Calculation Scheme Research Articles

First-principles study of geometric and electronic structures, and optical transition energies of Mn4+ impurity ions: K2SiF6 as a prototype

In this study, we present the results of first-principles calculations conducted within the density functional theory to investigate the geometric and electronic structures of the ground 4A2 and excited 2E and 4T2 states, as well as the optical transition energies between these states, in the prototype system of K2SiF6:Mn4+. To achieve this, we employed a comprehensive evaluation of the five representative exchange-correlation functionals, enabling the development of a state-of-art calculation scheme that effectively describes the geometric and electronic structures of the excited 2E and 4T2 states. The calculated excitation, emission and zero-phonon line energies of the optical transitions between the ground 4A2 state and the excited 2E and 4T2 states demonstrate a better agreement with experimental results. However, we observed that the conventional and widely-used approach based on the analysis of the electronic density of states diagrams derived from the ground state calculations failed to accurately evaluate the vertical optical transition energies from the 4A2 ground state to the excited 2E and 4T2 states when compared to experimental data. The calculation technique developed in this study holds the potential for widespread application to other combinations of host materials and impurity ion, which is of great importance for future developments in the field of optical materials.

LOD of a Computational Numerical Model for Evaluating the Mechanical Safety of Steel Structures

The article addressed the relevant problem of building information modeling. The suggestion was to introduce a BIM-based expert system into the design process. The proposed expert system encompasses the development of three levels of detail for a calculation model and digital interactive models of applicable regulatory documents. The proposed expert model has a modular structure, and it has a control module, a calculation scheme development module, a module for interaction with FEM solvers, and a module in charge of the database of interactive digital design standards. Standard operating conditions and non-standard emergency impacts are taken into account. The case of design standards for steel structures was used to describe the interaction between the expert system and the information model, and the characteristics and the structure of a digital model of a regulatory document. The data, calculated using the proposed LOD, were compared with the experimental findings. The structure of a real industrial building was designed, and its safety was evaluated. The proposed approach is a proven method applicable for designing safe bearing structures. In addition, their adequate deformation is most accurately taken account of at the stage of normal accident-free operation and in emergency situations.

Development of a calculation scheme for selecting the optimal mode of operation of a gas condensate well taking into account the deformation conditions of the formation

To establish premature optimal well operation modes, it is necessary to consider the process of well operation within the framework of ongoing processes in the common reservoir-well hydrodynamic system and take into account the peculiarities of changes in the properties of the gas condensate mixture and the thermobaric conditions of the reservoir in it. Therefore, the object of the study is the operation of a gas condensate well in the event of technological complications in it, which requires the selection of the necessary optimal operating mode to prevent these complications by comprehensively taking into account the factors influencing this process in the “reservoir-well” system.
 The article proposes a calculation scheme for establishing the optimal operating mode of a gas condensate well without the formation of a liquid plug at the bottomhole, taking into account the formation deformation during field development in the depletion mode. The problem is solved by determining the required current working volume of produced gas (as well as condensate), bottomhole and contour values of reservoir pressure, condensate saturation and reservoir porosity. As a result of the study, it was revealed that the determined characteristics of the selected optimal mode of a gas condensate well are significantly affected by a change in the reservoir properties of the reservoir (for example, the permeability of the reservoir), which in turn leads to a change in the optimal working gas flow rate of the well.
 The considered problem has not been previously studied in its full formulation, which is presented in this article, where the solution of the problem under study is achieved taking into account the change in the physical properties of the reservoir fluid and gas, as well as the reservoir properties of the reservoir under conditions of a change in the state of the reservoir system due to emerging deformation processes in the reservoir

Improved calculation of soil hydraulic conductivity with the simplified evaporation method

AbstractNumerical modeling of soil water dynamics and storage is generally based on the Richards equation. Its solution requires knowledge of the soil hydraulic properties (SHP): the soil water retention function and the hydraulic conductivity function. To determine SHP, laboratory evaporation experiments are particularly popular because they provide data for both SHP functions. The evaluation by the simplified evaporation method (SEM) method, originally proposed by Schindler and subsequently improved by several authors, relies on linearization assumptions that allow for a relatively simple calculation scheme but result in biased conductivity data for some soils. The objective of this study is to propose and test an improved computational scheme for the hydraulic conductivity function. We present the new theory and show that it leads generally to higher accuracy of the conductivity function. The improvement is most pronounced for sandy soils and soil water pressure heads below −100 cm, where the original method provided data with bias.

Second order stabilized two-step Runge–Kutta methods

Stabilized methods for the numerical solution of ODEs, also called Chebyshev methods, are explicit methods with extended stability domains along the negative real axis. These methods are intended for large mildly stiff problems, originating mainly from parabolic PDEs. In this paper we present explicit two-step Runge–Kutta–Chebyshev methods of order two, which have more than 2.3 times larger stability intervals than the analogous one-step methods. Explicit formulae for stability intervals are derived, as well as an effective recurrent scheme for calculation of methods’ coefficients for arbitrary number of stages. Our numerical experiments confirm the accuracy and stability properties of the proposed methods and show that at least in the case of constant time steps they can compete with the well-known ROCK2 method.

A three-dimensional non-orthogonal multiple-relaxation-time phase-field lattice Boltzmann model for multiphase flows at large density ratios and high Reynolds numbers

This study proposes a three-dimensional non-orthogonal multiple-relaxation-time (NMRT) phase-field multiphase lattice Boltzmann (PFLB) model within a recently established unified lattice Boltzmann model (ULBM) framework [Luo et al., Phil. Trans. R. Soc. A 379, 20200397, 2021]. The conservative Allen-Cahn equation and the incompressible Navier-Stokes (NS) equations are solved. In addition, a local gradient calculation scheme for the order parameter of the Allen-Cahn equation is constructed with the non-equilibrium part of the distribution function. A series of benchmark cases are conducted to validate the proposed model, including the two-phase Poiseuille flow, Rayleigh-Taylor instability, binary liquid/metal droplet collision, and a bubble rise in water. The present simulation results are in good agreement with existing simulation and experimental data. In the simulation of the co-current two-phase Poiseuille flow, the present model is proven to resolve the discontinuity at the phase interface and provide accurate results at extremely high density ratios (i.e., up to 106). Finally, the proposed model is adopted to simulate two challenging cases: (1) water droplet splashing during its impacting on a thin liquid film and (2) liquid jet breakup. The simulation results demonstrate an excellent agreement with previous experimental results, both qualitatively and quantitatively. In these simulations, the Weber number and Reynolds number reach 105 and 6000, respectively, and the viscosity can be as low as ∼10−4, in the lattice unit.

A METHOD FOR ASSESSING ENERGY EFFICIENCY OF LIGHT-DUTY VEHICLES TAKING INTO ACCOUNT CHANGES IN THEIR DESIGN PARAMETERS

The present stage of development of the world market of vehicles, in particular, light-duty vehicles (LDVs) is marked by an increasing variety of types and designs. Therefore, while validating or renewing fleet vehicle of an enterprise, carriers are faced with the choice of cars setting conditions they can assess using existing fragmentary and cost-effective approaches. However, the latter ones do not meet the concepts of saving energy and resources. Therefore, the task of choosing an efficient car is complex requiring a science-based formation of demands and their satisfaction. Existing approaches to the selection and validation of LDVs are simplified and imperfect in terms of transport technology. They do not take into account a) resource and technical properties of LDVs as a means of transport; b) main design and technical characteristics of LDVs; c) parameters of its operation (running surface, traffic density, length of the driving cycle, etc.). This article considers a method for assessing energy efficiency of light-duty vehicles, which is based on the scheme of the vehicle operation as a dynamic tool. To develop this method, the provisions of the energy and resource efficiency theory of a car have been used, namely the calculation schemes of transport operations based on models of reference prototypes and test operations. These models are able to ensure the reasonable use of the vehicle fleet with design novelty under the given operating conditions. In order to analyse changes in the parameters of new vehicles and improve the parameters of transport technology, a universal design of a light-duty vehicle of a generic type has been developed and considered. This structural pattern covers all options of the vehicle’s design basis. New options for the vehicle design are created by changing the number of design modules and their parameters. The method proposed for consideration ensures the technical and technological properties of light-duty vehicles in accordance with the concept of energy and resource conservation in the transport system. The paper develops methods for comprehensive improvement of transport energy efficiency and formation of requirements for transportation projects of LDVs taking into account technical and technological factors within their life cycle.

ПРИМЕНЕНИЕ МОДУЛЯ ДИНАМИКА+ В ЛИРА-САПР 2022 ПРИ РАСЧЕТЕ БОЛЬШЕПРОЛЕТНЫХ ЗДАНИЙ ИЛИ СООРУЖЕНИЙ НА СЕЙСМИЧЕСКИЕ ВОЗДЕЙСТВИЯ

The article discusses the main goals of dynamic calculation of buildings and structures. The authors present a method for calculating a large-span steel spatial structure for seismic impacts using the Dynamics+ module in LIRA-CAD 2022 software package. The paper analyses the sequence of loading formation in the calculation scheme. It considers the cases when the calculation of buildings and structures for seismic impact must be carried out using accelerograms, seismograms or velocigrams. As a result, the authors obtained a calculation model that allows analyzing the dynamic behavior of a large-span spatial structure in different periods. Subsequently, it will be relevant for studying the resistance of this structure to progressive collapse under seismic impact.

BeDCV: Blockchain-Enabled Decentralized Consistency Verification for Cross-Chain Calculation

With the increase of data stored on the blockchain, the efficiency of storage and calculation of blockchain has gradually become a bottleneck restricting the development of blockchain. By storing data on multiple chains, blockchains can request data from other chains for calculation and the storage pressure can be alleviated. But the transfer of a large amount of data between chains suffers from low transfer efficiency and poor security. A reasonable design is to perform the calculation on the data storage chain and only transfer the results across chains. However, since the calculation process is invisible, blockchains cannot judge the consistency of calculation results from other chains. In this paper, we provide a blockchain-enabled decentralized consistency verification scheme for cross-chain calculation (BeDCV). Considering the decentralized characteristic of blockchain, we adopt the blockchain called <i>supervision chain</i> for decentralized auditing. We modify paillier homomorphic encryption to encrypt data involved in the calculation for correctness verification. Then, we aggregate the ciphertexts of data to generate the audit proof for integrity verification. Besides, we verify whether the data involved in the calculation are real-time by leveraging a counting bloom filter. The supervision chain can check the correctness, integrity, and real-time performance of cross-chain data calculation without revealing any original information about the data. The theoretical and experimental analysis demonstrates that BeDCV can verify the consistency of cross-chain data calculation result effectively, realizing secure and reliable expansion of blockchain.

Determination of the influence of geometrical parameters of rope blocks on the durability of a rope

Problem The durability of crane ropes is very important, as it provides not only the main costs of operating a lifting machine, but also the safety of loading and unloading operations. Rope operating conditions have a significant impact on the period of its use, but they are not always taken into account. Gool. The rope calculation methodology reflected in the standard does not take into account the operating conditions of the rope, so it is very difficult to predict its exact durability. In modern educational and reference literature, the influence of the size and geometry of rope blocks on the durability of hoisting ropes is underestimated. Methodology. The main criterion that is taken into account when choosing a rope according to existing methods is the tensile force of the rope, although studies by many well-known scientists show that the rope wires break as a result of bending on the blocks and drum. The diameter of the block is selected depending on the diameter of the rope and the mode of operation of the lifting mechanism. The material of the block and its geometry are not taken into account at all when choosing the type of rope and its diameter, while the wear of the surfaces of the rope and block greatly affects the durability of these elements of the hoisting mechanism. Determining the factors that affect rope wear and reduce its durability is a rather important task and requires not only theoretical but also experimental studies. Results. Ropes of various designs and diameters were considered. This made it possible to evaluate the influence of various elements of the rope and the block on the predicted durability of the rope. Originality. The studies made it possible to improve the formula of B.S. Kovalsky, which he proposed for selecting the diameter of the rope by service life. The dependence of the influence of the angle of opening of the block's groove, which is determined from the condition of reducing the torsion of the rope during its deviation, on the rope's durability was obtained. Practical value To obtain a more realistic picture of the load on a rope that is bent on a block and drum, the calculation scheme was improved and the number of factors that have a significant impact on the rope's durability was increased. The results of the study significantly bring the conditions of rope loading during its bending on the block and drum closer to real values.

OPTIMIZATION OF CALCULATIONS OF BUILDING STRUCTURES

Building structures are very diverse in their shapes, sizes, loading conditions, etc. Their durability depends on many factors, including how accurately the design scheme reflects the actual conditions of its operation. Because no matter how precise and complex calculation methods are used, if an incorrect calculation scheme is calculated, then the results of such calculations will not reflect the true picture. Therefore, the problem of optimization of design schemes is of great scientific and practical importance. Optimization parameters depend on specific conditions. One of the existing approaches for finding optimal solutions is based on mathematical modeling, when the model is an analytical dependence of the objective function on dependent (controlled) variables, the numerical values and range of which are set based on the actual operating conditions of this structure. The compilation of such models and the performance of appropriate calculations require a deep understanding of the essence of the phenomenon and knowledge of the mathematical apparatus. Of the existing methods, the most common and developed is linear programming, when the model is a linear function and the variables in the constraint system are also linear. The idea of the method is technically implemented in the add-in "Search for a solution" for Microsoft Excel. With its help, you can find the optimal (maximum or minimum) numerical value of the objective function contained in one cell, taking into account restrictions on the values of dependent variables in other cells. Most often, this superstructure is used in solving optimization problems of the economy (simplex method, transport problem, etc.). In the public domain, there are very few results of using this approach in the calculations of building structures at the initial design stage. In the proposed work, an attempt was made to use this add-on in the problem of optimizing the geometric dimensions of a structure, when the numerical value of the bending moment in a particular section was chosen as the optimization criterion. It is appropriate to solve such a problem at the stage of drawing up the design scheme of the structure. Keywords: calculation scheme, line of influence, search for solutions

Анализ устойчивости крепи нефтедобывающих скважин при проведении кумулятивной перфорации на основе результатов геомеханического моделирования

Well cement sheath stability analysis for two oil-producing wells in the completion of productive formations by shaped charge perforating was performed. The data of direct measurements of pressures in the borehole at different distances from the cable head of the perforating tool at the moment of detonation, which exceeded 50 MPa, were used in the studies. The pressure values were approximated along the wellbore using a power law. To reliably predict the stress-strain state of the near-wellbore zone of the perforation interval, the ANSYS finite-element modeling software was used. To determine the stress field, an axisymmetric finite-element calculation scheme was built, the height of the model along the wellbore was 39 m. During modeling, it was taken into account that the geological and physical parameters of the simulated reservoirs differed in depth and reservoir pressure value were different. Elastic-strength properties of the cement stone formed were determined during the laboratory experiments for different recipes of cement slurries. According to the results of modeling, the areas of destruction and strength reserve of cement stone, as well as the values of radial displacement of the production casing in the perforation interval were determined. The developed model of the near-wellbore zone and methodical approaches can be used in future for choosing optimal elastic and strength properties of cement stone, perforation tools and technological parameters of perforating-explosive operations.

An improved calculation scheme of electron flow in a propagator method for solving the Boltzmann equation

In order to accurately evaluate the electron acceleration process in the calculation of the time evolution of the electron velocity distribution function (EVDF) based on the Boltzmann equation, an improved scheme blending upwind and central differences is introduced into the propagator method (PM). While the previous PM based on the upwind scheme needs fine cells to obtain an accurate EVDF at low electric fields, the improved PM is robust against coarse cells, which allows the reduction of cell resolution. Calculations of the EVDF in Ar under RF electric fields demonstrated that the blending scheme can provide satisfactorily accurate results even with cells about tenfold larger than the upwind case at low reduced electric fields below 1 Td, which leads to much shorter computational time because the reduction in the number of cells satisfactorily compensates for the complexity of the blending scheme. This technique has been built into a new user-friendly PM software named BOSPROM.

ПРОТИЗСУВНА СПОРУДА ПІДВИЩЕНОЇ НЕСУЧОЇ ЗДАТНОСТІ ТА ЗНИЖЕНОЇ МАТЕРІАЛОМІСТКОСТІ

Recently, there has been active construction development of territories with difficult engineering and geological conditions. Construction on landslide and landslide-prone slopes leads to increased loads on individual areas, which can cause activation of old or the development of new landslides. As a result of the occurrence and activation of landslides, unacceptable deformations are formed, which lead to a violation of the stability of the slope, as well as the destruction of buildings and structures. Therefore, when performing construction works on slopes, it is necessary to provide measures for engineering protection of territories, buildings and structures located on or near slopes. On many sites, the placement of slopes and the erection of supporting prisms, buttresses and counterbanks is impossible. This is due to the need to observe the limits of alienation, the presence of residential and industrial buildings. In this case, the most rational means is the installation of pile retaining structures. They are optimal for shear strength of up to 15÷20 m. If it is necessary to contain deep landslides, bored piles are exposed to large bending moments, which leads to an increase in the number of piles or their diameters. As a result, the volume of drilling work and consumption of materials increases significantly. Therefore, issues of rationalization of retaining anti-slide structures are of particular practical interest. The paper calculation models were developed and numerical modeling of the interaction of elements of two structures of retaining anti-slide structures with the soil massif was performed. Numerical modeling was performed in the licensed geotechnical software complex Midas GTS NX, which implements the finite element method. The behavior of the soil in the calculation schemes was described by the Mohr-Coulomb elastic-plastic model. As a result of calculations of the stress-strain state of the elements of the retaining structures compatible with the soil, the coefficients of the reserve of stability were determined by the reduction method and the value of the internal forces (bending moments and transverse forces) arising in the elements of the structures. The reinforcement of the retaining elements was selected for the obtained internal forces using the "SCAD" software complex. On the basis of a comparison of the costs of the main materials necessary for the construction of structures, the economic feasibility of using a landslide protection retaining structure in the form of buttresses made of bored piles has been proven.

DYNAMICS OF VIBRATION GRINDING WITH REGARD TO THE INFLUENCE OF SORTING MATERIAL ON ITS WORKING PARAMETERS

The general calculation model of the screen system was determined - the material is based on the study of the interaction processes between the sieve and the crushed stone that was on the screen. The selected model of vibration movement of loose material made it possible to determine the qual-itative and quantitative characteristics of the dynamic impact on the working body. The sorting process is presented as some orderly process of movement of a large number of different particles in a layer on a sieve. The main provisions for the calculation of the main parameters of the screen are formulated, which ensure the specified modes of the process of sorting the material and obtaining the appropriate fractional composi-tion of crushed stone. The prerequisite for choosing the calculation scheme "screen-sieving material" is the determination of the vibrational movement of a material particle along a vibrating hard surface inclined to the horizon at an angle that carries out rectilinear oscillations at an angle to the plane of the screen. At the same time, weight, friction force and normal reaction act on the particle. The proposed model made it possible to determine the speed of transportation in the case when the screening screen performs a circular motion, which is the addition of two independent oscillations with different amplitudes and frequencies. The sorting process is significantly affected by the probability of grains passing through the holes of the sieve. This prob-ability depends on the size of passing particles, the dynamic parameters of screen vibrations, the design of the sieve, the shape of the sieve openings, the coefficient of the live section (the ratio of the area of the openings in the light to the total area of the sieve. The average speed of passage of particles through the sieve is determined by the frequency of contact of particles with the surface and the ratio of particle sizes and the hole. The frequency of particle contact with the sieve is affected by the amplitude and frequency of vibrations of the sieve surface. The probability of a particle passing through the sieve hole during one collision can be estimated based on the calculation charts.

THE OPTIMAL DESIGN OF THE 40.00-57 DUAL PURPOSE ORTHOTROPIC SHELL UNDER UNCERTAINTY CONDITIONS DESIGN

Problem statement. A feature of the modern technical systems’ design is that deterministic approaches dominate, while consideration of uncertainty can provide a more adequate representation of the research object in the appropriate calculation scheme, mathematical model. The consideration of uncertainties becomes especially relevant in the modeling of complex technical systems, where uncertainties can be quite abundant and the uncertainties themselves can be of different nature, namely stochastic, rough, fuzzy, or even combined. It is advisable to check whether the system is tolerant to uncertainties. This work is devoted to the construction of methods for the optimal design of the new rubber-cord shell 40.00-57 in the conditions of the fuzzy initial data. For a deterministic approach a special mathematical model can be used to calculate the output parameters. The mathematical model developed by Prof. E. Kvasha, at one time was truly revolutionary, because for the first time in the world the contact problem of the interaction of an elastic base with a layered orthotropic shell, which is part of a complex technical tire system, was solved. The main drawback, which could not be overcome by varying the input parameters, remained the uneven resource of the shell frame elements. So, variant design has shown its insufficient efficiency for such complex technical systems. The purpose of the research is to suggest a model and methods of optimal design for optotropic rubber-cord oversized shells under the conditions of real factors of uncertain nature. Conduct methods testing and design a new construction of tire 40.00-57 for civilian and military purposes. Conclusion. The authors proposed models and methods of optimal design of orthotropic rubber-cord shells under the condition of fuzzy data. Approbation of the symbiosis of Monte Carlo methods and the method of local variations for finding the optimal geometry of the shell was conducted. For new 40.00-57 tire shape, the difference between the largest frame resource and the smallest resource of the tire’s elements was about 18 %. Such a result could not be achieved by variant design. The temperature distribution in the cross-section of the tire under conditions of operation for 8 hours at an ambient temperature of 37 0C does not exceed the value of 110 0C, at which the thermal destruction of the rubber-cord material begins.

On accuracy of finite-difference schemes in calculations of centered rarefaction waves

Проведен сравнительный анализ точности разностных схем UpWind (первого порядка), TVD (второго порядка) и WENO5 (третьего порядка по времени) при расчете для нелинейного уравнения переноса задачи Коши с кусочно-линейными разрывными периодическими начальными данными. Показано, что в случае устойчивых начальных разрывов, из которых формируется последовательность ударных волн, порядок сходимости всех трех схем между ударными волнами совпадает с их формальной точностью. В случае неустойчивых начальных разрывов, при распаде которых формируется последовательность центрированных волн разрежения, все три схемы имеют первый порядок сходимости внутри этих волн. Получена явная формула для дисбалансов разностных решений в центрированной волне разрежения. В случае схем повышенной точности эта формула хорошо согласуется с численными расчетами, не зависит от типа схемы и определяется погрешностью аппроксимации начальных данных в окрестности неустойчивого сильного разрыва.

Yavno-neyavnye skhemy rascheta dinamiki uprugovyazkoplasticheskikh sred s malym vremenem relaksatsii

We consider the dynamic behavior of elastoviscoplastic media under the action of an external load. For the general case of a nonlinear viscosity function describing high-speed hardening, we construct an explicit–implicit calculation scheme of the second order of approximation that permits one to obtain a numerical solution of the original semilinear hyperbolic problem. A distinctive feature of this approach is that it does not use the method of splitting by physical processes. Despite this, an explicit computational algorithm was obtained that allows efficient implementation on modern computing systems.

Removing singularities in the Bateman radioactive transformation equations using partial fraction decomposition

This paper deals with the problem of singularities caused by repeated decay constants in the Bateman equations for nuclide concentrations in the radioactive transformation chains. Using partial fraction decomposition with the Bateman equations, the general solution for the nuclide concentrations in the radioactive transformation linear chains with repeated decay constants has been derived. The derived equations are similar to the solutions obtained by other authors, with the difference being the improved calculation scheme. A comparative analysis was conducted to assess the computational efficiency in determining concentration changes within transmutation chains, particularly in the presence of repetitive reaction rates. The investigation involved evaluating several methodologies.

Comparison of Receptor-Ligand Restraint Schemes for Alchemical Absolute Binding Free Energy Calculations.

Alchemical absolute binding free energy calculations are of increasing interest in drug discovery. These calculations require restraints between the receptor and ligand to restrict their relative positions and, optionally, orientations. Boresch restraints are commonly used, but they must be carefully selected in order to sufficiently restrain the ligand and to avoid inherent instabilities. Applying multiple distance restraints between anchor points in the receptor and ligand provides an alternative framework without inherent instabilities which may provide convergence benefits by more strongly restricting the relative movements of the receptor and ligand. However, there is no simple method to calculate the free energy of releasing these restraints due to the coupling of the internal and external degrees of freedom of the receptor and ligand. Here, a method to rigorously calculate free energies of binding with multiple distance restraints by imposing intramolecular restraints on the anchor points is proposed. Absolute binding free energies for the human macrophage migration inhibitory factor/MIF180, system obtained using a variety of Boresch restraints and rigorous and nonrigorous implementations of multiple distance restraints are compared. It is shown that several multiple distance restraint schemes produce estimates in good agreement with Boresch restraints. In contrast, calculations without orientational restraints produce erroneously favorable free energies of binding by up to approximately 4 kcal mol-1. These approaches offer new options for the deployment of alchemical absolute binding free energy calculations.