Approximate Calculation Research Articles

IMPEDANCE BOUNDARY CONDITION OF NON-UNIFORM ELECTROMAGNETIC FIELD PENETRATION INTO CONDUCTING HALF-SPACE

The influence of the non-uniformity of the external field to its distribution on the surface of the conducting half-space is investigated on the basis of exact analytical and approximate asymptotic calculation methods of an arbitrary three-dimensional electromagnetic field. The function that generalizes the impedance boundary condition for diffusion of non-uniform field into conducting body is proposed. On the basis of calculations results comparison by exact and approximate methods for concrete model of electromagnetic system the admissible value of the upper limit of the introduced small parameter is established. References 10, figures 5.

Оптимизация решеток ферменных конструкций из профильных труб (гнутосварных профилей

The article presents a new method of manufacturing lattices with faceless assemblies for truss structures made of profile pipes (bent-welded profiles), tested on their triangular and diagonal systems including flat and cross modifications. Its efficiency and rationality are shown in nodes where the belt elements of square pipes differ in a rhombic arrangement relative to the plane of the structure, which are more preferably replaced by triangular and pentagonal profiles. The versatility of the manufacturing method ensures its relevance in structures made of tubular and rolled profiles, preserves the accepted layout of standardized trusses with faceless assemblies and flange connections. The regularity of the optimization calculation of the unification zones in relation to the core elements of the lattices with the determination of their design coefficients is given. A comparative calculation of the design coefficients and the averaged coeffi cients of the use of the core elements of the grid of square and rectangular profiles is carried out on the example of their implementation in the same semi-truss, when the number of unification zones coincides. The noticeable reduction in the structural material (steel) and the lowering of the construction height of the truss structure were revealed. The acceptable correctness of the approximate calculation method for its application in solving optimization and variant problems, as well as at different stages of the design of load-bearing structures, is confirmed.

Approximate calculation method of hydrodynamic solution of an array with a large number of truncated cylinders

Based on linear wave theory, the hydrodynamic problem of the array of truncated cylinders with relative motion is studied, and the calculation formulas of hydrodynamic force/moment, added mass, and added damping coefficients are given. Firstly, the effect of the evanescent mode on the hydrodynamic coefficients are studied by the truncated two-cylinders as an example. And based on this, an approximation formula for the heave added mass of the truncated two-cylinders is given. After that, a fast formula for calculating the added mass coefficient of an oscillating cylinder of the rectangularly arranged array with a large number of cylinders caused by evanescent mode is presented. Finally, the approximate calculation method of the hydrodynamic coefficients for a large number of rectangular arrays with a given amplitude are summarized. The method is able to efficiently solve the hydrodynamic coefficients of the array with a large number of cylinders, providing an idea to evaluate the performance of such models in engineering.

Development of a model of an electrical complex for gas air cooling devices of gas field №1 gazprom dobycha Yamburg LLC with a centralized power supply system in the MATLAB/SIMULINK program

THE PURPOSE. To develop a model in MATLAB/SIMULINK environment for the system of mechatronic movement modules (MMD) of the electrical complex, which includes gas air coolers with centralized system of power supply of the gas field 1 of "Gazprom dobycha Yamburg" LLC. To analyze the energy efficiency of MMD ETC ACHE. To perform the experimental research of the EMD EMD ETC ACHE model in the dynamic modes in order to determine the regularity of the influence of single (group) starts on the power supply source overload. To develop a switching algorithm for MMD ETK AHE at direct starts of asynchronous motors (AD), providing restoration of the technological mode within the optimum time after the voltage disappearance for the centralized power supply system.METHODS. The results presented in work are received with use of methods of the theory of electric and magnetic circuits, the theory of electric drive and electric machines, methods of optimization of power supply systems, analytical and numerical methods of applied mathematics, methods of mathematical and computer modeling.RESULTS. In article urgency of a theme is described, features of construction and modelling of ETK GP in the environment MATLAB/SIMULINK with the centralized system of power supply are considered. The comparative analysis of existing methods and calculation of parameters of the substitution schemes of the MMD ETK GP was carried out. Approximate calculation of mechanical and inertial characteristics for creating a model of load (resistance moment) for the motor. The model of EMD of electric motor drive compressor unit was created, as close as possible to the real existing system on the basis of catalog (passport) data of individual elements of electric motor drive unit. There were analyzed and developed proposals to enhance power efficiency of EMD ETC AHE and algorithms, which provide optimal direct start-up of the AHE fan group within the set time after the power failure without overloading of the power supply source, were proposed.CONCLUSIONS. On the basis of results of computer modeling, the peculiarities of operation of EMD ETH ACHE, which require further study and development of corrective measures to improve energy efficiency and reliability of power supply system of GP. Combination of direct starts of single (group) fans of ACHE, obtained at this stage of research of EMD EMD ETC ACHE model, will create the basis (algorithm) for automated control system of this complex, which will ensure restoration of technological mode within optimum time after power outage without overloading of centralized power supply source. Calculation of parameters of individual elements of MMD model of ETC AVO will allow to use data to create other models of ETC GP, which will allow to conduct in-depth research and improve the energy efficiency of the entire system of power supply of GP.

Public Value Capture, Climate Change, and the ‘Infrastructure Gap’ in Coastal Development: Examining Evidence from France and Greece

This paper examines the role that two Public Value Capture (PVC) mechanisms could play in providing a source of funding for urban infrastructure in the case of two coastal areas in France and Greece. High development pressures in those areas have been exacerbated in recent times by the growing ‘informality of desire’. Therefore, in a context of climate change the two case study areas face the dual challenge of an increasing ‘investment gap’ and increasing vulnerability. Although the estimated costs are still based on approximate calculations, they are substantive. Using primary and secondary data, as well as analysis of the legal and policy framework, the paper shows that ‘informality of desire’ is not only tolerated but actually incentivised in both countries. This leads to substantial short-term financial benefits for private developers and property owners but also some gains for local authorities and central governments. However, the value captured via the legalisation fees and property taxation is not adequately ringfenced and in any case it is not enough to cover the infrastructure gap and the potential compensation in case of natural disasters.

The lower partial moments risk measure in a novel fuzzy framework based on possibility density function

As a comprehensive and flexible risk measure, the lower partial moments (LPM) can be converted into a wide range of the downside risk measures by modifying its target parameter and degree of moment. However, the distribution function of the return rate is hard to recognize, and the existing calculation methods have great calculation difficulties, so it has limited application. In previous studies, the historical data was mostly used to simulate the distribution function of return rate for approximate calculation of LPM risk, resulting in a huge computational complexity. In this paper, based on the possibility density function, the LPM risk measure is creatively defined in a novel fuzzy framework instead of a traditional random framework. By deriving the trapezoidal fuzzy number of return rate from the historical data, the LPM risk can be easily calculated according to its possibility density function, which can significantly improve the calculation process. Based on this idea, this paper derives the specific expression when the rate of return is a trapezoidal fuzzy number under the definition of fuzzy LPM. Furthermore, stock-driven and portfolio-driven methods are used to calculate the portfolio risk, and then two fuzzy mean-LPM models are constructed respectively. Finally, a numerical example based on global stock market index is used to illustrate the feasibility and validity of the proposed methods and models. Compared with the classic mean–variance model, our proposed model with adjustable target parameter and degree of moment is more flexible in reflecting investors’ attitude towards risk.

Approximate Thermal Calculation of the Superheated Steam Condenser of Heat Pumps

A comparative analysis of the methods of approximate thermal calculation of the superheated steam condenser of the steam compression heat pump of the heat supply system is presented. The working substance of the heat pump and the condensing steam is the refrigerant R410a. When the single-zone method is applied, the condenser is calculated by one area with the inclusion of the heat of overheating in the heat of condensation and the use of the overheating coefficient. The two-zone method assumes the calculation of the condenser in two separate areas, viz. the cooling of superheated steam and its actual condensation. The approbation was carried out during a numerical study of a condenser of a low-temperature heat pump system for heating and hot water supply, with a heat exchange surface in the form of a spiral coil pipe in a pipe immersed in a heated liquid. In the first approach, the flow rate and temperature of the heated water are limited by the saturation temperature of the condensing refrigerant, regardless of the flow pattern of the working media. The method of two-zone calculation of the superheated steam condenser with a counter-current or cross-counter-current flow scheme of working media makes it possible to obtain real results of the temperature of the heated water that exceeds the temperature of the saturated refrigerant vapor, taking into account the flow rate of the heated water. In this case, the wall temperature in the cooling area is higher than the saturation temperature, and during condensation it is lower, which further confirms the adequacy of the presented technique. The use of a two-zone technique with a separate averaging of the physical properties of the working media in the areas of superheated steam and condensation cooling, as well as temperature pressures, provides a more accurate value of the heat exchange surface, which in the case under consideration is reduced to 20%. Based on the conducted studies, it is recommended to use a two-zone technique that makes it possible to obtain reliable data on the parameters of the superheated steam condenser.

Evaluation of anterolateral thigh flap dimensions with virtual flap models

Free flaps are commonly used for head and neck reconstruction. However, flap dimensions are still evaluated by visual and tactile assessment. The aim of this study was to enable preoperative planning of flap dimensions for soft tissue reconstruction based on clinical parameters. Computed tomography records from 230 patients dated from 2009 to 2019 were analysed retrospectively. A virtual, three-dimensional anterolateral thigh flap model was standardized, aligned to segmented leg models in two positions, and flap thicknesses and volumes were determined. Associations of flap thickness and volume with clinical parameters were evaluated, and an approximative calculation method was derived. The laterally positioned anterolateral thigh flap showed an average (interquartile range) thickness of 15.6 mm (8.7 mm) and volume of 1.5 cm3 (0.9 cm3) per cm2. The medially positioned anterolateral thigh flap showed an average (interquartile range) thickness of 16.3 mm (8.7 mm) and volume of 1.6 cm3 (0.9 cm3) per cm2. For both flap positions, leg circumference was the strongest predictor of flap thickness (β = 0.545, P < 0.001 and β = 0.529, P < 0.001) and flap volume (β = 0.523, P < 0.001 and β = 0.480, P < 0.001). Flap dimensions can be calculated based on leg circumference, and this preoperative planning of flap dimensions can help the surgeon to select the appropriate flap.

Floatplane vs wig: a very fast approach

In this short paper a fast comparison between a seaplane and a WIG craft is presented, based on the approximate calculation of the required power at level flight and cruising speed. Two similar capacity generic crafts are used, one seaplane flying at 10000 ft at 300 km/h IAS and the other one flying at 7 m from the sea surface also at 300 km/h. It was found as expected, especially if an improvement is added, that the one flying in ground effect requires less power than the seaplane.

Hydrodynamics of interacting spinons in the magnetized spin- 12 chain with a uniform Dzyaloshinskii-Moriya interaction

We use a hydrodynamic approach to investigate dynamic spin susceptibility of the antiferromagnetic spin-$1/2$ Heisenberg chain with a uniform Dzyaloshinskii-Moriya (DM) interaction in the presence of an external magnetic field. We find that transverse (with respect to the magnetic field) spin susceptibility harbors two (respectively, three) spin excitation modes when the magnetic field is parallel (respectively, orthogonal) to the DM axis. In all cases, the marginally irrelevant backscattering interaction between the spinons creates a finite energy splitting between optical branches of excitations at $k = 0$. Additionally, for the orthogonal geometry, the two lower spin branches exhibit avoided crossing at finite momentum which is determined by the total magnetic field (the sum of the external and internal molecular fields) acting on spinons. Our approximate analytical calculations compare well with numerical results obtained using matrix-product-state (MPS) techniques. Physical consequences of our findings for the electron spin resonance experiments are discussed in detail.

Optimal control using to approximate probability distribution of observation set

The paper treats the problem of an approximate calculation of unknown probability distribution function defining an observation set. The observation set is usually used as a supervised set to train a neural network or to build functions for machine learning. In order to solve the problem, we propose applying optimal control tools. To this effect following Vapnik, we define the risk functional depending on probability distribution functions, and we construct a set of functions based on the observation set. The construction draw on using only those functions that satisfy some differential equation with suitable properties as it is usually done in optimal control theory. Next, we apply a dual dynamic programming to formulate a new optimal control problem. As a consequence, we state and prove a verification theorem for an approximation of an unknown probability distribution function defining the observation set. We estimate the difference between the approximate probability distribution function and the best probability distribution with distance defined by the risk functional.

Modern technologies of venous ulcers treatment in elderly population

Venous trophic ulcers take place in the terminal stage of chronic venous insufficiency. The problem of venous trophic disorders is extremely relevant due to the high prevalence among the population. This review considers the comparative characteristics of morbidity data on the example of Germany and the Russian Federation. Particular attention paid to the influence of the course of the disease on patient’s life quality during treatment. The causes of high-cost treatment are reported with approximate calculations for 1 clinical case and total annual costs according to foreign researchers (Australia, Great Britain, USA). The risk factors are discussed in the form of certain concomitant nosologies that significantly aggravate the healing process of ulcers with a brief description of the pathogenesis. The review defines the main goals of the treatment of venous trophic ulcers, as well as separate groups of directions in which it is reasonable to carry out therapeutic measures. Article presents a comparative analysis between the methods of applying compression therapy (elastic bandaging, the use of special stockings) and the influence of the choice on the quality of life of patients. Various methods of topical wound care are described with the obligatory consideration of the stage of the wound process, alternative methods of local treatment are listed (for example, the use of autologous platelet-rich plasma). The efficacy of systemic pharmacotherapy in trophic disorders and the treatment potential of various groups of drugs on the rate of ulcer healing were evaluated. The advantages of using surgical treatment are determined, the main surgical techniques are listed, highlighting the advantages and disadvantages of each. Possible treatment strategies for elderly patients also discussed. The complexity of evaluating the effectiveness of new techniques and an integrated approach to treatment is shown, which in the future will help to correct the direction of finding new ways to solve the problem of venous ulcers in this specific group of patients.

SOFTWARE COMPLEX FOR THE ANALYSIS OF THE STOCHASTIC PROGRAMMING PROBLEMS WITH PROBABILITY CRITERION

This paper describes the software complex for the construction of a smooth approximation of the probability function and its derivatives. The structural parts of the complex, its functionality and mathematical background are described. The software complex constructs an approximation of the probability that some loss function does not exceed a certain level of loss. The program supports lossfunctions defined in a LaTeX format and contains predefined standard functions, variables and mathematical signs. The software supports different variable types, such as constants, control variables, stochastic variables with known distribution and parameters and samples of stochastic variables with unknown distribution. The software complex supports a variety of predefined random distributions and allows to tune the result by setting other service parameters. The implemented approximation is based on the replacement of the Heaviside function inside the probability function expression with the sigmoid function. Next, the approximated probability function and its derivatives are represented as volume integrals. These integrals can be calculated numerically using the Monte-Carlo method. This approach provides a relatively quick and universal method of approximate calculation of the probability function and its derivatives. The software complex has a graphical user interface and produces a graphical representation of approximated functions along with their points data. The program also supports the construction of the surface approximations for the case of the loss function having two control variables. Obtained graphical and point data can be used in the solution of stochastic programming problems with probability criteria. Examples using the software complex as a tool for analyzing stochastic programming problems are given.

The Error of Approximate Calculations of the Weak Binary Electrolyte Dissociation Degree

The Error of Approximate Calculations of the Weak Binary Electrolyte Dissociation Degree

Design of a Computable Approximate Reasoning Logic System for AI

The fuzzy logic reasoning based on the “If... then...” rule is not the inaccurate reasoning of AI against ambiguity because fuzzy reasoning is antilogical. In order to solve this problem, a redundancy theory for discriminative weight filtering containing six theorems and one M(1,2,3) model was proposed and the approximate reasoning process was shown, the system logic of AI handling ambiguity as an extension of the classical logic system was proposed. The system is a generalized dynamic logic system characterized by machine learning, which is the practical-application logic system of AI, and can effectively deal with practical problems including conflict, noise, emergencies and various unknown uncertainties. It is characterized by combining approximate reasoning and computing for specific data conversion through machine learning. Its core is data and calculations and the condition is “sufficient” high-quality training data. The innovation is that we proposed a discriminative weight filtering redundancy theory and designed a computable approximate reasoning logic system that combines approximate reasoning and calculation through machine learning to convert specific data. It is a general logic system for AI to deal with uncertainty. The study has significance in theory and practice for AI and logical reasoning research.

ОПТИМИЗАЦИЯ ФЕРМЕННЫХ КОНСТРУКЦИЙ С ПОЯСАМИ ИЗ ПЯТИУГОЛЬНЫХ РАВНОКАТЕТНЫХ И РАВНОБЕДРЕННЫХ ПРОФИЛЬНЫХ ТРУБ.

The article determines the specified values of optimal parameters of pentagonal profile pipes (bent-welded profiles), equally stable out of and within the truss structure. The efficiency and rationality of their use in chord elements are shown due to the functionality of the layout design of cross sections, including one flange (horizontal face), a pair of walls (vertical faces) and a pair of inclined faces symmetrically arranged to the vertical at angles of 45° in the first modification (equilateral) and 60° in the second modification (isosceles). Both modifications disclose the certain prospect for high functional layout design in the updated faceless nodes typical for truss structures made of tubular profiles. The article gives the comparative calculation of the design coefficients and the averaged coefficients of the use of chord core elements made of pentagonal profiles with the example of their implementation in the same semi-truss, when the number of unification zones coincides. A noticeable decrease in the mass (weight) and reduction of the structural material (steel) of the chords and, as a consequence, the entire structure was revealed by the increased values of static (geometric) characteristics of the design sections. The acceptable correctness of the approximate calculation method is confirmed for its application in solving optimization and variant problems as well as at different stages of load-bearing structures’ design.

Scattering of Laguerre-Gauss light beam by a sphere: the angular spectrum decomposition method and a comparison with the localized approximation method

Evaluation of the beam shape coefficients (BSC) in the spherical wave expansion of the incident beam is vital in analyzing light scattering by spherical particles. Different methods have been developed for this purpose. In this work, the formulas of the BSCs for the Laguerre-Gauss beam (LGB) are derived in the angular spectrum decomposition (ASD) method. Under the paraxial condition, these ASD-BSCs are approximated to the expressions in either series or single integrals. Besides, the BSCs for the LGB are also obtained in the localized approximation (LA) method. It is found that the approximate ASD-BSCs are same as those LA-BSCs. Numerical calculation is implemented for verifying the BSC calculations. The validity of the approximate BSC calculation is discussed, together with the distribution of the angular spectrum of the beam. The work offers another example of the shaped beams for mathematically justifying the LA method and suggests another way to discuss the validity of the LA method.

Transient uniform electron gases

The uniform electron gas (UEG), a hypothetical system with finite homogenous electron density composed by an infinite number of electrons in a box of infinite volume, is the practical pillar of density-functional theory (DFT) and the foundation of the most acclaimed approximation of DFT, the local-density approximation (LDA). In the last thirty years, the knowledge of analytical parametrizations of the infinite UEG (IUEG) exchange-correlation energy has allowed researchers to perform a countless number of approximate electronic structure calculations for atoms, molecules, and solids. Recently, it has been shown that the traditional concept of the IUEG is not the unique example of UEGs, and systems, in their lowest-energy state, consisting of electrons that are confined to the surface of a sphere provide a new family of UEGs with more customisable properties. Here, we show that, some of the excited states associated with these systems can be classified as transient UEGs (TUEGs) as their electron density is only homogenous for very specific values of the radius of the sphere even though the electronic wave function is not rotationally invariant. Concrete examples are provided in the case of two-electron systems.

Simulation of primary current distribution in Tesla-type pulse generators.

In a Tesla-type pulse generator, self-inductance of the primary coil is a crucial parameter to determine the final oscillating condition. However, the accurate value of this inductance might be changed due to the uneven primary current distribution caused by practical configuration of the primary side. Consequently, in order to precisely design the transformer, it is helpful to evaluate the primary inductance based on electromagnetic simulation instead of conventional approximate calculation. In this paper, a simulation model based on the finite integration technique is established to solve the uneven primary current problem. A primary coil with multiple contacting points is designed, and hexahedral mesh generation of the coil is also discussed. Hence, a series of verification tests using different primary structures are performed to support the results of simulation. Both results of the simulation model and the verification test presented that the variation of the primary inductance will affect the performance of the generator, and the number of contacting points is the main cause to determine the maximum current density of the coil.

Linear Skorokhod SDE: Evaluation of Expectations of Functionals

This paper considers a linear stochastic differential equation (SDE) containing the Skorokhod integral. A formula for the approximate calculation of functionals of solutions of this equation is constructed, which is approximately exact for polynomials of the third order.