Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1450

Search results for: block backward differentiation formulae

1450 On the Derivation of Variable Step BBDF for Solving Second Order Stiff ODEs

Authors: S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, M. Suleiman


The method of solving second order stiff ordinary differential equation (ODEs) that is based on backward differentiation formula (BDF) is considered in this paper. We derived the method by increasing the order of the existing method using an improved strategy in choosing the step size. Numerical results are presented to compare the efficiency of the proposed method to the MATLAB’s suite of ODEs solvers namely ode15s and ode23s. The method was found to be efficient to solve second order ordinary differential equation.

Keywords: backward differentiation formulae, block backward differentiation formulae, stiff ordinary differential equation, variable step size

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1449 Modification of Newton Method in Two Point Block Backward Differentiation Formulas

Authors: Khairil I. Othman, Nur N. Kamal, Zarina B. Ibrahim


In this paper, we present modified Newton method as a new strategy for improving the efficiency of Two Point Block Backward Differentiation Formulas (BBDF) when solving stiff systems of ordinary differential equations (ODEs). These methods are constructed to produce two approximate solutions simultaneously at each iteration The detailed implementation of the predictor corrector BBDF with PE(CE)2 with modified Newton are discussed. The proposed modification of BBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing Block Backward Differentiation Formula. Numerical results show the advantage of using the new strategy for solving stiff ODEs in improving the accuracy of the solution.

Keywords: newton method, two point, block, accuracy

Procedia PDF Downloads 271
1448 Development of Variable Order Block Multistep Method for Solving Ordinary Differential Equations

Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman


In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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1447 Implementation of Fuzzy Version of Block Backward Differentiation Formulas for Solving Fuzzy Differential Equations

Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman


Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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1446 Modification of Newton Method in Two Points Block Differentiation Formula

Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim


Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

Procedia PDF Downloads 254
1445 The Development of a New Block Method for Solving Stiff ODEs

Authors: Khairil I. Othman, Mahfuzah Mahayaddin, Zarina Bibi Ibrahim


We develop and demonstrate a computationally efficient numerical technique to solve first order stiff differential equations. This technique is based on block method whereby three approximate points are calculated. The Cholistani of varied step sizes are presented in divided difference form. Stability regions of the formulae are briefly discussed in this paper. Numerical results show that this block method perform very well compared to existing methods.

Keywords: block method, divided difference, stiff, computational

Procedia PDF Downloads 275
1444 Viability of Rice Husk Ash Concrete Brick/Block from Green Electricity in Bangladesh

Authors: Mohammad A. N. M. Shafiqul Karim


As a developing country, Bangladesh has to face numerous challenges. Self Independence in electricity, contributing to climate change by reducing carbon emission and bringing the backward population of society to the mainstream is more challenging for them. Therefore, it is essential to ensure recycled use of local products to the maximum level in every sector. Some private organizations have already worked alongside government to bring the backward population to the mainstream by developing their financial capacities. As rice husk is the largest single category of the total energy supply in Bangladesh. As part of this strategy, rice husk can play a great as a promising renewable energy source, which is readily available, has considerable environmental benefits and can produce electricity and ensure multiple uses of byproducts in construction technology. For the first time in Bangladesh, an experimental multidimensional project depending on Rice Husk Electricity and Rice Husk Ash (RHA) concrete brick/block under Green Eco-Tech Limited has already been started. Project analysis, opportunity, sustainability, the high monitoring component, limitations and finally evaluated data reflecting the viability of establishing more projects using rice husk are discussed in this paper. The by-product of rice husk from the production of green electricity, RHA, can be used for making, in particular, RHA concrete brick/block in Bangladeshi aspects is also discussed here.

Keywords: project analysis, rice husk, rice husk ash concrete brick/block, compressive strength of rice husk ash concrete brick/block

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1443 Backward Erosion Piping through Vertically Layered Sands

Authors: K. Vandenboer, L. Dolphen, A. Bezuijen


Backward erosion piping is an important failure mechanism for water-retaining structures, a phenomenon that results in the formation of shallow pipes at the interface of a sandy or silty foundation and a cohesive cover layer. This paper studies the effect of two soil types on backward erosion piping; both in case of a homogeneous sand layer, and in a vertically layered sand sample, where the pipe is forced to subsequently grow through the different layers. Two configurations with vertical sand layers are tested; they both result in wider pipes and higher critical gradients, thereby making this an interesting topic in research on measures to prevent backward erosion piping failures.

Keywords: backward erosion piping, embankments, physical modeling, sand

Procedia PDF Downloads 311
1442 The Comparison of Backward and Forward Running Program on Balance Development and Plantar Flexion Force in Pre Seniors: Healthy Approach

Authors: Neda Dekamei, Mostafa Sarabzadeh, Masoumeh Bigdeli


Backward running is commonly used in different sports conditioning, motor learning, and neurological purposes, and even more commonly in physical rehabilitation. The present study evaluated the effects of six weeks backward and forward running methods on balance promotion adaptation in students. 12 male and female preseniors with the age range of 45-60 years participated and were randomly classified into two groups of backward running (n: 6) and forward running (n: 6) training interventions. During six weeks, 3 sessions per week, all subjects underwent stated different models of backward and forward running training on treadmill (65-80 of HR max). Pre and post-tests were performed by force plate and electromyogram, two times before and after intervention. Data were analyzed using by T test. On the basis of obtained data, significant differences were recorded on balance and plantar flexion force in backward running (BR) and no difference for forward running (FR). It seems the training model of backward running can generate more stimulus to achieve better plantar flexion force and strengthening ankle protectors which leads to balance improvement in pre aging period. It can be recommended as an effective method to promote seniors life quality especially in balance neuromuscular parameters.

Keywords: backward running, balance, plantar flexion, pre seniors

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1441 FEM Investigation of Inhomogeneous Wall Thickness Backward Extrusion for Aerosol Can Manufacturing

Authors: Jemal Ebrahim Dessie, Zsolt Lukacs


The wall of the aerosol can is extruded from the backward extrusion process. Necking is another forming process stage developed on the can shoulder after the backward extrusion process. Due to the thinner thickness of the wall, buckling is the critical challenge for current pure aluminum aerosol can industries. Design and investigation of extrusion with inhomogeneous wall thickness could be the best solution for reducing and optimization of neck retraction numbers. FEM simulation of inhomogeneous wall thickness has been simulated through this investigation. From axisymmetric Deform-2D backward extrusion, an aerosol can with a thickness of 0.4 mm at the top and 0.33 mm at the bottom of the aerosol can have been developed. As the result, it can optimize the number of retractions of the necking process and manufacture defect-free aerosol can shoulder due to the necking process.

Keywords: aerosol can, backward extrusion, Deform-2D, necking

Procedia PDF Downloads 91
1440 Differentiation: A Risky Route To An Inclusive Reality

Authors: Marie C. Ryan


The current paper seeks to reconsider differentiation in order to establish whether differentiation has succeeded in its benevolent aim to support individual needs through teaching adaptations or whether paradoxically our attention to differentiation has served to exclude and marginalise. This paper does not deny variation in learner needs and accepts that inclusion requires teachers to adapt and modify curricular content; rather it seeks to examine whether differentiation as it is conceptualised and implemented is fit for purpose when it comes to adapting teaching in view of learner differences. The paper will also explore an alternative approach to supporting learner differences through teaching modifications which may offer a safer path to an inclusive educational reality.

Keywords: inclusion, differentiation, special education, universal design for learning

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1439 Numerical Study of Heat Transfer and Laminar Flow over a Backward Facing Step with and without Obstacle

Authors: Hussein Togun, Tuqa Abdulrazzaq, S. N. Kazi, A. Badarudin, M. K. A. Ariffin, M. N. M. Zubir


Heat transfer and laminar fluid flow over backward facing step with and without obstacle numerically studied in this paper. The finite volume method adopted to solve continuity, momentum and energy equations in two dimensions. Backward facing step without obstacle and with different dimension of obstacle were presented. The step height and expansion ratio of channel were 4.8mm and 2 respectively, the range of Reynolds number varied from 75 to 225, constant heat flux subjected on downstream of wall was 2000W/m2, and length of obstacle was 1.5, 3, and 4.5mm with width 1.5mm. The separation length noticed increase with increase Reynolds number and height of obstacle. The result shows increase of heat transfer coefficient for backward facing step with obstacle in compared to those without obstacle. The maximum enhancement of heat transfer observed at 4.5mm of height obstacle due to increase recirculation flow after the obstacle in addition that at backward. Streamline of velocity showing the increase of recirculation region with used obstacle in compared without obstacle and highest recirculation region observed at obstacle height 4.5mm. The amount of enhancement heat transfer was varied between 3-5% compared to backward without obstacle.

Keywords: separation flow, backward facing step, heat transfer, laminar flow

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1438 Analysis of Backward Supply Chain in Beverages Industry of Pakistan

Authors: Faisal Mehmood


In this globalization era, the supply chain management has acquired strategic importance in diverse business environments. In the current highly competitive business environment, the success of any business considerably depends on the efficiency of the supply chain. Management has now realized that due to the inefficiency of any member of supply chain, the profitability of the business will be affected. This paper proposes an analysis of backward supply chain in the beverages industry of Pakistan. Although reuse of products and materials is a common phenomenon, companies have long ignored this important part of the supply chain, known as backward supply chain or reverse logistics. The beverage industry is among the pioneers of backward supply chain or reverse logistics in Pakistan. The empty glass bottles are returned back from the point of consumption to the warehouse for refilling and reusability purposes. Due to the lack of information on reverse flow of logistics and more attention on the forward distribution, beverages industry in Pakistan is facing high rate of inefficiencies and ineffectiveness. Analysis of backward or reverse logistics practiced in beverages industry is the subject of this study in which framework dictating the current needs of market will be developed.

Keywords: backward supply chain, reverse logistics, refilling, re-usability

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1437 An Efficient Backward Semi-Lagrangian Scheme for Nonlinear Advection-Diffusion Equation

Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim


In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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1436 Case Study Approach Using Scenario Analysis to Analyze Unabsorbed Head Office Overheads

Authors: K. C. Iyer, T. Gupta, Y. M. Bindal


Head office overhead (HOOH) is an indirect cost and is recovered through individual project billings by the contractor. Delay in a project impacts the absorption of HOOH cost allocated to that particular project and thus diminishes the expected profit of the contractor. This unabsorbed HOOH cost is later claimed by contractors as damages. The subjective nature of the available formulae to compute unabsorbed HOOH is the difficulty that contractors and owners face and thus dispute it. The paper attempts to bring together the rationale of various HOOH formulae by gathering contractor’s HOOH cost data on all of its project, using case study approach and comparing variations in values of HOOH using scenario analysis. The case study approach uses project data collected from four construction projects of a contractor in India to calculate unabsorbed HOOH costs from various available formulae. Scenario analysis provides further variations in HOOH values after considering two independent situations mainly scope changes and new projects during the delay period. Interestingly, one of the findings in this study reveals that, in spite of HOOH getting absorbed by additional works available during the period of delay, a few formulae depict an increase in the value of unabsorbed HOOH, neglecting any absorption by the increase in scope. This indicates that these formulae are inappropriate for use in case of a change to the scope of work. Results of this study can help both parties in deciding on an appropriate formula more objectively, considering the events on a project causing the delay and contractor's position in respect of obtaining new projects.

Keywords: absorbed and unabsorbed overheads, head office overheads, scenario analysis, scope variation

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1435 Effect of Tube Backward Extrusion (TBE) Process on the Microstructure and Mechanical Properties of AZ31 Magnesium Alloy

Authors: H. Abdolvand, M. Riazat, H. Sohrabi, G. Faraji


An experimental investigation into the Tube Backward Extrusion (TBE) process on AZ31 magnesium alloy is studied. Microstructures and grain size distribution of the specimens before and after TBE process are investigated by optical microscopy. Tensile and Vickers microhardness tests along extrusion direction were performed at room temperature. It is found that the average grain size is refined remarkably from the initial 33 µm down to 3.5 µm after TBE process. Also, the microhardness increased significantly to 58 HV after the process from an initial value of 36 HV.

Keywords: tube backward extrusion, AZ31, grain size distribution, grain refinement

Procedia PDF Downloads 337
1434 Linking Metabolism, Pluripotency and Epigenetic Changes during Early Differentiation of Embryonic Stem Cells

Authors: Arieh Moussaieff, Bénédicte Elena-Herrmann, Yaakov Nahmias, Daniel Aberdam


Differentiation of pluripotent stem cells is a slow process, marked by the gradual loss of pluripotency factors over days in culture. While the first few days of differentiation show minor changes in the cellular transcriptome, intracellular signaling pathways remain largely unknown. Recently, several groups demonstrated that the metabolism of pluripotent mouse and human cells is different from that of somatic cells, showing a marked increase in glycolysis previously identified in cancer as the Warburg effect. Here, we sought to identify the earliest metabolic changes induced at the first hours of differentiation. High-resolution NMR analysis identified 35 metabolites and a distinct, gradual transition in metabolism during early differentiation. Metabolic and transcriptional analyses showed the induction of glycolysis toward acetate and acetyl-coA in pluripotent cells, and an increase in cholesterol biosynthesis during early differentiation. Importantly, this metabolic pathway regulated differentiation of human and mouse embryonic stem cells. Acetate delayed differentiation preventing differentiation-induced histone de-acetylation in a dose-dependent manner. Glycolytic inhibitors upstream of acetate caused differentiation of pluripotent cells, while those downstream delayed differentiation. Our data suggests that a rapid loss of glycolysis in early differentiation down-regulates acetate and acetyl-coA production, causing a loss of histone acetylation and concomitant loss of pluripotency. It demonstrate that pluripotent stem cells utilize a novel metabolism pathway to maintain pluripotency through acetate/acetyl-coA and highlights the important role metabolism plays in pluripotency and early differentiation of stem cells.

Keywords: pluripotency, metabolomics, epigenetics, acetyl-coA

Procedia PDF Downloads 387
1433 Impact of Grassroot Democracy on Rural Development of Villages in the State of Haryana

Authors: Minakshi Jain, Sachin Yadav


Gram Panchayat is the smallest unit of Democracy in India. Grassroots Democracy has been further strengthened by implementation of the 73rd Constitutional Amendment act (CAA) in 1992. To analyse the impact of grassroots democracy the three villages are selected, which have the representation of each section of the society. The selected villages belongs to the same block and district of Haryana state. Villages are selected to access the marginalized group such as women and other backward class. These groups are isolated and do not participate in the grassroots level development process. The caste continue to be a relevant factor in determining the rural leadership. The earlier models of Panchayati Raj failed to benefit the marginalized groups of the society. The 73rd CAA, advocates a uniform three tier system of Panchayat at District level (Zilla Panchayat), Taluka/Block level (Block Panchayat), and village level (Gram Panchayat). The socio-economic profile of representatives in each village is important factor in rural development. The study will highlight the socio-economic profile of elected members at gram Panchayat level, Block Level and District level. The analysis reveals that there is a need to educate and develop the capacity and capability of the elected representative. Training must be imparted to all of them to enable them to function as per provision in the act. The paper will analyse the impact of act on rural development than propose some measures to further strengthen the Panchayati Raj Institution (PRI’s) at grassroots level.

Keywords: democracy, rural development, marginalized people, function

Procedia PDF Downloads 266
1432 Formulation, Nutritive Value Assessment And Effect On Weight Gain Of Infant Formulae Prepared From Locally Available Materia

Authors: J. T. Johnson, R. A. Atule, E. Gbodo


The widespread problem of infant malnutrition in developing countries has stirred efforts in research, development and extension by both local and international organizations. As a result, the formulation and development of nutritious weaning foods from local and readily available raw materials which are cost effective has become imperative in many developing countries. Thus, local and readily available raw materials where used to compound and develop nutritious new infant formulae. The materials used for this study include maize, millet, cowpea, pumpkin, fingerlings, and fish bone. The materials where dried and blended to powder. The powders were weighed in the ratio of 4:4:4:3:1:1 respectively and were then mixed properly. Analysis of nutritive value was conducted on the formulae and compared with NAN-2 standard and results reveals that the formulae had reasonable amount of moisture, lipids, carbohydrate, protein, and fibre. Although NAN-2 was superior in both carbohydrate and protein, the new infant formula was higher in mineral elements, vitamins, fibre, and lipids. All the essentials vitamins and both macro and micro minerals where found in appreciable quantity capable of meeting the biochemical and physiological demand of the body while the anti-nutrients composition were significantly below FAO and WHO safe limits. Finally, the compounded infant formulae was feed to a set of albino Wistar rats while some other set of rats was feed with NAN-2 for the period of twenty seven (27) days and body weight was measure at three days intervals. The results of body weight changes was spectacular as their body weight over shot or almost double that of those animals that were feed with NAN-2 at each point of measurement. The results suggest that the widespread problem of infant malnutrition in the developing world especially among the low income segment of the society can now be reduced if not totally eradicated since nutritive and cost effective weaning formulae can be prepared locally from common readily available materials.

Keywords: formulation, nutritive value, local, materials

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1431 Reduction of Dynamic Influences in Composite Rubber-Concrete Block Designed to Walls Construction

Authors: Maciej Major, Izabela Major


The aim of this paper is a numerical analysis of three-layered block design to walls construction subjected to the dynamic load. The block consists of the layers: concrete with rubber pads in shape of crosses, space filled with air and concrete with I-shape rubber pads. The main purpose of rubber inserts embedded during the production process is additional protection against the transversal dynamic load. For the analysis, as rubber, the Zahorski hyperelastic incompressible material model was assumed. A concentrated force as dynamic load applied to the external block surface was investigated. The results for the considered block observed as the stress distribution plot were compared to the results obtained for the solid concrete block. In order to estimate the percentage damping of proposed composite, rubber-concrete block in relation to the solid block the numerical analysis with the use of finite element method based on ADINA software was performed.

Keywords: dynamics, composite, rubber, Zahorski

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1430 Generation of Photo-Mosaic Images through Block Matching and Color Adjustment

Authors: Hae-Yeoun Lee


Mosaic refers to a technique that makes image by gathering lots of small materials in various colours. This paper presents an automatic algorithm that makes the photomosaic image using photos. The algorithm is composed of four steps: Partition and feature extraction, block matching, redundancy removal and colour adjustment. The input image is partitioned in the small block to extract feature. Each block is matched to find similar photo in database by comparing similarity with Euclidean difference between blocks. The intensity of the block is adjusted to enhance the similarity of image by replacing the value of light and darkness with that of relevant block. Further, the quality of image is improved by minimizing the redundancy of tiles in the adjacent blocks. Experimental results support that the proposed algorithm is excellent in quantitative analysis and qualitative analysis.

Keywords: photomosaic, Euclidean distance, block matching, intensity adjustment

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1429 Compromising Relevance for Elegance: A Danger of Dominant Growth Models for Backward Economies

Authors: Givi Kupatadze


Backward economies are facing a challenge of achieving sustainable high economic growth rate. Dominant growth models represent a roadmap in framing economic development strategy. This paper examines a relevance of the dominant growth models for backward economies. Cobb-Douglas production function, the Harrod-Domar model of economic growth, the Solow growth model and general formula of gross domestic product are examined to undertake a comprehensive study of the dominant growth models. Deductive research method allows to uncover major weaknesses of the dominant growth models and to come up with practical implications for economic development strategy. The key finding of the paper shows, contrary to what used to be taught by textbooks of economics, that constant returns to scale property of the dominant growth models are a mere coincidence and its generalization over space and time can be regarded as one of the most unfortunate mistakes in the whole field of political economy. The major suggestion of the paper for backward economies is that understanding and considering taxonomy of economic activities based on increasing and diminishing returns to scale represent a cornerstone of successful economic development strategy.

Keywords: backward economies, constant returns to scale, dominant growth models, taxonomy of economic activities

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1428 The Study on Blast Effect of Polymer Gel by Trazul Lead Block Test and Concrete Block Test

Authors: Young-Hun Ko, Seung-Jun Kim, Khaqan Baluch, Hyung- Sik Yang


In this study, the polymer gel was used as coupling material in a blasting hole and its comparison was made with other coupling materials like sand, water, and air. Trazul lead block test and AUTODYN numerical analysis were conducted to analyze the effects of the coupling materials on the intensity of the explosion, as well as the verification tests were conducted by using concrete block test. The emulsion explosives were used in decoupling conditions, sand, water, and polymer gel were used as the coupling materials. The lead block test and the numerical analysis showed that the expansion of the blast hole in the lead block was similar to that of the water and gelatin and followed by sand and air conditions. The validation of concrete block test result showed the similar result as Trazul lead block test and the explosion strength was measured at 0.8 for polymer gel, 0.7 for sand, and 0.6 for no coupling material, in comparison to the full charge (1.0) case.

Keywords: Trazul lead block test, AUTODYN numerical analysis, coupling material, polymer gel, soil covering concrete block explosion test

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1427 On a Continuous Formulation of Block Method for Solving First Order Ordinary Differential Equations (ODEs)

Authors: A. M. Sagir


The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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1426 On Block Vandermonde Matrix Constructed from Matrix Polynomial Solvents

Authors: Malika Yaici, Kamel Hariche


In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

Procedia PDF Downloads 98
1425 Effect of the Initial Billet Shape Parameters on the Final Product in a Backward Extrusion Process for Pressure Vessels

Authors: Archana Thangavelu, Han-Ik Park, Young-Chul Park, Joon-Hong Park


In this numerical study, we have proposed a method for evaluation of backward extrusion process of pressure vessel made up of steel. Demand for lighter and stiffer products have been increasing in the last years especially in automobile engineering. Through detailed finite element analysis, effective stress, strain and velocity profile have been obtained with optimal range. The process design of a forward and backward extrusion axe-symmetric part has been studied. Forging is mainly carried out because forged products are highly reliable and possess superior mechanical properties when compared to normal products. Performing computational simulations of 3D hot forging with various dimensions of billet and optimization of weight is carried out using Taguchi Orthogonal Array (OA) Optimization technique. The technique used in this study can be used for newly developed materials to investigate its forgeability for much complicated shapes in closed hot die forging process.

Keywords: backward extrusion, hot forging, optimization, finite element analysis, Taguchi method

Procedia PDF Downloads 237
1424 Relationships among Parentification, Self-Differentiation, and Ambivalence over Emotional Expression for Children of Migratory Families

Authors: Wan-Chun Chang, Yi-Jung Lee


Due to cultural factors, expressing emotions may not be encouraged in collectivist cultures, which emphasize the needs of the group over the needs of the individual. This phenomenon is more prominent for children of migratory families. Due to the absence of one parent, children were often parentified by adults, which then impacted on their self-differentiation process. It made them more difficult to express their needs and emotions freely and openly. This study aimed to investigate the meditation effect of self-differentiation between parentification, and ambivalence over emotional expression for children of migratory families in Taiwan. Participants included 460 (326 females, 134 males) Taiwanese adults (age 18-25 years). The data were collected through questionnaires and analyzed using descriptive statistics and multiple regression analysis. The questionnaire included informed consent form, 'Filial Responsibility Scale-Adult', 'Chinese version of the Differentiation of Self Inventory', 'Ambivalence over Emotion Expressiveness Questionnaire', and the demographic sheet. Results indicated that self-differentiation mediated the relationship between parentified experience and ambivalence over emotional expression. In other words, parentified experience itself does not have the power to affect ambivalence over emotional expression. Only by affecting self-differentiation can it make an actual difference. The results were as expected and confirmed the hypothesis. Implications for clinical practice, research, and training were discussed.

Keywords: ambivalence over emotional expression, children of migratory families, parentification, self-differentiation

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1423 Implementation of Complete Management Practices in Managing the Cocoa Pod Borer

Authors: B. Saripah, A. Alias


Cocoa Theobroma cacao (Linnaeus) (Malvales: Sterculiaceae) is subjected to be infested by various numbers of insect pests, and Conopomorpha cramerella Snellen (Lepidoptera: Gracillariidae) is the most serious pest of cocoa in Malaysia. The pest was indigenous to the South East Asia. Several control measures have been implemented and the chemicals have been a major approach if not unilateral, in the management of CPB. Despite extensive use of insecticides, CPB continues to cause an unacceptable level of damage; thus, the combination of several control approaches should be sought. The study was commenced for 12 months at three blocks; Block 18C with complete management practices which include insecticide application, pruning, fertilization and frequent harvesting, Block 17C was treated with frequent harvesting at intervals of 7-8 days, and Block 19C was served as control block. The results showed that the mean numbers of CPB eggs were recorded higher in Block 17C compared with Block 18C in all sampling occasions. Block 18C shows the lowest mean number of CPB eggs in both sampling plots, outside and core plots and it was found significantly different (p ≤ 0. 05) compared to the other blocks. The mean number of CPB eggs was fluctuated throughout sampling occasions, the lowest mean number of eggs was recorded in January (17C) and November (18C), while the highest was recorded in April (17C) and December 2012 (18C). Frequent spraying with insecticides at the adjacent block (18C) helps in reducing CPB eggs in the control block (Block 19C), although there was no spraying was implemented Block 19C. In summary, the combination of complete management practices at Block 18C seems to have some effect on the CPB population at Blocks 17 and 19C because all blocks are adjacent to each other.

Keywords: cocoa, theobroma cacao, cocoa pod borer, conopomorpha cramerella

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1422 Effective Slab Width for Beam-End Flexural Strength of Composite Frames with Circular-Section Columns

Authors: Jizhi Zhao, Qiliang Zhou, Muxuan Tao


The calculation of the ultimate loading capacity of composite frame beams is an important step in the design of composite frame structural systems. Currently, the plastic limit theory is mainly used for this calculation in the codes adopted by many countries; however, the effective slab width recommended in most codes is based on the elastic theory, which does not accurately reflect the complex stress mechanism at the beam-column joints in the ultimate loading state. Therefore, the authors’ research group put forward the Compression-on-Column-Face mechanism and Tension-on-Transverse-Beam mechanism to explain the mechanism in the ultimate loading state. Formulae are derived for calculating the effective slab width in composite frames with rectangular/square-section columns under ultimate lateral loading. Moreover, this paper discusses the calculation method of the effective slab width for the beam-end flexural strength of composite frames with circular-section columns. The proposed design formula is suitable for exterior and interior joints. Finally, this paper compares the proposed formulae with available formulae in other literature, current design codes, and experimental results, providing the most accurate results to predict the effective slab width and ultimate loading capacity.

Keywords: composite frame structure, effective slab width, circular-section column, design formulae, ultimate loading capacity

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1421 Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations

Authors: A. M. Sagir


Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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