-scale modeling, currently there is active development of reduced-physics models, which are used, first of all, in conditions when it is required to make an operational decision, and computational resources are limited. One of the most popular simplified models is the material balance model, which makes it possible to directly capture the relationship between reservoir pressure, flow rates and the integral reservoir characteristics. In this paper, it is proposed to consider a hierarchical approach when solving the problem of oil field waterflooding control using material balance models in successive approximations: first for the field as a whole, then for hydrodynamically connected blocks of the field, then for wells. When moving from one level of model detailing to the next, the modeling results from the previous levels of the hierarchy are used in the form of additional regularizing information, which ultimately makes it possible to correctly solve the history matching problem (identification of the filtration model) in conditions of incomplete input information.

Modeling and visualizing of the formation of a snub dodecahedron in the AutoCAD system

The article is devoted to modeling and visualization of the formation of flat-nosed (snub-nosed) dodecahedron (snub dodecahedron). The purpose of the research is to model the snub dodecahedron (flat-nosed dodecahedron) and visualize the process of its formation. The formation of the faces of the flat-nosed dodecahedron consists in the truncation of the edges and vertices of the Platonic dodecahedron with the subsequent rotation of the new faces around their centers. The values of the truncation of the dodecahedron edges, the angle of rotation of the faces and the length of the edge of the flat-nosed dodecahedron are the parameters of three equations composed as the distances between the vertices of triangles located between the faces of the snub dodecahedron. The solution of these equations was carried out by the method of successive approximations. The results of the calculations were used to create an electronic model of the flat-nosed dodecahedron and visualize its formation. The task was generally achieved in the AutoCAD system using programs in the AutoLISP language. Software has been created for calculating the parameters of modeling a snub dodecahedron and visualizing its formation.

MODELING OF STRESS-DEFORMED STATE OF BENDED REINFORCED CONCRETE ELEMENTS IN ZONES OF CLEAN AND TRANSVERSE BEND

The article deals with the analysis of the stress-strain state (SSS) of a bent reinforced concrete element in zones of pure and transverse bending. It is assumed that a bent element in the process of loading (after the formation of normal and oblique cracks) is divided into blocks, united by uncracked concrete and reinforcement that has adhesion to concrete. SSS was formed using the results of experimental studies of special prototypes in the PC “Lira-SAPR”. A fi nite element model of a prototype has been developed in the form of a reinforced concrete rectangular beam loaded with two identical concentrated forces in the span. By the method of successive approximations, the process of formation and formation of a system of cracks is realized, with which the beam is divided into blocks during loading. The results of calculating the fi nite element model and their comparison with experimental data are presented.

Application of the recurrent mathematical model for estimating the electric-traction NetWare parameters at their dynamic change

The article is devoted to the possibility of applying the methods of successive approximations in the analysis of the instantaneous scheme of the electric-traction netware. The described approach makes it possible to improve the accuracy of modeling the dynamic modes of traction power supply sections operation, and also makes it possible to significantly improve the process of modeling diagnostic and control systems for electric rolling stock at the design stage, based on a more accurate model of dynamically changing input parameters of the electric-traction netware, depending on their required level.

Financial Innovation and Technology after COVID-19: a few Directions for Policy Makers and Regulators in the View of Old and New Disruptors

Innovation and technology have led to the redefinition of business models and development of new ones in many bricks and mortar sectors. Similarly, blockchain and fintech have impacted the finance and banking industries and are expected to further affect them in the future, leading some media to coin the expression “Uberization of banking”. The authors extrapolate from sharing economy models to conclude that while blockchain and fintech are poised to advance finance and banking, there are no disruptive features that corroborate the term. By analogy and successive approximations, this article identifies the limitations of the arguments for disruption in finance and banking. Besides, hinging upon stylized facts, the article establishes similarities with sharing economy models to identify potential threats stemming from financial innovations such as Tokenomics, tagged as “no-ABSs”. Eventually, the authors identify entry points and ways forward arising from the COVID-19 pandemic for policy makers and regulators to regain their pivotal role in policing the market and ensuring transparency while driving innovation.

Оn the Analysis of Certain Flotation Processes with Velocities Depending on Time and Height of the Column

— The present paper is an extension of the previous paper of the author where the flotation column dynamics has been investigated. Here we consider the case when particle sedimentation rate and bubble lifting speed depend on time and position in the column. We use the methods for examining the transmission lines set out in the papers mentioned in the References. We formulate a mixed problem for the system describing the processes in the column and present it in a suitable operator form. Then we prove an existence - uniqueness of generalized solution by the fixed point method. We show an explicit approximated solution as a step in the sequence of successive approximations.

Calculation of the Shaping of a Space Umbrella Antenna During Strong Bending of Radial Rods Connected Along Parallels by Tensile Cables

Abstract— A cyclically symmetric umbrella antenna is considered, the frame of which consists of flexible inextensible radial rods connected in nodes along parallels by tensile cables. In the initial transport position, the multilink rods are packed in packages oriented in the direction of the system axis. After the packing ties are removed, the rods are deployed in radial planes under the action of elastic springs connecting the links, and are fixed in rectilinear positions at a given angle with respect to the axis, at which all cables connecting the same type of rod nodes take the form of regular polygons, while remaining loose. Further, under the action of the force of a damping hydraulic cylinder with pre-compressed springs, the root parts of all rods are slowly turned to the stops. In the final position, the radial rods, connected at the nodes by tensioned cables, take a curved shape. The tensile stiffnesses of the cables are determined so that the radial and axial coordinates of the nodes of the curved rods coincide with the coordinates of the points of the given surface of revolution. A model of strong bending of a flexible inextensible rod is constructed taking into account the unknown radial reactions of tensioned cables acting on it at the nodes. The links of the rod are considered as “cantilever” elements connected in series at the nodes in local coordinate systems, which can make large displacements and turns. The bending of each element is described by two specified functions, the shrinkage of the element due to bending is taken into account in a quadratic approximation. The obtained nonlinear deformation equations of the system, taking into account the geometric connections at the nodes, are solved by the method of successive approximations with respect to the unknown reactions of the cables. The obtained values of the reactions are then used to determine the required tensile stiffness of the cables at the given coordinates of the nodes. As an example of the calculation, a parabolic antenna is considered for various numbers of radial rods and components of links. The estimates of the accuracy of the proposed computational model of the antenna shaping are carried out.

Numerical Solution of Two-Dimensional Fredholm–Volterra Integral Equations of the Second Kind

The paper presents an iterative numerical method for approximating solutions of two-dimensional Fredholm–Volterra integral equations of the second kind. As these equations arise in many applications, there is a constant need for accurate, but fast and simple to use numerical approximations to their solutions. The method proposed here uses successive approximations of the Mann type and a suitable cubature formula. Mann’s procedure is known to converge faster than the classical Picard iteration given by the contraction principle, thus yielding a better numerical method. The existence and uniqueness of the solution is derived under certain conditions. The convergence of the method is proved, and error estimates for the approximations obtained are given. At the end, several numerical examples are analyzed, showing the applicability of the proposed method and good approximation results. In the last section, concluding remarks and future research ideas are discussed.

Algorithm for simulating the self-starting of a group of asynchronous electric motors with a short-circulated rotor

PURPOSE. To consider the problems of modeling the processes of run-out, self-starting of a group of asynchronous electric motors (AM) in case of short-term power outages (NEC) and voltage drops in external short circuits (SC), convenient for programming and practical use. To establish the integral reaction of the AM group during self-start to the disturbing effect, taking into account their characteristics and duration to establish the permissible limit values of the NEC. To develop an algorithm for the transient process of self-starting of the AM group when using matrix and vector data representation when solving the basic equation of the rotor motion and its computer implementation. METHODS. When solving the problem, the following methods were used: successive approximations when solving the basic electromechanical equation, taking into account electromagnetic transient processes; Gauss-Seidel method with accelerating the convergence of the iterative process when solving the equations of the parameters of the regime; method of nodal stresses. The algorithm is implemented in VBA and tested in Matlab Simulink. RESULTS. The article describes the relevance of the topic, considers a model of AM according to catalog data, an algorithm for self-starting a group of an AM with NEC and external short circuits, taking into account electromagnetic transient processes, which has high accuracy and is convenient for practical use. CONCLUSION. The use of asynchronous motor catalogs makes it possible not to carry out laborious preliminary calculations of the parameters of asynchronous motors. The application of the Gauss-Seidel method with acceleration of convergence provides a decrease in the number of iterations. Taking into account electromagnetic transients and the effect of displacement of the rotor current allows you to evaluate the mutual influence of motors and increase the accuracy of calculations. The use of the method of nodal voltages makes it possible to determine the residual voltage on the busbar section with AM, if at the first moment the motors are switched on to short circuit. The implementation of the algorithm in the VBA environment is convenient for practical use.