Automated Framework for Water Looped Network Equilibrium

Cemara Hijau Housing Complex is an elite housing complex located on the outskirts of Medan which each year has an increasing number of consumers not followed by increased network capacity and clean water supply. This study aims to analyze the pattern of water consumption of customers in the Green Pine complex, analyzing the availability of PDAM Tirtanadi water of Cemara branches with water needs of Cemara Hijau customers and analyzing the clean water distribution system in Cemara Hijau housing using Hardy Cross method with Hazen William and Epanet 2.0 equations. The research method used is to first conduct literature studies related to clean water distribution system and Epanet 2.0 application. Then collect the required data that is primary data and secondary data. Then the data data is analyzed by manual calculation of Hardy Cross with Hazen William equation and using computer software that is Epanet 2.0. The result of research is the pattern of clean water consumption in the green pine complex with the highest factor is 1.69 while the lowest is 0.21, then the water loss at the Cemara Hijau Housing Complex is 52.93%, then the clean water distribution network system in the Cemara Hijau Housing Complex does not meet in terms of flow and pressure, so that the solution given is the addition of 50 mm diameter made in parallel, the last of the total difference obtained from Epanet 2.0 with a large enough field for the hourly of 0.0766 m3/sec and for 24 hours of 4.3878 m3/sec, and the total difference between Epanet 2.0 with Hardy Cross method with Hazen William equation is not too large with a total difference of 0.00048 m3/sec or 0.48 liter/sec.

A theoretical analysis of steady and unsteady magnetohydrodynamic (MHD) flow of blood through a stenosed artery with variable viscosity and slip conditions is presented in this work. Slip conditions and variable viscosity dependent on hematocrit for both steady and unsteady blood flow models are taken into consideration in this study. The governing equations have been derived by treating blood as incompressible magnetohydrodynamic (MHD) Newtonian fluid. Galerkin Weighted Residual method, Newton Raphson method and fourth order Runge-Kutta method are used to solve the non-linear differential equations for velocity profiles of the blood flow, flow rate, shear stress and flow resistance for different values of hematocrit parameter, magnetic field parameter and slip velocity. The Galerkin Weighted Residual method is applied to transform the partial differential equations describing the flow into systems of non-linear equations and system of non-linear first order differential equations for the time independent and time dependent MHD flow models respectively. Newton Raphson’s method with the aid of maple software is used to solve the system of non-linear equations while the fourth order Runge-Kutta method is used to solve the system of non-linear first order differential equations. The research analyzed how the flow velocity, flow rate, shear stress and resistance to fluid flow respond to changes in some key parameters such as hematocrit parameter, magnetic field parameter and slip velocity. The results as presented graphically reveal that flow velocity and flow rate decrease while shear stress and resistance to flow increase when the hematocrit parameter increases. Also, flow velocity, flow rate and shear stress increase while resistance to flow decrease when the slip velocity increases. Finally, the increase in magnetic field parameter led to a decrease in flow velocity, flow rate and shear stress but increased the flow resistance. The flow velocity of the unsteady blood flow model is higher when compared to steady blood flow model.

Subject. This article focuses on the problems of solving systems of homogeneous linear algebraic equations in the pricing problems of an alternative financial model. Objectives. The article aims to develop a non-trivial approach to solving the problem of pricing from the scratch in the construction of a national alternative financial model, which boils down to solving large homogeneous systems of linear algebraic equations, complicated by the fuzzy setting of initial parameters (initial data) within the framework of creating a State model of a socially oriented economy, guaranteed to ensure economic, military and other types of integrated security of the Russian Federation. Methods. For the study, we used tensorial notations involving the use of elements of linear algebra, including operations with matrices and vectors, the apparatus of the fuzzy set theory (interval arithmetic), as well as methods and principles of scientific research and complex logical analysis and modeling of pricing and technological processes. Results. The article shows that an effective non-zero (different from zero, i.e. classical, trivial) solution of systems of homogeneous algebraic equations in pricing problems of an alternative financial model from the scratch is possible if the initial parameters are specified by fuzzy sets, which significantly simplifies the procedure of the computational process and the volume of arithmetic operations. Conclusions. The results obtained can be used in structures involved in the creation and testing of financial and economic models both at the federal and the Russian Federation constituent entity levels, as well as in governmental and non-governmental organizations dealing with the issues of pricing, planning and logistics support for business entities not only in the Russian Federation, but also in other countries experiencing problems in the field of financing.

A mathematical model is developed for predicting the steady-state flow pattern for a water distribution system consisting of conduits, pumps, pressure-reducing valves, and reservoirs. The model is a computerized numerical simulation of the network. Because each component of the network is governed by a nonlinear flow formula, the equilibrium of flow in the network is governed by a system of nonlinear equations. The solution to this system is sought by the Newton iteration method. The model is verified against the Hardy Cross method and applied to the determination of the flow pattern of an actual water network.

In this study, Newton–Raphson Based (NRB) scalar speed control (SSC) is recommended to control the speed of Induction Motors (IM). As is known, the Newton–Raphson method, which is often used in numerical analysis, is one of the methods that provide a rapid convergence of the desired value. In this study, the frequency value required for the desired speed value is calculated by Newton–Raphson method. Three different models including Newton–Raphson Based + Scalar Speed Control (NRB_SSC), Difference Speed + NRB_SSC (DS_NRB_SSC), DS + NRB_SSC + Difference Frequency (DS_NRB_SSC_DF) were used for optimization tests. Simulation of the work was done in Matlab/Simulink programme. According to obtained test results DS_NRB_SSC_DF has produced better results.

Stokes flow in the branches of structured looped networks with successive identical square loops and T-junction branches is studied. Analytical expressions of the flow rate in the branches are determined for network of one, two, three, or four loops with junction head loss neglected relative to regular one. Then, a general expression of the flow rate is deduced for networks with more loops. This expression contains particularly a sequence of coefficients obeying to a recurrence formula. This sequence is a part of the fusion of Fibonacci and Tribonacci sequences. Furthermore, a general formula that expresses the quotient of flow rate in successive junction flow branches is given. The limit of this quotient for an infinite number of junction branches is found to be equal to 2+3. When the inlet and outlet flow rates are equal, this quotient obeys to a sequence of invariant numbers whatever the ratio of flow rate in the outlet branches is. Thus, the flow rate distribution for any configuration of inlet and outlet flow rates can be calculated. This study is also performed using Hardy–Cross method and a commercial solver of Navier-Stokes equation. The analytical results are approached very well with Hardy–Cross method. The numerical resolution agrees also with analytical results. However, the difference with the numerical results becomes significant for low flow rate in the junction branches. The flow streamlines are then determined for some inlet and outlet flow rate configurations. They particularly illustrate that recirculation flow takes place in branches of low flow rate.

At the core of every system for the efficient control of the network steady-state operation is the AC-power-flow problem solver. For local distribution networks to continue to operate effectively, it is necessary to use the most powerful and numerically stable AC-power-flow problem solvers within the software that controls the power flows in these networks. This communication presents the results of analyses of the computational performance and stability of three methods for solving the AC-power-flow problem. Specifically, this communication compares the robustness and speed of execution of the Gauss–Seidel (G–S), Newton–Raphson (N–R), and Newton–Raphson method with Iwamoto multipliers (N–R–I), which were tested in open-source pandapower software using a meshed electrical network model of various topologies. The test results show that the pandapower implementations of the N–R method and the N–R–I method are significantly more robust and faster than the G–S method, regardless of the network topology. In addition, a generalized Python interface between the pandapower and the SciPy package was implemented and tested, and results show that the hybrid Powell, Levenberg–Marquardt, and Krylov methods, a quasilinearization algorithm, and the continuous Newton method can sometimes achieve better results than the classical N–R method.

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command “while”.

In this article, the authors report the Chebyshev pseudospectral method for solving twodimensional nonlinear Schrodinger equation with fractional order derivative in time and space both. The modified Riemann-Liouville fractional derivatives are used to define the new fractional derivatives matrix at CGL points. Using the Chebyshev fractional derivatives matrices, the given problem is reduced to a diagonally block system of nonlinear algebraic equations, which will be solved using Newton's Raphson method. The proposed methods have shown error analysis without any dependency on time and space step restrictions. Some model examples of the equations, defined on a convex and rectangular domain, have tested with various values of fractional order <i>α</i> and <i>β</i>. Moreover, numerical solutions are demonstrated to justify the theoretical results.

PurposeThe paper aims to improve convergence characteristics of the Newton–Raphson (NR) method applied to time-periodic finite element method using various line searches, as time-periodic finite element method causes deterioration of convergence characteristic of nonlinear analysis based on NR method. The study also aims to accelerate and improve accuracy of electromagnetic field analysis for improvement of the performance of electrical machine.Design/methodology/approachThe paper proposes new type line searches that set approximate step size for NR method. The line search evaluated step size using higher-order interpolation of functional derivative. In addition, two criteria for applying these line search were proposed. First method set one scalar value for every NR iteration that is named constant step size. Second method define different step size in each time step of time-periodic finite element method to update solution vector that is named different step size.FindingsThe paper provides efficient line searches to improve convergence characteristics for NR method. Nonlinear magnetic field analysis of two transformer models is demonstrated. The proposed methods achieve the following results: higher-order functional NR is efficient in improving convergence characteristics, and the proposed methods succeeded about twice faster in both models.Originality/valueThe paper fulfills improvement of convergence characteristics of the NR method applied to time-periodic finite element method using proposed line searches and accelerate electromagnetic field analysis.

The exact Riemann Solver to the Shallow Water equations for natural channels with bottom steps

Publication Rights Reserved This paper was prepared for the Society of Petroleum Engineers Gas Technology Symposium to be held in Omaha, Nebr. Sept. 15–16, 1966. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper attacks the problem of computing transient flow in gas pipeline networks by means of finite differences and digital computation. Pressure (P) and flow (Q) are assumed to he dependent upon a single space variable (x) along the pipe and on the time (t). A greatly simplified but generally accepted mathematical model consistent, of a system of nonlinear partial differential equations is the point of departure: Following simple changes of variable (w = p2, v = Q2), the problem is reduced to the solution of: A stable predictor-corrector method of finite difference approximation due to Jim Douglas, Jr. and B.R. Jones, Jr. is employed to reduce the computation to the solution of a system of linear algebraic equations (matrix inversion). The incorporation of initial conditions, boundary conditions, and internal flow conservation equations, all of which in finite difference form become linear algebraic equations, results in a single matrix equation for the calculation of pressures and flows in the pipeline network. DERIVATION OF FINITE DIFFERENCE EQUATIONS The computation of transient flow in gas pipeline networks is complicated mathematically by the nonlinearity of the governing partial differential equations. This is in marked contrast, of course, to the situation in steady state flow, where the corresponding equations, at least in their simplest form, have exact mathematical solutions. The mathematical model we assume has resulted from a number of simplifications, including the neglect of altitude and temperature variation. Although it is beyond the scope of this note to discuss the validity and significance of these simplifications, it is generally believed that the equations we will discuss are an accurate first order description of the actual physical system.

The program FANTOM (fast Newton–Raphson torsion angle energy minimizer) performs minimizations of the ECEPP/2 energy function for proteins with the Newton–Raphson method. It is implemented for use with conventional computer hardware. The torsion angles are chosen as independent variables. The first and second derivatives are calculated with a previously described rapid algorithm. For the matrix inversion a modified Cholesky factorization is used. A line search adjusts the step length and nonbonded interactions can be calculated with a cutoff. The following tests of the program are described: All local minima of the ECEPP/2 energy function for the amino acids glycine and alanine were determined. An exhaustive search by more than 16,000 independent energy minimizations was used to identify low‐energy structures of Met‐enkephalin, which were then compared with previously published structures of this pentapeptide. To investigate the use of FANTOM with disulfide bonds, it was applied with conotoxin. As an illustration of the intended primary use of the program, an energy refinement of the structure of the basic pancreatic trypsin inhibitor determined by nmr spectroscopy in solution is described.

It is difficult to accurately simulate supercurrent in high-temperature superconducting bulk even by adopting the finite-element method. The equivalent electrical conductivity of high-temperature superconducting bulk, which has a strong nonlinearity according to the E-J power law, is introduced for the supercurrent analysis. However, the strong nonlinearity results in bad convergency of the nonlinear equation solvers, i.e., the Newton-Raphson (NR) method. Consequently, the unsuitable and/or undulating supercurrent is observed. Therefore, in this paper, the accuracy of the supercurrent analysis in the high-temperature superconducting bulk is discussed and a new method is proposed for the accurate high-temperature superconducting bulk simulation. Then, the method combined a line search with the NR method is adopted as a nonlinear equation solver, and the improvement of convergency and computation time are investigated.

In this paper, a simple waveguide measurement technique is presented to determine the complex permittivity of a dielectric material. The dielectric sample is loaded in a short-circuited rectangular waveguide. The reflection coefficient of the waveguide is measured by Network analyser and calculated as a function of the complex permittivity using theory of transmissions lines. The Newton Raphson method is then used to determine de complex permittivity by matching the calculated value with the measured value. The results obtained using Newton Raphson are in good agreement with the results obtained by the Nicholson-Ross technique.