Search results for: Newton- Cotes formula

Authors: Ayse Bicer, Filiz Kar

Abstract:

This paper describes an experimental investigation of the drying behavior and conditions of rosehip in a convective cyclone-type dryer. Drying experiments were conducted at air inlet temperatures of 50, 60 and 70 o C and air velocities of 0.5, 1 and 1.5 ms–1. The parametric values obtained from the experiments were fitted to the Newton mathematical models. Consequently, the drying model developed by Newton model showed good agreement with the data obtained from the experiments. Concluding, it was obtained that; (i) the temperature is the major effect on the drying process, (ii) air velocity has low effect on the drying of rosehip, (iii) the C-vitamin is observed to change according to the temperature, moisture, drying time and flow types. The changing ratio is found to be in the range of 0.70-0.74.

Keywords: Rosehip, drying, food quality.

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two dimensional Helmholtz equation. The formulation is based on the nine-point fourth order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: Explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula.

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Authors: Olusheye Akinfenwa, Samuel Jator, Nianmin Yoa

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A block backward differentiation formula of uniform order eight is proposed for solving first order stiff initial value problems (IVPs). The conventional 8-step Backward Differentiation Formula (BDF) and additional methods are obtained from the same continuous scheme and assembled into a block matrix equation which is applied to provide the solutions of IVPs on non-overlapping intervals. The stability analysis of the method indicates that the method is L0-stable. Numerical results obtained using the proposed new block form show that it is attractive for solutions of stiff problems and compares favourably with existing ones.

Keywords: Stiff IVPs, System of ODEs, Backward differentiationformulas, Block methods, Stability.

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Authors: Jose William Porras Ferreira

Abstract:

This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power  and power  and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between  and power  through the Pascal’s triangle or  Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

zⁿ=xⁿ+yⁿ for n>2 and (x, y, z) E Z⁺ - {0}

 

Keywords: Fermat’s Last Theorem, Pythagorean Theorem, Newton Binomial Coefficients, Pascal’s Triangle, Well Ordering Principle.

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Authors: Kreangkri Ratchagit

Abstract:

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.

Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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Authors: Elena Kotevska

Abstract:

This paper presents a generalization kernel for gravitational potential determination by harmonic splines. It was shown in [10] that the gravitational potential can be approximated using a kernel represented as a Newton integral over the real Earth body. On the other side, the theory of geopotential approximation by harmonic splines uses spherically oriented kernels. The purpose of this paper is to show that in the spherical case both kernels have the same type of representation, which leads us to conclusion that it is possible to consider the kernel represented as a Newton integral over the real Earth body as a kind of generalization of spherically harmonic kernels to real geometries.

Keywords: Geopotential, Reproducing Kernel, Approximation, Regular Surface

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Authors: Warachate Khobjai, Suriyan Sukati, Khemjira Jarmkom, Pattaranut Eakwaropas, Surachai Techaoei

Abstract:

The propose of this study was to investigate in vitro thrombolytic activity of Zingiber cassumunar Roxb. and Prasaplai, a Thai herbal formulation of Z. cassumunar Roxb. Herbs were extracted with boiling water and concentrated by lyophilization. To observe their thrombolytic potential, an in vitro clot lysis method was applied where streptokinase and sterile distilled water were used as positive and negative controls, respectively. Crude aqueous extracts from Z. cassumunar Roxb. and Prasaplai formula showed significant thrombolytic activity by clot lysis of 17.90% and 25.21%, respectively, compared to the negative control water (5.16%) while the standard streptokinase revealed 64.78% clot lysis. These findings suggest that Z. cassumunar Roxb. exhibits moderate thrombolytic activity and cloud play an important role in the thrombolytic properties of Prasaplai formula. However, further study should be done to observe in vivo clot dissolving potential and to isolate active component(s) of these extracts.

Keywords: Aqueous extract, prasaplai formula, thrombolytic activity, Zingiber cassumunar Roxb.

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Authors: Hsian Ming Goo

Abstract:

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: Young Hoon Lee, Bong Jin Kang, Won Ho Kang

Abstract:

Antiseismic property of telecommunication equipment is very important for the grasp of the damage and the restoration after earthquake. Telecommunication business operators are regulating seismic standard for their equipments. These standards are organized to simulate the real seismic situations and usually define the minimum value of first natural frequency of the equipments or the allowable maximum displacement of top of the equipments relative to bottom. Using the finite element analysis, natural frequency can be obtained with high accuracy but the relative displacement of top of the equipments is difficult to predict accurately using the analysis. Furthermore, in the case of simulating the equipments with access floor, predicting the relative displacement of top of the equipments become more difficult. In this study, using enormous experimental datum, an empirical formula is suggested to forecast the relative displacement of top of the equipments. Also it can be known that which physical quantities are related with the relative displacement.

Keywords: Empirical formula, First natural frequency, Seismic test, Telecommunication equipments.

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Authors: Tan K. B., Norhashidah Hj. M. Ali

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In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Kholod M. Abu-Alnaja

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In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: O. Benaziz, A. Dorbane, S. Djeraba

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The objective of this work is to formulate a dry dispersible form of furosemide in the context of pediatric dose adjustment. To achieve this, we have produced a set of formulas that will be tested in process and after compression. The formula with the best results will be improved to optimize the final shape of the product. Furosemide is the most widely used pediatric diuretic because of its low toxicity. The manufacturing process was chosen taking into account all the data relating to the active ingredient and the excipients used and complying with the specifications and requirements of dispersible tablets. The process used to prepare these tablets was wet granulation. Different excipients were used: lactose, maize starch, magnesium stearate and two superdisintegrants. The mode of incorporation of super-disintegrant changes with each formula. The use of super-disintegrant in the formula allowed optimization of the disintegration time. Prepared tablets were evaluated for weight, content uniformity, hardness, disintegration time, friability and in vitro dissolution test. 

Keywords: Formulation, dispersible tablets, wet granulation, superdisintegrants, disintegration.

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Authors: C. Vrekos, C. Evagelides, N. Samarinas, G. Arampatzis

Abstract:

As known, the water energy is a renewable and clean source of energy. Energy production from hydropower has been the first, and still is today a renewable source used to generate electricity. The optimal location and sizing of a small hydropower plant is a very important issue in engineering design which encourages investigation. The aim of this paper is to present a formula that can be utilized for locating the position of a small hydropower plant although there is a high dependence on economic, environmental, and social parameters. In this paper, the economic and technical side of the problem is considered. More specifically, there is a critical terrain slope that determines if the plant should be located at the end of the slope or not. Of course, this formula can be used for a first estimate and does not include detailed economic analysis. At the end, a case study is presented for the location of a small hydropower plant in order to demonstrate the validity of the proposed formula.

Keywords: Critical terrain slope, economic analysis, hydropower plant locating, renewable energy.

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Authors: Aymen Laadhari

Abstract:

We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

Keywords: Finite element method, Newton method, level set, Navier-Stokes, inextensible membrane, liquid drop.

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Authors: Rana Khalid Naeem, Asif Mansoor

Abstract:

In this communication an expression for mean velocity of waste flow via an open channel is proposed which is an improvement over Manning formula. The discharges, storages and depths are computed at all locations of the Lyari river by utilizing proposed expression. The results attained through proposed expression are in good agreement with the observed data and better than those acquired using Manning formula.

Keywords: Comparison, Depth, Flow, Open Channel, Proposed Model, Storage

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Authors: M. Oloomi-Buygi, M. Reza Salehizadeh

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In this paper a new approach for transmission pricing is presented. The main idea is voltage angle allocation, i.e. determining the contribution of each contract on the voltage angle of each bus. DC power flow is used to compute a primary solution for angle decomposition. To consider the impacts of system non-linearity on angle decomposition, the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow. Then, the contribution of each contract on power flow of each transmission line is computed based on angle decomposition. Contract-related flows are used as a measure for “extent of use" of transmission network capacity and consequently transmission pricing. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system.

Keywords: Deregulation, Power electric markets, Transmission pricing methodologies, decoupled Newton-Raphson power flow.

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Authors: Aymen Laadhari, Gábor Székely

Abstract:

This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the presented method. We show that stability is maintained for significantly larger time steps.

Keywords: Fluid-membrane interaction, stretching, Eulerian, finite element method, Newton, implicit.

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Authors: Khalid Minaoui, Thierry Chonavel, Benayad Nsiri, Driss Aboutajdine

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This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

Keywords: Gauss-Legendre, Clenshaw-Curtis, quadrature, Peano kernel, irregular sampling.

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Authors: Nisa Rachmania Mubarik, Tedja Imas, Aris Tri Wahyudi , Triadiati , Suharyanto, Happy Widiastuti

Abstract:

Land with low pH soil spread widely in Indonesia can be used for soybean (Glycine max) cultivation, however the production is low. The use of acid tolerant soybean and acidaluminium tolerant nitrogen-fixing bacteria formula was an alternative way to increase soybean productivity on acid soils. Bradyrhizobium japonicum is one of the nitrogen fixing bacteria which can symbiose with soybean plants through root nodule formation. Most of the nitrogen source required by soybean plants can be provided by this symbiosis. This research was conducted to study the influence of acid-aluminium tolerant B. japonicum strain BJ 11 formula using peat as carrier on growth of Tanggamus and Anjasmoro cultivar soybean planted on acid soil fields (pH 5.0- 5.5). The results showed that the inoculant was able to increase the growth and production of soybean which were grown on fields acid soil at Sukadana (Lampung) and Tanah Laut (South Kalimantan), Indonesia.

Keywords: Bradyrhizobium japonicum, acid-aluminium tolerant mutant, Tanggamus cultivar soybean, acid soils

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Authors: Y. A. Chan, H. J. Liu, K. C. Tseng, T. C. Kuo

Abstract:

Green propellants used for satellite-level propulsion system become attractive in recent years because the non-toxicity and lower requirements of safety protection. One of the green propellants, high-concentration hydrogen peroxide H2O2 solution (≥70% w/w, weight concentration percentage), often known as high-test peroxide (HTP), is considered because it is ITAR-free, easy to manufacture and the operating temperature is lower than traditional monopropellant propulsion. To establish satellite propulsion technology, the National Space Organization (NSPO) in Taiwan has initialized a long-term cooperation project with the National Cheng Kung University to develop compatible tank and thruster. An experimental propulsion payload has been allocated for the future self-reliant satellite to perform orbit transfer and maintenance operations. In the present research, an 1-Newton thruster prototype is designed and the thrusting force is measured by a pendulum-type platform. The preliminary hot-firing test at ambient environment showed the generated thrust and the specific impulse are about 0.7 Newton and 102 seconds, respectively.

Keywords: Hydrogen peroxide, propulsion, RCS, satellite.

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Authors: Zeyu Zhang, Guisheng Yin, Ziying Zhang, Liguo Zhang

Abstract:

This paper mainly studies the path planning method based on ant colony optimization (ACO), and proposes heuristic integration ant colony optimization (HIACO). This paper not only analyzes and optimizes the principle, but also simulates and analyzes the parameters related to the application of HIACO in path planning. Compared with the original algorithm, the improved algorithm optimizes probability formula, tabu table mechanism and updating mechanism, and introduces more reasonable heuristic factors. The optimized HIACO not only draws on the excellent ideas of the original algorithm, but also solves the problems of premature convergence, convergence to the sub optimal solution and improper exploration to some extent. HIACO can be used to achieve better simulation results and achieve the desired optimization. Combined with the probability formula and update formula, several parameters of HIACO are tested. This paper proves the principle of the HIACO and gives the best parameter range in the research of path planning.

Keywords: Ant colony optimization, heuristic integration, path planning

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Authors: Jiří Primas, Michal Malík, Darina Jašíková, Václav Kopecký

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When a high DC voltage is applied to a capacitor with strongly asymmetrical electrodes, it generates a mechanical force that affects the whole capacitor. This phenomenon is most likely to be caused by the motion of ions generated around the smaller of the two electrodes and their subsequent interaction with the surrounding medium. A method to measure this force has been devised and used. A formula describing the force has also been derived. After comparing the data gained through experiments with those acquired using the theoretical formula, a difference was found above a certain value of current. This paper also gives reasons for this difference.

Keywords: Capacitor with asymmetrical electrodes, Electricalfield, Mechanical force, Motion of ions.

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Authors: Udomsak Thongkrajay, Padej Pao-La-Or, Thanatchai Kulworawanichpong

Abstract:

Installation of power compensation equipment in some cases places additional buses into the system. Therefore, a total number of power flow equations and voltage unknowns increase due to additional locations of installed devices. In this circumstance, power flow calculation is more complicated. It may result in a computational convergence problem. This paper presents a power flow calculation by using Newton-Raphson iterative method together with the proposed load transfer technique. This concept is to eliminate additional buses by transferring installed loads at the new buses to existing two adjacent buses. Thus, the total number of power flow equations is not changed. The overall computational speed is expectedly shorter than that of solving the problem without applying the load transfer technique. A 15-bus test system is employed for test to evaluate the effectiveness of the proposed load transfer technique. As a result, the total number of iteration required and execution time is significantly reduced.

Keywords: Load transfer technique, Newton-Raphson power flow, ill-condition

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Authors: Guoyuan Qi , Yskandar Hamam, Barend Jacobus van Wyk, Shengzhi Du

Abstract:

The majority of existing predictors for time series are model-dependent and therefore require some prior knowledge for the identification of complex systems, usually involving system identification, extensive training, or online adaptation in the case of time-varying systems. Additionally, since a time series is usually generated by complex processes such as the stock market or other chaotic systems, identification, modeling or the online updating of parameters can be problematic. In this paper a model-free predictor (MFP) for a time series produced by an unknown nonlinear system or process is derived using tracking theory. An identical derivation of the MFP using the property of the Newton form of the interpolating polynomial is also presented. The MFP is able to accurately predict future values of a time series, is stable, has few tuning parameters and is desirable for engineering applications due to its simplicity, fast prediction speed and extremely low computational load. The performance of the proposed MFP is demonstrated using the prediction of the Dow Jones Industrial Average stock index.

Keywords: Forecast, model-free predictor, prediction, time series

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Authors: Abdulrahman Abdulrahman

Abstract:

A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

Keywords: Analytical solution, combined channel, exponential channel, side weirs, trapezoidal channel, water surface profile.

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Authors: Yang Chengmei

Abstract:

In this paper, taking Chinese Nanjing Metro ALSTOM vehicle synthesis brake as an example, the subway with synthetic brake shoe formula components of final product performance, has done a lot of research and performance test, final is drawn with hybrid fiber as reinforcing material, modified phenolic resin as matrix material, and then filling friction modifier performance, by the hot pressing process made a new type of domestic subway brake shoe. The product of the test performance indicators that can replace the similar foreign products.

Keywords: Metro, synthetic brake shoe, component analysis, formula research.

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Authors: Mutuku Muvengei, John Kihiu

Abstract:

This paper focuses on the development of bond graph dynamic model of the mechanical dynamics of an excavating mechanism previously designed to be used with small tractors, which are fabricated in the Engineering Workshops of Jomo Kenyatta University of Agriculture and Technology. To develop a mechanical dynamics model of the manipulator, forward recursive equations similar to those applied in iterative Newton-Euler method were used to obtain kinematic relationships between the time rates of joint variables and the generalized cartesian velocities for the centroids of the links. Representing the obtained kinematic relationships in bondgraphic form, while considering the link weights and momenta as the elements led to a detailed bond graph model of the manipulator. The bond graph method was found to reduce significantly the number of recursive computations performed on a 3 DOF manipulator for a mechanical dynamic model to result, hence indicating that bond graph method is more computationally efficient than the Newton-Euler method in developing dynamic models of 3 DOF planar manipulators. The model was verified by comparing the joint torque expressions of a two link planar manipulator to those obtained using Newton- Euler and Lagrangian methods as analyzed in robotic textbooks. The expressions were found to agree indicating that the model captures the aspects of rigid body dynamics of the manipulator. Based on the model developed, actuator sizing and valve sizing methodologies were developed and used to obtain the optimal sizes of the pistons and spool valve ports respectively. It was found that using the pump with the sized flow rate capacity, the engine of the tractor is able to power the excavating mechanism in digging a sandy-loom soil.

Keywords: Actuators, bond graphs, inverse dynamics, recursive equations, quintic polynomial trajectory.

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Authors: Martin Cermak, Stanislav Sysala

Abstract:

In this paper we present the efficient parallel implementation of elastoplastic problems based on the TFETI (Total Finite Element Tearing and Interconnecting) domain decomposition method. This approach allow us to use parallel solution and compute this nonlinear problem on the supercomputers and decrease the solution time and compute problems with millions of DOFs. In our approach we consider an associated elastoplastic model with the von Mises plastic criterion and the combination of linear isotropic-kinematic hardening law. This model is discretized by the implicit Euler method in time and by the finite element method in space. We consider the system of nonlinear equations with a strongly semismooth and strongly monotone operator. The semismooth Newton method is applied to solve this nonlinear system. Corresponding linearized problems arising in the Newton iterations are solved in parallel by the above mentioned TFETI. The implementation of this problem is realized in our in-house MatSol packages developed in MatLab.

Keywords: Isotropic-kinematic hardening, TFETI, domain decomposition, parallel solution.

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Authors: Alena Zemanová, Jan Zeman, Michal Šejnoha

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The polymer foil used for manufacturing of laminated glass members behaves in a viscoelastic manner with temperature dependance. This contribution aims at incorporating the time/temperature-dependent behavior of interlayer to our earlier elastic finite element model for laminated glass beams. The model is based on a refined beam theory: each layer behaves according to the finite-strain shear deformable formulation by Reissner and the adjacent layers are connected via the Lagrange multipliers ensuring the inter-layer compatibility of a laminated unit. The time/temperature-dependent behavior of the interlayer is accounted for by the generalized Maxwell model and by the time-temperature superposition principle due to the Williams, Landel, and Ferry. The resulting system is solved by the Newton method with consistent linearization and the viscoelastic response is determined incrementally by the exponential algorithm. By comparing the model predictions against available experimental data, we demonstrate that the proposed formulation is reliable and accurately reproduces the behavior of the laminated glass units.

Keywords: Laminated glass, finite element method, finite-strain Reissner model, Lagrange multipliers, generalized Maxwell model, Williams-Landel-Ferry equation, Newton method.

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