Search results for: projection method

Authors: Ka Lei Au

Abstract:

The Dalcroze method has been emerging in music classrooms, and music teachers are encouraged to integrate music and movement in their teaching. Music programs in colleges in Hong Kong have been introducing method courses such as Orff and Dalcroze method in music teaching as teacher’s education program. Since the targeted students of the course are music teachers who are making the decision of what approach to use in their classroom, their perception is significantly valued to identify how this approach is applicable in their teaching in regards to the teaching and learning culture and environment. This qualitative study aims to explore how the Dalcroze method as a teacher’s education course is perceived by music teachers from three aspects: 1) application in music teaching, 2) self-enhancement, 3) expectation. Through the lens of music teachers, data were collected from 30 music teachers who are taking the Dalcroze method course in music teaching in Hong Kong by the survey. The findings reveal the value and their intention of the Dalcroze method in Hong Kong. It also provides a significant reference for better development of such courses in the future in adaption to the culture, teaching and learning environment and teacher’s, student’s and parent’s perception of this approach.

Keywords: Dalcroze method, music teaching, perception, self-enhancement, teacher’s education

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Authors: Mahmoudi Noureddine, Bouregba Rachid

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In this paper the stress intensity factors of a slant-cracked plate of AISI 304 stainless steel, have been calculated using extended finite element method and finite element method (FEM) in ABAQUS software, the results were compared with theoretical values.

Keywords: stress intensity factors, extended finite element method, stainless steel, abaqus

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Authors: Nesrine T. Lamie

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Four, accurate, precise, and sensitive spectrophotometric methods are developed for the simultaneous determination of a binary mixture containing amlodipine besylate (AM) and atenolol (AT) where AM is determined at its λmax 360 nm (0D), while atenolol can be determined by different methods. Method (A) is absorpotion factor (AFM). Method (B) is the new Ratio Difference method(RD) which measures the difference in amplitudes between 210 and 226 nm of ratio spectrum., Method (C) is novel constant center spectrophotometric method (CC) Method (D) is mean centering of the ratio spectra (MCR) at 284 nm. The calibration curve is linear over the concentration range of 10–80 and 4–40 μg/ml for AM and AT, respectively. These methods are tested by analyzing synthetic mixtures of the cited drugs and they are applied to their commercial pharmaceutical preparation. The validity of results was assessed by applying standard addition technique. The results obtained were found to agree statistically with those obtained by a reported method, showing no significant difference with respect to accuracy and precision.

Keywords: amlodipine, atenolol, absorption factor, constant center, mean centering, ratio difference

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Authors: James Adewale, Joshua Sunday

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In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods.

Keywords: predictor, corrector, collocation, interpolation, approximate solution, independent solution, zero stable, consistent, convergent

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Authors: Edamana Vasudevan Krishnan

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This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: C. Bunsanit

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This paper presents the refinement method for two beams formation of wideband smart antenna. The refinement method for weighting coefficients is based on Fully Spatial Signal Processing by taking Inverse Discrete Fourier Transform (IDFT), and its simulation results are presented using MATLAB. The radiation pattern is created by multiplying the incoming signal with real weights and then summing them together. These real weighting coefficients are computed by IDFT method; however, the range of weight values is relatively wide. Therefore, for reducing this range, the refinement method is used. The radiation pattern concerns with five input parameters to control. These parameters are maximum weighting coefficient, wideband signal, direction of mainbeam, beamwidth, and maximum of minor lobe level. Comparison of the obtained simulation results between using refinement method and taking only IDFT shows that the refinement method works well for wideband two beams formation.

Keywords: fully spatial signal processing, beam forming, refinement method, smart antenna, weighting coefficient, wideband

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: G. Venkatesha, Urs Samarth, H. K. Ramaraju, Arun Kumar Sharma

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The projection for Groundwater states that the total domestic water demand for greater Bangalore would increase from 1,170 MLD in 2010 to 1,336 MLD in 2016. Dependence on groundwater is ever increasing due to rapid Industrialization & Urbanization. It is estimated that almost 40% of the population of Bangalore is dependent on groundwater. Due to the unscientific disposal of domestic and industrial waste generated, groundwater is getting highly polluted in the city. The scale of this impact will depend mainly upon the water-service infrastructure, the superficial geology and the regional setting. The quality of ground water is equally important as that of quantity. Jointed and fractured granites and gneisses constitute the major aquifer system of BBMP area. Two new observatory Borewells were drilled and lithology report has been prepared. Petrographic Analysis (XRD/XRF) and Water quality Analysis were carried out as per the standard methods. Petrographic samples were analysed by collecting chip of rock from the borewell for every 20ft depth, most of the samples were similar and samples were identified as Biotite-Gneiss, Schistose Amphibolite. Water quality analysis was carried out for individual chemical parameters for two borewells drilled. 1st Borewell struck water at 150ft (Total depth-200ft) & 2nd struck at 740ft (Total depth-960ft). 5 water samples were collected till end of depth in each borewell. Chemical parameter values such as, Total Hardness (360-348, 280-320) mg/ltr, Nitrate (12.24-13.5, 45-48) mg/ltr, Chloride (104-90, 70-70)mg/ltr, Fe (0.75-0.09, 1.288-0.312)mg/ltr etc. are calculated respectively. Water samples were analysed from various parts of BBMP covering 750 sq kms, also thematic maps (IDW method) of water quality is generated for these samples for Post-Monsoon season. The study aims to explore the sub-surface Lithological layers and the thickness of weathered zone, which indirectly helps to know the Groundwater pollution source near surface water bodies, dug wells, etc. The above data are interpreted for future ground water resources planning and management.

Keywords: lithology, petrographic, pollution, urbanization

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Muhammad Fajar Suardi, Fathimatufzzahra, Dela Isnaini Sendra

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Learning is an activity that has been used to do, especially for a student or academics. But a handful of people have not been using and maximizing their brains work and some also do not know a good brain work time in capturing the lessons, so that knowledge is absorbed is also less than the maximum. Indonesia Memory Sports Council (IMSC) is an institution which is engaged in the performance of the brain and the development of effective learning methods by using several techniques that can be used in considering the lessons and knowledge to grasp well, including: loci method, substitution method, and chain method. This study aims to determine the techniques and benefits of using the method given in learning and memorization by applying memory techniques taught by Indonesia Memory Sports Council (IMSC) to students and the difference if not using this method. This research uses quantitative research with survey method addressed to students of Indonesian Memory Sports Council (IMSC). The results of this study indicate that learn, understand and remember the lesson using the techniques of memory which is taught in Indonesia Memory Sport Council is very effective and faster to absorb the lesson than learning without using the techniques of memory, and this affects the academic achievement of students in each educational institution.

Keywords: chain method, Indonesia memory sports council, loci method, substitution method

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Authors: T. Kritsana, P. Sawitri, P. Teeratas

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This article aims to study the effect of pressure on rocket motor case by Finite Element Method simulation to select optimal material in rocket motor manufacturing process. In this study, cylindrical tubes with outside diameter of 122 mm and thickness of 3 mm are used for simulation. Defined rocket motor case materials are AISI4130, AISI1026, AISI1045, AL2024 and AL7075. Internal pressure used for the simulation is 22 MPa. The result from Finite Element Method shows that at a pressure of 22 MPa rocket motor case produced by AISI4130, AISI1045 and AL7075 can be used. A comparison of the result between AISI4130, AISI1045 and AL7075 shows that AISI4130 has minimum principal stress and confirm the results of Finite Element Method by the used of calculation method found that, the results from Finite Element Method has good reliability.

Keywords: rocket motor case, finite element method, principal stress, simulation

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Authors: Mohammad Ghandehari Motlagh

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Purpose: Comparing anterior chamber depth (ACD) measured with Orbscan II and Pentacam HR compared with the Smith method results. Methods: Smith method (1979) is a reliable method of measuring ACD only with help of slit lamp. In this study 102 phakic eyes as PRK candidates were imaged with both OrbScan and Pentacam and finally ACD was measured thru Smith method with slit lamp. ACD measured with Smith method was presumed as the gold standard and was compared with ACD of the 2 imaging devices. Contraindication cases for PRK and pseudophakic eyes have been excluded from the study. Results: Mean age of the patients was 35.2 ±14.8 yrs/old including 56 M(54.9%)and 46 F(45.09%).Acceptable correlation of ACD measured thru Smith method with Orbscan and Pentacam are R=0.958 and R=0.942 respectively and so Orbscan results can be used in procedures relying on ACD. Conclusion: ACDs measured with OrbScan is more precise than Pentacam and so can be more useful in some surgery procedures relying ACD results such as phakic IOLs and in cycloplegia contraindications.

Keywords: orbscan, pentacam, anterior chamber depth, slit lamp

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Authors: Mahmoud Lot

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In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

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Authors: Nada Jasim Habeeb, Rana Saad Mohammed, Muntaha Khudair Abbass

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For more efficient and fast video summarization, this paper presents a surveillance video summarization method. The presented method works to improve video summarization technique. This method depends on temporal differencing to extract most important data from large video stream. This method uses histogram differencing and Sum Conditional Variance which is robust against to illumination variations in order to extract motion objects. The experimental results showed that the presented method gives better output compared with temporal differencing based summarization techniques.

Keywords: temporal differencing, video summarization, histogram differencing, sum conditional variance

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Tohru Kawabe

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In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: sliding mode control, model predictive control, integral action, electric vehicle, slip suppression

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Authors: Nikhat Nawaz, S. Srinivasulu, P. Kesava Rao

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Feature extraction plays an important role in many remote sensing applications. Automatic extraction of water bodies is of great significance in many remote sensing applications like change detection, image retrieval etc. This paper presents a procedure for automatic extraction of water information from remote sensing images. The algorithm uses the relative location of R-colour component of the chromaticity diagram. This method is then integrated with the effectiveness of the spatial scale transformation of whole method. The whole method is based on water index fitted from spectral library. Experimental results demonstrate the improved accuracy and effectiveness of the integrated method for automatic extraction of water bodies.

Keywords: feature extraction, remote sensing, image retrieval, chromaticity, water index, spectral library, integrated method

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: evapotranspiration, hargreaves, equation, FAO-Penman method

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Authors: F. Boufera, F. Debbat

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This paper deals with an approach based on limit-cycles method for the problem of obstacle avoidance of mobile robots in unknown environments for any form of obstacles. The purpose of this approach is the improvement of limit-cycles method in order to obtain safe and flexible navigation. The proposed algorithm has been successfully tested in different configuration on simulation.

Keywords: mobile robot, navigation, avoidance of obstacles, limit-cycles method

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Authors: A. H. Choudhury

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In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Shaikah Alsubayae, Gianluigi Casse, Carlos Chavez, Jon Taylor, Alan Taylor, Mohammad Alsulimane

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Achieving precise radiotherapy through carbon therapy necessitates the accurate monitoring of radiation dose distribution within the patient's body. This process is pivotal for targeted tumor treatment, minimizing harm to healthy tissues, and enhancing overall treatment effectiveness while reducing the risk of side effects. In our investigation, we adopted a methodological approach to monitor secondary proton doses in carbon therapy using Monte Carlo (MC) simulations. Initially, Geant4 simulations were employed to extract the initial positions of secondary particles generated during interactions between carbon ions and water, including protons, gamma rays, alpha particles, neutrons, and tritons. Subsequently, we explored the relationship between the carbon ion beam and these secondary particles. Interaction vertex imaging (IVI) proves valuable for monitoring dose distribution during carbon therapy, providing information about secondary particle locations and abundances, particularly protons. The IVI method relies on charged particles produced during ion fragmentation to gather range information by reconstructing particle trajectories back to their point of origin, known as the vertex. In the context of carbon ion therapy, our simulation results indicated a strong correlation between some secondary particles and the range of carbon ions. However, challenges arose due to the unique elongated geometry of the target, hindering the straightforward transmission of forward-generated protons. Consequently, the limited protons that did emerge predominantly originated from points close to the target entrance. Fragment (protons) trajectories were approximated as straight lines, and a beam back-projection algorithm, utilizing interaction positions recorded in Si detectors, was developed to reconstruct vertices. The analysis revealed a correlation between the reconstructed and actual positions.

Keywords: radiotherapy, carbon therapy, monitor secondary proton doses, interaction vertex imaging

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Authors: Lars Andersen

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The development of design and engineering in large construction projects are characterized by an increased degree of flattening out of formal structures, extended use of parallel and integrated processes (‘Integrated Concurrent Engineering’) and an increased number of expert disciplines. The integration process is based on ongoing collaborations, dialogues, intercommunication and comments on each other’s work (iterations). This process based on reciprocal communication between actors and disciplines triggers value creation. However, communication between equals is not in itself sufficient to create effective decision making. The complexity of the process and time pressure contribute to an increased risk of a deficit of decisions and loss of process control. The paper refers to a study that aims at developing a resilient decision-making system that does not come in conflict with communication processes based on equality between the disciplines in the process. The study includes the construction of a hospital, following the phases design, engineering and physical building. The Research method is a combination of formative process research, process tracking and phenomenological analyses. The study tracked challenges and problems in the building process to the projection substrates (drawing and models) and further to the organization of the engineering and design phase. A comparative analysis of traditional and new ways of organizing the projecting made it possible to uncover an implicit material order or structure in the process. This uncovering implied a development of a material process perspective. According to this perspective the complexity of the process is rooted in material-functional differentiation. This differentiation presupposes a structuring material (the skeleton of the building) that coordinates the other types of material. Each expert discipline´s competence is related to one or a set of materials. The architect, consulting engineer construction etc. have their competencies related to structuring material, and inherent in this; coordination competence. When dialogues between the disciplines concerning the coordination between them do not result in agreement, the disciplines with responsibility for the structuring material decide the interface issues. Based on these premises, this paper develops a self-organized expert-driven interdisciplinary decision-making system.

Keywords: collaboration, complexity, design, engineering, materiality

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Authors: Masoume Ehsani, Ning Zhu, Huu Doan, Ali Lohi, Amira Abdelrasoul

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Membrane fouling poses severe challenges in membrane-based wastewater treatment applications. Ultrasound (US) has been considered an effective fouling remediation technique in filtration processes. Bubble cavitation in the liquid medium results from the alternating rarefaction and compression cycles during the US irradiation at sufficiently high acoustic pressure. Cavitation microbubbles generated under US irradiation can cause eddy current and turbulent flow within the medium by either oscillating or discharging energy to the system through microbubble explosion. Turbulent flow regime and shear forces created close to the membrane surface cause disturbing the cake layer and dislodging the foulants, which in turn improve the cleaning efficiency and filtration performance. Therefore, the number, size, velocity, and oscillation pattern of the microbubbles created in the liquid medium play a crucial role in foulant detachment and permeate flux recovery. The goal of the current study is to gain in depth understanding of the influence of the US power intensity and frequency on the microbubble dynamics and its characteristics generated under US irradiation. In comparison with other imaging techniques, the synchrotron in-line Phase Contrast Imaging technique at the Canadian Light Source (CLS) allows in-situ observation and real-time visualization of microbubble dynamics. At CLS biomedical imaging and therapy (BMIT) polychromatic beamline, the effective parameters were optimized to enhance the contrast gas/liquid interface for the accuracy of the qualitative and quantitative analysis of bubble cavitation within the system. With the high flux of photons and the high-speed camera, a typical high projection speed was achieved; and each projection of microbubbles in water was captured in 0.5 ms. ImageJ software was used for post-processing the raw images for the detailed quantitative analyses of microbubbles. The imaging has been performed under the US power intensity levels of 50 W, 60 W, and 100 W, in addition to the US frequency levels of 20 kHz, 28 kHz, and 40 kHz. For the duration of 2 seconds of imaging, the effect of the US power and frequency on the average number, size, and fraction of the area occupied by bubbles were analyzed. Microbubbles’ dynamics in terms of their velocity in water was also investigated. For the US power increase of 50 W to 100 W, the average bubble number and the average bubble diameter were increased from 746 to 880 and from 36.7 µm to 48.4 µm, respectively. In terms of the influence of US frequency, a fewer number of bubbles were created at 20 kHz (average of 176 bubbles rather than 808 bubbles at 40 kHz), while the average bubble size was significantly larger than that of 40 kHz (almost seven times). The majority of bubbles were captured close to the membrane surface in the filtration unit. According to the study observations, membrane cleaning efficiency is expected to be improved at higher US power and lower US frequency due to the higher energy release to the system by increasing the number of bubbles or growing their size during oscillation (optimum condition is expected to be at 20 kHz and 100 W).

Keywords: bubble dynamics, cavitational bubbles, membrane fouling, ultrasonic cleaning

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Authors: Rahman Dashti, Ehsan Gord

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In this paper, an improved impedance based fault location method is proposed. In this method, online fault locating is performed using voltage and current information at the beginning of the feeder. Determining precise fault location in a short time increases reliability and efficiency of the system. The proposed method utilizes information about main component of voltage and current at the beginning of the feeder and distributed generation unit (DGU) in order to precisely locate different faults in acceptable time. To evaluate precision and accuracy of the proposed method, a 13-node is simulated and tested using MATLAB.

Keywords: distribution network, fault section determination, distributed generation units, distribution protection equipment

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Authors: W. S. Lawal, T. Akande

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Abstract— Four (4) difference methods were employed to detoxify Jatropha carcas, they were physical method (it include soaking and sun drying) Chemical (the use of methylated sprit, hexane and methane). Biological (the use of Aspergillus niger and then sundry for 7days and then Bacillus lichiformis) and Combined method (the combination of chemical and biological methods). Phobol esther analysis was carried out after the detoxification methods and it was found that the combined method is better off (P<0.05). Detoxified Jatropha from each of this methods was sundry and grinded for easy inclusion into poultry feed, detoxified jatropha was included at 0%, 0.5%, 1%, 2%, 3%, 4%, and 5% but the combined method was increased up to 7% because the birds were able to tolerate it, the 0% was the control experiment. 405 day old broiler chicks was used to test the effect of detoxified Jatropha carcas on their performance, there are 5birds per treatment and there are 3 replicates, the experiment lasted for 8weeks,highest number of mortality was obtained in physical method, birds in chemical method tolerated up to 3% Jatropha carcas, biological method is better, as birds there were comfortable at 5% but the best of them is combined method the birds did very well at 7% as there were less mortality and highest weight gain was achieved here (P<0.05) and it was recommended.

Keywords: phobol esther, inclusion level, tolerance level, Jatropha carcas

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Authors: Hadi Farhadian, Homayoon Katibeh

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In this paper, groundwater seepage into Amirkabir tunnel has been estimated using analytical and numerical methods for 14 different sections of the tunnel. Site Groundwater Rating (SGR) method also has been performed for qualitative and quantitative classification of the tunnel sections. The obtained results of above-mentioned methods were compared together. The study shows reasonable accordance with results of the all methods unless for two sections of tunnel. In these two sections there are some significant discrepancies between numerical and analytical results mainly originated from model geometry and high overburden. SGR and the analytical and numerical calculations, confirm the high concentration of seepage inflow in fault zones. Maximum seepage flow into tunnel has been estimated 0.425 lit/sec/m using analytical method and 0.628 lit/sec/m using numerical method occurred in crashed zone. Based on SGR method, six sections of 14 sections in Amirkabir tunnel axis are found to be in "No Risk" class that is supported by the analytical and numerical seepage value of less than 0.04 lit/sec/m.

Keywords: water Seepage, Amirkabir Tunnel, analytical method, DEM, SGR

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

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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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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Kirill Trapezon, Alexandr Trapezon

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A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.

Keywords: vibrations, plate, method of symmetries, differential equation, factorization, approximation

Procedia PDF Downloads 237