Search results for: inversion method

Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: L. Fridrichova, R. Knížek, V. Bajzík

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Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: drape, drape shape, automated drapemeter, fabric

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Ting Pan, Jiacheng Wang, Pengcheng Lin, Ying Chen, Songping Mo

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Phase change materials (PCMs) are widely used in latent heat thermal energy storage because of their good properties such as high energy storage density and constant heat-storage/release temperature. Microencapsulation techniques can prevent PCMs from leaking during the liquid-solid phase transition and enhance thermal properties. This technique has been widely applied in architectural materials, thermo-regulated textiles, aerospace fields, etc. One of the most important processes during the synthesis of microcapsules is to form a stable emulsion of the PCM core and reactant solution for the formation of the shell of the microcapsules. The use of surfactants is usually necessary for the formation of a stable emulsion system because of the difference in hydrophilia/lipophilicity of the PCM and the solvent. Unfortunately, the use of surfactants may cause pollution to the environment. In this study, modified kaolinite was used as an emulsion stabilizer for the microencapsulation of octodecane as PCM. Microcapsules were synthesized by phase inversion emulsification method, and the shell of polymethyl methacrylate (PMMA) was formed through free radical polymerization. The morphologies, crystalloid phase, and crystallization properties of microcapsules were investigated using scanning electron microscopy (SEM), X-ray diffractometer (XRD), and Fourier transforms infrared spectrometer (FTIR). The thermal properties and thermal stability were investigated by a differential scanning calorimeter (DSC) and a thermogravimetric analyzer (TG). The FT-IR, XRD results showed that the octodecane was well encapsulated in the PMMA shell. The SEM results showed that the microcapsules were spheres with an average size of about 50-100nm. The DSC results indicated that the latent heat of the microcapsules was 152.64kJ/kg and 164.23kJ/kg. The TG results confirmed that the microcapsules had good thermal stability due to the PMMA shell. Based on the results, it can be concluded that the modified kaolinite can be used as an emulsifier for the synthesis of PCM microcapsules, which is valid for reducing part of the possible pollution caused by the utilization of surfactants.

Keywords: kaolinite, microencapsulation, PCM, thermal energy storage

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Authors: Chui Ka Shing

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This case study research attempts to examine the use of the Bar Model Method approach in learning and teaching mathematics in a primary school in Hong Kong. The objectives of the study are to find out to what extent (a) the Bar Model Method approach enhances the construction of students’ mathematics concepts, and (b) the school-based mathematics curriculum development with adopting the Bar Model Method approach. This case study illuminates the effectiveness of using the Bar Model Method to solve mathematics problems from Primary 1 to Primary 6. Some effective pedagogies and assessments were developed to strengthen the use of the Bar Model Method across year levels. Suggestions including school-based curriculum development for using Bar Model Method and further study were discussed.

Keywords: bar model method, curriculum development, mathematics education, problem solving

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Authors: Yang Zhong, Heng Liu

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The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Azizakhanim Maharramli

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The gradual transition from entrenched traditional technology and organization of construction production to innovative additive construction technology inevitably meets technological, technical, organizational, labour, and, finally, social difficulties. Therefore, the chosen nodal method will lead to the elimination of the above difficulties, combining some of the usual methods of construction and the myth in world practice that the labour force is subjected to a strong stream of reduction. The nodal method of additive technology will create favourable conditions for the optimal degree of distribution of labour across facilities due to the consistent performance of homogeneous work and the introduction of additive technology and traditional technology into construction production.

Keywords: parallel method, sequential method, stream method, combined method, nodal method

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Authors: Mahacine Amrani

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A simple and rapid method for the determination of alcohol in gasoline-alcohol mixtures using density measurements is described. The method can determine a minimum of 1% of alcohol by volume. The precision of the method is ± 3%.The method is more useful for field test in the quality assessment of alcohol blended fuels.

Keywords: gasoline-alcohol, mixture, alcohol determination, density, measurement, Morocco

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Jiankang Wang, Hongyang Yu

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This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.

Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Devinder Singh, Rajneesh Kumar, Arvind Kumar

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The present investigation deals with the deformation of micropolar generalized thermoelastic solid subjected to thermo-mechanical loading due to a thermal laser pulse. Laplace transform and Fourier transform techniques are used to solve the problem. Thermo-mechanical laser interactions are taken as distributed sources to describe the application of the approach. The closed form expressions of normal stress, tangential stress, coupled stress and temperature are obtained in the domain. Numerical inversion technique of Laplace transform and Fourier transform has been implied to obtain the resulting quantities in the physical domain after developing a computer program. The normal stress, tangential stress, coupled stress and temperature are depicted graphically to show the effect of relaxation times. Some particular cases of interest are deduced from the present investigation.

Keywords: pulse laser, integral transform, thermoelastic, boundary value problem

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Alkaben Patel

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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

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Authors: Phawichsak Prapassornpitaya, Wanida Jinsart

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Daily monitoring PM₁₀ and PM₂.₅ data from 2007 to 2017 were analyzed to provide baseline data for prediction of the air pollution in Bangkok in the period of 2018 -2020. Two statistical models, Autoregressive Integrated Moving Average model (ARIMA) were used to evaluate the trends of pollutions. The prediction concentrations were tested by root means square error (RMSE) and index of agreement (IOA). This evaluation of the traffic PM₂.₅ and PM₁₀ were studied in association with the regulatory control and emission standard changes. The emission factors of particulate matter from diesel vehicles were decreased when applied higher number of euro standard. The trends of ambient air pollutions were expected to decrease. However, the Bangkok smog episode in February 2018 with temperature inversion caused high concentration of PM₂.₅ in the air environment of Bangkok. The impact of traffic pollutants was depended upon the emission sources, temperature variations, and metrological conditions.

Keywords: fine particulate matter, ARIMA, RMSE, Bangkok

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Authors: Geeta Partap, Nitika Chugh

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The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: microstretch, deflection, exponential load, Laplace transforms, residue theorem, simply supported

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Guettal Djaouida, Ziadi Abdelkader

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In this paper, we study a coupling of the Alienor method with the algorithm of Piyavskii-Shubert. The classical multidimensional global optimization methods involves great difficulties for their implementation to high dimensions. The Alienor method allows to transform a multivariable function into a function of a single variable for which it is possible to use efficient and rapid method for calculating the the global optimum. This simplification is based on the using of a reducing transformation called Alienor.

Keywords: global optimization, reducing transformation, α-dense curves, Alienor method, Piyavskii-Shubert algorithm

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

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The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: exponential smoothing method, open data, operation estimation, train schedule

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Authors: Nanine Fouche

Abstract:

The Cape Flats is a low-lying sand-covered expanse of approximately 460 square kilometres, situated to the southeast of the central business district of Cape Town in the Western Cape of South Africa. The aeolian sands masking this area are often loose and compressible in the upper 1m to 1.5m of the surface, and there is a general exceedance of the maximum allowable settlement in these sands. The settlement of shallow foundations on Cape Flats sands is commonly predicted using the results of in-situ tests such as the SPT or DPSH due to the difficulty of retrieving undisturbed samples for laboratory testing. Varying degrees of accuracy and reliability are associated with these methods. More recently, shear wave velocity (Vs) profiles obtained from seismic testing, such as continuous surface wave tests (CSW), are being used for settlement prediction. Such predictions have the advantage of considering non-linear stress-strain behaviour of soil and the degradation of stiffness with increasing strain. CSW tests are rarely executed in the Cape Flats, whereas SPT’s are commonly performed. For this reason, and to facilitate better settlement predictions in Cape Flats sand, equations representing shear wave velocity (Vs) as a function of SPT blow count (N60) and vertical effective stress (v’) were generated by statistical regression of site investigation data. To reveal the most appropriate method of overburden correction, analyses were performed with a separate overburden term (Pa/σ’v) as well as using stress corrected shear wave velocity and SPT blow counts (correcting Vs. and N60 to Vs1and (N1)60respectively). Shear wave velocity profiles and SPT blow count data from three sites masked by Cape Flats sands were utilised to generate 80 Vs-SPT N data pairs for analysis. Investigated terrains included sites in the suburbs of Athlone, Muizenburg, and Atlantis, all underlain by windblown deposits comprising fine and medium sand with varying fines contents. Elastic settlement analysis was also undertaken for the Cape Flats sands, using a non-linear stepwise method based on small-strain stiffness estimates, which was obtained from the best Vs-N60 model and compared to settlement estimates using the general elastic solution with stiffness profiles determined using Stroud’s (1989) and Webb’s (1969) SPT N60-E transformation models. Stroud’s method considers strain level indirectly whereasWebb’smethod does not take account of the variation in elastic modulus with strain. The expression of Vs. in terms of N60 and Pa/σv’ derived from the Atlantis data set revealed the best fit with R2 = 0.83 and a standard error of 83.5m/s. Less accurate Vs-SPT N relations associated with the combined data set is presumably the result of inversion routines used in the analysis of the CSW results showcasing significant variation in relative density and stiffness with depth. The regression analyses revealed that the inclusion of a separate overburden term in the regression of Vs and N60, produces improved fits, as opposed to the stress corrected equations in which the R2 of the regression is notably lower. It is the correction of Vs and N60 to Vs1 and (N1)60 with empirical constants ‘n’ and ‘m’ prior to regression, that introduces bias with respect to overburden pressure. When comparing settlement prediction methods, both Stroud’s method (considering strain level indirectly) and the small strain stiffness method predict higher stiffnesses for medium dense and dense profiles than Webb’s method, which takes no account of strain level in the determination of soil stiffness. Webb’s method appears to be suitable for loose sands only. The Versak software appears to underestimate differences in settlement between square and strip footings of similar width. In conclusion, settlement analysis using small-strain stiffness data from the proposed Vs-N60 model for Cape Flats sands provides a way to take account of the non-linear stress-strain behaviour of the sands when calculating settlement.

Keywords: sands, settlement prediction, continuous surface wave test, small-strain stiffness, shear wave velocity, penetration resistance

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