Gauss Method Research Articles

Machine-learning aided calibration and analysis of porous media CFD models used for rotating packed beds

The proposed research is an attempt to advance the state-of-the-art of the numerical modelling of RPB by combining Computational Fluid Dynamics and Machine Learning approaches. The latter creates an accurate framework that should help quantify the potential of Rotating Packed Beds (RPB) technology to intensify conventional CO2 capture processes. To this end, a direct sensitivity analysis is detailed to supplement a machine-learning (ML) algorithm built for calibrating resistance coefficients needed for porous media modelling. The algorithm is used to improve CFD predictions of dry pressure drop in rotating packed beds (RPBs) for a wide range of operating conditions. The sensitivity derivatives with respect to the packing resistance coefficients are demonstrated for the first time in RPBs, which is not available in the current CFD open source and commercial codes. In this regard, sensitivity differential equations are derived from three-dimensional Navier-Stokes equations for porous media in a rotating reference frame. These sensitivity equations are discretized using a finite volume scheme and solved to obtain the sensitivity pressure drop differences at the packing edges. The results are validated against the predictions of the analytical sensitivity analysis and the finite difference approximation. After, the Newton – Gauss method that employs the sensitivity pressure drop derivatives, is used to minimize the error (cost function) between the pressure drop obtained from CFD simulations and the available experimental data. This is achieved by tuning the packing resistance coefficients to the RBPs' operating conditions (gas flowrate and rotating speed) and correlate them using an artificial neural network (ANN). The results of the proposed approach show a significant improvement in porous media-based CFD predictions of RPBs' pressure drop across a wide range of operating conditions and this over conventional porous media-based CFD models. This is necessary for CFD models to be reliably used as a tool that can efficiently improve existing RPBs' designs and/or participate in RPBs' design innovation.

Runge–Kutta convolution quadrature based on Gauss methods

An error analysis of Runge–Kutta convolution quadrature based on Gauss methods applied to hyperbolic operators is given. Order reduction is observed, with the order of convergence depending heavily on the parity of the number of stages, a more favourable situation arising for the odd cases than the even ones. An exception is observed when the associated kernel exhibits exponential decay. In this case, for the 2-stage Gauss method full order is obtained. For particular situations the order of convergence is higher than for Radau IIA or Lobatto IIIC methods when using the same number of odd stages. We investigate an application to transient acoustic scattering where, for certain scattering obstacles, the favourable situation occurs in the important case of the exterior Dirichlet-to-Neumann map. Numerical experiments and comparisons illustrate the performance of the method.

A new mathematical technique and its Python program to assess wind potential

BackgroundA new approach based on the Newton–Gauss method is used to find the Weibull parameters.ResultsA Python program was developed to employ the Newton–Gauss method. It is implemented to find Weibull parameters and wind potential of Pakistan’s eight cities (Hyderabad, Khuzdar, Multan, Quetta, Bahawalpur, Islamabad, Lahore, and Peshawar). Wind speed data recorded at an interval of ten minutes for 2016 is used to implement a Python program to calculate wind potential. To compare the values of the parameters, five known methods, the empirical method, method of moments, energy pattern factor method, maximum likelihood method, and modified maximum likelihood method, were also used to model and determine the wind potential. The root mean square error, mean absolute error, coefficient of determination, and Akaike information criterion were calculated to compare values of wind parameters and average wind speed. The correlation between recorded and modeled Weibull pdf was almost 99% for each city.ConclusionsThe new method only caters to those wind speeds that contribute to the wind potential; therefore, the average value of the wind speed is the least in the case of the new method. The maximum wind potential was observed for Hyderabad.

A comparative study between laser hemorrhoidoplasty with digital-guided hemorrhoidal artery ligation and conventional (Milligan-Morgan) hemorrhoidectomy

Background: Hemorrhoids have a much higher incidence than rectum and colon diseases worldwide. The prevalence was estimated to be between 2.9% and 27.9% among the worldwide population, of which 4% are symptomatic. Based on the Gauss method, the highest incidence was present in patients aged between 45 and 65 years. Aims and Objectives: To compare laser hemorrhoidoplasty with digital-guided hemorrhoidal artery ligation (DGHAL) and conventional (Milligan-Morgan) open hemorrhoidectomy procedures. Materials and Methods: A prospective follow-up study was undertaken in the Department of Surgery, Maharani Laxmi Bai Medical College, Jhansi, from January 2020 to June 2021. In this comparative and prospective study, 60 patients were included, of whom 30 were treated with open surgical hemorrrhoidectomy (Milligan-Morgan) and 30 were treated with laser hemorrhoidoplasty with the DGHAL method. Results: Male patients numbered 41 and female patients numbered 19. Between laser hemorrhoidoplasty with DGHAL and the open surgical hemorrrhoidectomy (Milligan-Morgan) approach, there were significant differences in operating time, blood loss, bleeding; and early postoperative pain. In terms of early postoperative pain, there were statistically significant differences between the two groups (P<0.001). The mean operational time for laser hemorrhoidoplasty with DGHAL was 22.57±1.794 min, compared to 29.43±3.664 min for the open surgical hemorrrhoidectomy (Milligan-Morgan) method (P<0.002). Conclusion: Laser hemorrhoidoplasty with Doppler-guided hemorrhoidal artery ligation (DGHAL) is safe and effective in cases of all grades of hemorrhoids as compared to open surgical (Milligan-Morgan) hemorrhoidectomy.

Analiza izazvanog dinamičkog ponašanja funkcionalno stepenovanih greda pod harmoničnim pokretnim opterećenjem na elastičnoj osnovi pomoću metode konačnih elemenata

Introduction/purpose: This paper presents a numerical study of the forced dynamic behavior of a functionally graded beam subjected to a harmonically varying transversely concentrated moving force using a higher-order shear deformation theory. Methods: The governing equations are derived using Hamilton's principle. These equations are then transformed into the weak form using the Galerkin method. The problem is solved using the finite element method by developing a three-node finite element with four degrees of freedom per node. The Newmark beta method is chosen for the time integration and the Gauss method for the spatial integration. Results: The effects of several parameters were investigated, including the slenderness ratio, the material index, foundation stiffness, velocity and the frequency of the moving load. Good agreement was observed with the results obtained from the literature. Conclusion: This study illustrates the importance of using a higher order theory in the case of short beams and clearly shows the change in the behavior of the FGM beam as a function of different parameters.

Конечно-элементная модель перегрузочного крана КПП 16/32т для перевалки грузов в речных и морских портах

Transshipment cranes of the checkpoint of the Lenpodyemtransmash plant are widely used in river and sea ports, at industrial enterprises for grappling transshipment of bulk cargo and for working with piece loads or containers, as well as for transshipment of scrap metal and rolled metal using lifting electromagnets. It is proposed to eliminate the uncertainties caused by the incompatibility of one-dimensional (rod) and two-dimensional (plate) finite elements having a different number of degrees of freedom, 12 and 20, when developing digital twins of portal cranes of the Lenpodyemtransmash plant on the example of the CHECKPOINT 16/32t crane by approximating axisymmetric shells of the portal head with rod finite elements. The method is based on the equality of the potential shear energy of the finite element model of the plate and the potential energy of the approximating rod model, the elements of which work on tension/compression, which made it possible to move from the finite element model of the GEARBOX 16/32t reloading crane, built on the basic finite elements of Kirchhoff plates, to the finite element model of the crane based on the core base finite elements. A mathematical model of a matrix equation of static equilibrium with many degrees of freedom is proposed, the numerical solution of which by the Gauss method allows us to proceed to six-component internal forces in each finite element due to the corresponding vector of external loads reduced to the degrees of freedom of the calculated finite element model. The possibility of inter-pretation of bearing elements of spatial metal structures of portal cranes by both one-dimensional rod and two-dimensional plate finite elements is investigated, a re-evaluation of traditional views on the computational analysis of the stress-strain state of metal structures of portal cranes in the field of reliable determination of their bearing capacity during operation in ports, especially in the field of assessing post-repair risk analysis and the resource of reloading cranes is proposed, those who have completed the standard service life in the port and have undergone capital repairs. A calculated rod finite element idealized model of a PPC 16/32t gantry crane for transshipment of cargo in river and sea ports is constructed, demonstrating the transition from a real design to a calculation model based on geometric principles of discretization of both rod and continuum elements by the basic rod end elements of the crane, as a result of which the digital calculation model should be detailed and complex, like a system with many degrees of freedom. The algorithm of application of the digital calculation model of the crane is given on the example of static finite element calculation analysis of the KPP 16/32t crane.

Initial Orbit Determination Based on Intelligent Optimization Algorithm

Classical methods for initial orbit determination (IOD) include Laplace method, Gauss method, and their variations. In addition to this, based on the characteristic of optical observation data nowadays, experts propose some other IOD methods, like Double-r method and admissible region method. One of the ways to determinate the orbit through double-r method is to guess distances of the target from the observer at two epochs—usually at the first and the last one. By doing so, we can solve the Lambert problem, and use its solution as the initial guess of the orbit. Furthermore, we can improve the initial guess by iterations to reduce the root mean square (RMS) of the observations. The admissible method is based on the concept of attributable (longitude, latitude, and their rates). With some conceptions, the admissible region described by the range and range rate from the observer is characterized. Using triangulation we can find the nodal point that makes the RMS minimal. In our work, we apply one intelligent optimization method—the particle swarm optimization method to the two methods, based on simulated and real data, and compare the results with that of modified Laplace method. At last, we briefly discuss the possibility of applying the double-r method to the orbit link problem.

Solving Linear Systems with Column Reduction

Summary In order to solve a system of linear equations, students or teachers are used to performing a row reduction with the Gauss method. In this paper we propose to adopt a column point of view through two fundamental subspaces of a matrix—its kernel and its image—linked to the homogeneous system and to a particular solution of the system. This paper provides a method to find the set of solutions of a system by performing a column reduction of a double augmented matrix of the system.

Comparative Study of Numerical Methods for Solving the Fresnel Integral in Aperiodic Diffractive Lenses

In this work, we present a comparative analysis of different numerical methods to obtain the focusing properties of the zone plates based on Fibonacci and Cantor sequences. The Fresnel approximation was solved numerically in order to obtain the axial irradiance provided by these diffractive lenses. Two different methods were applied. The first one is based on numerical integration, specifically the Simpson integration method and the two-dimensional Gaussian quadrature. The second consisted in the implementation of the Fast Fourier Transform in both one and two dimensions. The axial irradiance of the lenses, the relative error with respect to the analytical solution, and the calculation time required by each method are analyzed and compared. From this analysis it was concluded that the Gauss method presents the best balance between accuracy and computation time. This analysis could be useful to decide the most convenient numerical method to be used for the study of more complex diffractive structures.

Comparison of Basic Iterative Methods Used to Solve of Heat and Fluid Flow Problems

In this research, a comparison of the convergence rate of different basic methods is made in order to solve the Poisson equation, which is similar to some of the resulting equations in computational fluid mechanics. The Jacobi method, the point Gauss-Seidel method, the successive over-relaxation method (SOR), the line Gauss method (TDMA), the ADI method and Strongly Implicit (SIP) method are among the iterative approaches investigated, which are then compared to find the most optimal method. The selection criteria included the number of iterations and the time needed to reach convergence. In both selection criteria, the SIP approach has been shown to be the most efficient.

Guassian Lattice Reduction Algorithm in Two-Dimensions

An approximation approach for the shortest vector problem, the Lenstra-Lenstra-Lovasz (LLL) Algorithm completes its computations in polynomial time and produces an estimate that is within an exponential factor of the true solution. It's a technique that can be used in practice and is accurate enough to crack cryptosystems, factor polynomials over integers, and solve integer linear programming problems. For the purpose of using the Gauss method "inside" We present a comprehensive examination of the LLL method in the context of a collection of realistic probabilistic models. The proofs focus on both the underlying dynamical systems and the transfer operators. Finding a lattice of Euclidean space with a short basis from a skewed starting point is known as the lattice reduction problem. Especially in cryptology, lattice reduction techniques offer remarkable use in mathematics and computer science.

New Aspects for the Estimation of the State of the Natural Water

This paper presents a study of the hydrochemical composition and physicochemical properties of natural water samples from various sources in the Voronezh and Moscow regions. Two model systems are proposed for assessing the state of the aquatic environment: UV spectroscopy with spectrum decomposition by the Gauss method and spontaneous aggregation of lecithin in a polar medium. Based on the performed investigation, it was determined that the size of lecithin aggregates decreases, and the value of their zeta potential increases with an increase in the content of hydrophobic compounds in natural water.

Модельные системы для оценки воздействия компонентов водной среды на биологические объекты

Following four model systems on the base on the natural lipids to estimate the action of the water medium components on the biological objects were presented by using the earlier obtained data about the similarity functioning of the physicochemical regulatory system of the oxidation processes in the biological objects of varying complexity and the ability of phospholipids to the self-aggregation in the polar medium: the low temperature autoxidation of lecithin in the polar medium, the mathematic analysis of UV-spectra of lecithin and its mixtures with the water medium components by Gauss method, the self-aggregation of lecithin in the different polar medium, the ξ-potential value of the formed particles. As the model toxicants sodium thiophosphate and copper(II) ions were used. Scale of the sodium thiophosphate influence on the lecithin oxidation kinetics is shown to depend on the initial intensity of the lecithin oxidation and composition of its phospholipids. It is agree with the earlier obtained data about the influence of the chemical toxic agents under their intake into the body on the lipid peroxidation state in tissues of animals. In is established that the copper ions participate in the initiation of lecithin oxidation and form complex with its phospholipids. This influences on the ability of lecithin to the self-aggregation and electrophoretic properties of formed particles. Thus, the lipid component lability of the natural lipids allows us to reveal the action of components of the natural medium on the biological systems of various complexity even on the level of the complex biological model systems.

A New Approached Method for Solving the Four Index Transportation Problem with Fuzzy Parameters and Application Perspective in Industry

The four index transportation problem (4ITP: origin, destination, goods type, vehicle type) is an extension of the Hitchcock problem, a problem best suited for the goods allocation planning in the case for using the shuttle type. Based on the research results in 1979, in 2011, we developed an exact method for fully solving the 4ITP with determinist parameters. However, because of the limitation of human in recognizing the imprecise natural events in the decision making science, it is necessary to use fuzzy numbers for uncertain condition. By extending the problem toward this direction, in this paper, we develop a method, an extension of fuzzy programming, solving the 4ITP when all parameters such as the cost coefficients, the supply and demand quantities, the goods type and vehicle type quantities are fuzzy numbers and obey the Gaussian law in order 2. We use Gauss method in the fuzzy programming to obtain the costs under form of point cloud. From these results, we use Pham’s method, a method for the conventional 4ITP, to obtain a point cloud with the agglomerating costs. By using Kronechker’s method, we extract the obtained minimal cost under form of an interval for a given solution. It allows us to obtain a goods allocation planning with the minimal total transportation cost.

Программные средства высокоуровневого синтеза для многокристальных реконфигурируемых вычислительных систем

The article describes an original complex of high-level synthesis that converts sequential programs into a circuit configuration of specialized hardware for reconfigurable computing systems. An absolutely parallel form, an information graph, is constructed from the original sequential program. Further, the graph is transformed into a resource-independent parallel–pipeline form — a personnel structure that can be adapted to various hardware resources. The transformation of the personnel structure into an information-equivalent structure, but occupying a smaller hardware resource, is performed using formalized methods of performance reduction, which allows you to automatically obtain a rational solution for a given multi-chip reconfigurable computing system. Unlike the known means of high-level synthesis, the result of the transformation is not the IP core of a computationally time-consuming fragment, but an automatically synchronized solution of an applied problem for all FPGA crystals of a reconfigurable computing system. Compared with parallelizing compilers, the number of analyzed variants of the synthesis of a rational solution is significantly less, which is a distinctive feature of the described complex. The application of high-level synthesis software is considered by the example of the problem of solving a system of linear algebraic equations by the Gauss method containing information-interdependent computational fragments with significantly different degrees of parallelism.

A sequential direct hybrid algorithm to compute stationary distribution of continuous-time Markov chain

In modeling a wide variety of problems of the real world using Markov processes, we usually get large sparse Markov chains. In the case of non-Markovian process, the behavior of a stochastic phenomenon or system can be approximated by continuous-time Markov chains (CTMC) using Phase-type distributions. However, this substantially increases the number of states, which requires a large amount of computation time and operational memory resources. Even the most recent computer hardware is not enough to provide a solution in almost real time, unless a specific algorithm is designed.In this paper, a new hybrid algorithm for the computation of a stationary distribution of a large ergodic homogeneous Markov chains with a finite state space and continuous time is suggested. This algorithm would solve the aforementioned challenges. Depending on model size and sparsity, it significantly reduces a computational time when compared with other recent methods, such as the SparseLU solver from Eigen library (version 3.9.9) and the MUMPS solver (MUltifrontal Massively Parallel sparse direct Solver, version 5.4.0). It is important to note that the algorithm works well independently on the structure of the generator matrix of a continuous-time Markov chain. For the study of the developed hybrid algorithm, the generator matrix is constructed randomly using a special algorithm, based on combining two methods: the slightly modified Grassmann, Taskar and Heyman (GTH) algorithm and the Gauss elimination method. The new idea is to remove the majority of states in a near-optimal order by the GTH method and complete computations for the remaining states by the Gauss method. The robust approach to identify a switching position from one algorithm to another one has been proposed and tested.

Information-modeling forecasting system for thermal mode of top converter lance

On basis of mathematical modeling and object-oriented programming, a computer information-modeling forecasting system (IMFS) for thermal mode of top lance barrel (TLB) of oxygen converter was developed in order to fulfill the urgent and economically feasible task of determining the compliance of input technological parameters with certain safety criteria for conducting converter melting.The program was created in the form of a Windows-oriented application by refining the previously developed mathematical model of the temperature mode of the top converter lance barrel using the object-oriented programming language C# in Microsoft Visual Studio 2019 IDE. The mathematical model provides the solution of differential heat conduction equation in cylindrical coordinates (two-dimensional formulation) with assignment of the initial (temperature distribution in the computational domain) and boundary conditions of the II and III kind (respectively, on the outer and inner surfaces of the TLB). The finite-difference approximation of the heat conduction equation and boundary conditions was obtained by the integro-interpolation method (balance method). A numerical sweep method (modified Gauss method) and an unconditionally stable implicit scheme were used to calculate the temperature field. Thermophysical values were obtained by approximating the corresponding tabular values. The application does not put forward special requirements for the computer infrastructure, operates locally (without the need for access to Internet), does not require special skills to work with it, having an intuitive user interface: the working area of the program consists of three windows (sections), in which the results of calculating the thermal mode of the TLB are displayed. The developed IMFS allows evaluating the design and technological parameters of the top blowing device as a criterion for its safe operation. Its application in the “advisor” mode ensures the optimal design of the top oxygen lances with a rational water cooling system in order to ensure the proper thermal mode of the TLB throughout the entire operation period, as well as trouble-free operation of the blowing device, which is especially important for the conditions of converter shops in Ukraine equipped with outdated designs of top lances with low service life.

Сравнение эффективности методов решения систем линейных уравнений в задаче моделирования контактного взаимодействия элементов твэла в термоупругой постановке

Various algorithms for solving systems of linear algebraic equations that arise when modeling problems of contact interaction of thermoelastic bodies with a changing configuration of the contact surface are considered. The implementations of modified iterative methods, the Uzawa method, as well as algorithms based on the use of the Gauss method and the generalized method of minimal residuals (GMRES) with two iterative refinement options allowing for the exit from contact of individual sections of the contact boundary are presented. The efficiency of the presented algorithms is compared in relation to a problem simulating thermomechanical processes in a section of a fuel element that includes up to 100 fuel pellets.

INHIBITORY EFFICIENCY AND PHYSICOCHEMICAL PROPERTIES OF LIPIDS FROM LEAVES AND JUICE OF ALOE ARBORESCENS Mill.

The composition of lipids isolated from leaves and juice of A. arborescens (7 years ago) and the inhibitory efficiency of lipids from leaves of A. arborescens were studied. The phospholipid (PL) fractions were divided by means of TLC method. The quantitative proportion of PL fractions was determined by spectrophotometrically. The more substantial differences in the composition of PL from leaves and juice of A. arcorescens are revealed in the proportion of the more poorly oxidizable fractions of PL. The more low relative content of PL in the total lipid composition from leaves compared with than in lipids from juice, and shares of sterols are the same for lipids from leaves and juice cause 16% diminution of the molar ratio of [sterols]/[PL] in lipids from juice of A. arborescens. Lipids from leaves are known to characterize the high inhibitory efficiency that is demonstrated by model of the low temperature autoxidation of methyl oleate in the thin layer. Using UV-spectroscopy and the mathematic analysis of spectra by Gauss method the presence of the biologically active substances which contain in lipids was analysed. There are only flavonoids in the chloroform solution of lipids from juice and flavonoids and carotenoids in the small quantity in the chloroform solution of lipids from the leaves of A. arborescens.

The Investigation of Nonlinear Polynomial Control Systems

The paper considers methods for estimating stability using Lyapunov functions, which are used for nonlinear polynomial control systems. The apparatus of the Gro¨bner basis method is used to assess the stability of a dynamical system. A description of the Gro¨bner basis method is given. To apply the method, the canonical relations of the nonlinear system are approximated by polynomials of the components of the state and control vectors. To calculate the Gro¨bner basis, the Buchberger algorithm is used, which is implemented in symbolic computation programs for solving systems of nonlinear polynomial equations. The use of the Gro¨bner basis for finding solutions of a nonlinear system of polynomial equations is considered, similar to the application of the Gauss method for solving a system of linear equations. The equilibrium states of a nonlinear polynomial system are determined as solutions of a nonlinear system of polynomial equations. An example of determining the equilibrium states of a nonlinear polynomial system using the Gro¨bner basis method is given. An example of finding the critical points of a nonlinear polynomial system using the Gro¨bner basis method and the Wolfram Mathematica application software is given. The Wolfram Mathematica program uses the function of determining the reduced Gro¨bner basis. The application of the Gro¨bner basis method for estimating the attraction domain of a nonlinear dynamic system with respect to the equilibrium point is considered. To determine the scalar potential, the vector field of the dynamic system is decomposed into gradient and vortex components. For the gradient component, the scalar potential and the Lyapunov function in polynomial form are determined by applying the homotopy operator. The use of Gro¨bner bases in the gradient method for finding the Lyapunov function of a nonlinear dynamical system is considered. The coordination of input-output signals of the system based on the construction of Gro¨bner bases is considered.