Search results for: precipitation method

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: 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: Krasimir Ivanov, Elitsa Kolentsova, Nguyen Nguyen, Alexander Peltekov, Violina Angelova

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The nanosized zinc hydroxide nitrate has been recently estimated as perspective foliar fertilizer, which has improved zinc solubility, but low phytotoxicity, in comparison with ZnO and other Zn containing compounds. The main problem is obtaining of stable particles with dimensions less than 100 nm. This work studies the effect of preparation conditions on the chemical compositions and particle size of the zinc hydroxide nitrates, prepared by precipitation. Zn(NO3)2.6H2O and NaOH with concentrations, ranged from 0.2 to 3.2M and the initial OH/Zn ratio from 0.5 to 1.6 were used at temperatures from 20 to 60 °C. All samples were characterized in detail by X-ray diffraction, scanning electron microscopy, differential thermal analysis and ICP. Stability and distribution of the zinc hydroxide nitrate particles were estimated too.

Keywords: zinc hydroxide nitrate, nanoparticles, preparation, foliar fertilizer

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Authors: T. A. Prikhna, A. V. Shaternik, V. E. Moshchil, M. Eisterer, V. E. Shaternik

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The paper presents the results of studying the structure, phase composition, relief, and superconducting characteristics of oxygen-containing thin films of magnesium diboride (MgB₂) deposited on a dielectric substrate by magnetron sputtering of diboride-magnesium targets. The possibility of forming films of varying degrees of crystalline perfection and phase composition in the process of precipitation and annealing is shown, depending on the conditions of deposition and annealing. In the films, it is possible to realize various combinations of the Abrikosov vortex pinning centers (in the places of fluctuations of the critical temperature of the superconducting transition (T

Keywords: critical current density, diboride, superconducting thin films, upper critical field

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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: Kanika S. Raheja, A. Pandey, Shaila Bahl, Pratik Kumar, S. P. Lochab

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The subject of undertaking for this paper is the study of BaSO4 nanophosphor doped with Europium in which mainly the concentration of the rare earth impurity Eu (0.05, 0.1, 0.2, 0.5, and 1 mol %) has been varied. A comparative study of the thermoluminescence(TL) properties of the given nanophosphor has also been done using a well-known standard dosimetry material i.e. TLD-100.Firstly, a number of samples were prepared successfully by the chemical co-precipitation method. The whole lot was then compared to a well established standard material (TLD-100) for its TL sensitivity property. BaSO4:Eu ( 0.2 mol%) showed the highest sensitivity out of the lot. It was also found that when compared to the standard TLD-100, BaSo4:Eu (0.2mol%) showed surprisingly high sensitivity for a large range of doses. The TL response curve for all prepared samples has also been studied over a wide range of doses i.e 10Gy to 2kGy for gamma radiation. Almost all the samples of BaSO4:Eu showed a remarkable linearity for a broad range of doses, which is a characteristic feature of a fine TL dosimeter. The graph remained linear even beyond 1kGy for gamma radiation. Thus, the given nanophosphor has been successfully optimised for the concentration of the dopant material to achieve its highest TL sensitivity. Further, the comparative study with the standard material revealed that the current optimised sample shows an astonishingly better TL sensitivity and a phenomenal linear response curve for an incredibly wide range of doses for gamma radiation (Co-60) as compared to the standard TLD-100, which makes the current optimised BaSo4:Eu quite promising as an efficient gamma radiation dosimeter. Lastly, the present phosphor has been optimised for its annealing temperature to acquire the best results while also studying its fading and reusability properties.

Keywords: gamma radiation, nanoparticles, radiation dosimetry, thermoluminescence

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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: P. Mirahmadpour, M. H. Banitaba, D. Nematollahi

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The chemistry of coordination polymers in recent years has grown exponentially not only because of their interesting architectures but also due to their various technical applications in many fields including ion exchange, chemical catalysis, small molecule separations, and drug release. The use of bridging ligands for the controlled self-assembly of one, two or three dimensional metallo-supramolecular species is the subject of serious study in last decade. Numerous different synthetic methods have been offered for the preparation of coordination polymers such as (a) diffusion from the gas phase, (b) slow diffusion of the reactants into a polymeric matrix, (c) evaporation of the solvent at ambient or reduced temperatures, (d) temperature controlled cooling, (e) precipitation or recrystallisation from a mixture of solvents and (f) hydrothermal synthesis. The electrosynthetic process suggested several advantages over conventional approaches. A general advantage of electrochemical synthesis is that it allows synthesis under milder conditions than typical solvothermal or microwave synthesis. In this work we have introduced a simple electrochemical method for growing metal coordination polymers based on copper with a flexible 2,2’-thiodiacetic acid (TDA) and rigid 1,2,4,5-benzenetetracarboxylate (BTC) ligands. The structure of coordination polymers were characterized by scanning electron microscopy (SEM), X-ray powder diffraction (XRD), elemental analysis, thermal gravimetric (TG) and differential thermal analyses (DTA). The single-crystal X-ray diffraction analysis revealed that different conformations of the ligands and different coordination modes of the carboxylate group as well as different coordination geometries of the copper atoms. Electrochemical synthesis of coordination polymers has different advantages such as faster synthesis at lower temperature in compare with conventional chemical methods and crystallization of desired materials in a single synthetic step.

Keywords: 1, 2, 4, 5-benzenetetracarboxylate, coordination polymer, copper, 2, 2’-thiodiacetic acid

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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: S. Wisutmethangoon, S. Pannaray, T. Plookphol, J. Wannasin

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2024 Aluminium alloy was squeezed cast by the Gas Induced Semi Solid (GISS) process. Effect of artificial aging on microstructure and mechanical properties of this alloy was studied in the present work. The solutionized specimens were aged hardened at temperatures of 175°C, 200°C, and 225°C under various time durations. The highest hardness of about 77.7 HRE was attained from specimen aged at the temperature of 175 °C for 36 h. Upon investigation the microstructure by using Transmission Electron Microscopy (TEM), the phase was mainly attributed to the strengthening effect in the aged alloy. The apparent activation energy for precipitation hardening of the alloy was calculated as 133,805 J/mol.

Keywords: 2024 aluminium alloy, gas induced semi solid, T6 heat treatment, aged hardening, transmission electron microscopy

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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: Tatyana T. Tabakova, Elitsa N. Kolentsova, Dimitar Y. Dimitrov, Krasimir I. Ivanov, Yordanka G. Karakirova, Petya Cv. Petrova, Georgi V. Avdeev

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The catalytic oxidation of CO and volatile organic compounds (VOCs) is considered as one of the most efficient ways to reduce harmful emissions from various chemical industries. The effectiveness of gold-based catalysts for many reactions of environmental significance was proven during the past three decades. The aim of this work was to combine the favorable features of Au and Cu-Ce mixed oxides in the design of new catalytic materials of improved efficiency and economic viability for removal of air pollutants in waste gases from formaldehyde production. Supported oxides of copper and cerium with Cu: Ce molar ratio 2:1 and 1:5 were prepared by wet impregnation of g-alumina. Gold (2 wt.%) catalysts were synthesized by a deposition-precipitation method. Catalysts characterization was carried out by texture measurements, powder X-ray diffraction, temperature programmed reduction and electron paramagnetic resonance spectroscopy. The catalytic activity in the oxidation of CO, CH₃OH and (CH₃)₂O was measured using continuous flow equipment with fixed bed reactor. Both Cu-Ce/alumina samples demonstrated similar catalytic behavior. The addition of gold caused significant enhancement of CO and methanol oxidation activity (100 % degree of CO and CH₃OH conversion at about 60 and 140 ^oC, respectively). The composition of Cu-Ce mixed oxides affected the performance of gold-based samples considerably. Gold catalyst on Cu-Ce/γ-Al₂O₃ 1:5 exhibited higher activity for CO and CH₃OH oxidation in comparison with Au on Cu-Ce/γ-Al₂O₃ 2:1. The better performance of Au/Cu-Ce 1:5 was related to the availability of highly dispersed gold particles and copper oxide clusters in close contact with ceria.

Keywords: CO and VOCs oxidation, copper oxide, Ceria, gold catalysts

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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

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Authors: Maysam Shahsavari, Seyed Jamalaldin Haddadi

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There are several methods to localize a mobile robot such as relative, absolute and probabilistic. In this paper, particle filter due to its simple implementation and the fact that it does not need to know to the starting position will be used. This method estimates the position of the mobile robot using a probabilistic distribution, relying on a known map of the environment instead of predicting it. Afterwards, it updates this estimation by reading input sensors and control commands. To receive information from the surrounding world, distance to obstacles, for example, a Kinect is used which is much cheaper than a laser range finder. Finally, after explaining the Adaptive Particle Filter method and its implementation in detail, we will compare this method with the dead reckoning method and show that this method is much more suitable for situations in which we have a map of the environment.

Keywords: particle filter, localization, methods, odometry, kinect

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Authors: Mohammad Mojtahedpoor

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In this paper, it has been studied the method of optimal design of the supersonic nozzle. It could make viscous axisymmetric nozzles that the quality of their outlet flow is quite desired. In this method, it is optimized the divergent nozzle, at first. The initial divergent nozzle contour is designed through the method of characteristics and adding a suitable boundary layer to the inviscid contour. After that, it is made a proper grid and then simulated flow by the numerical solution and AUSM+ method by using the operation boundary condition. At the end, solution outputs are investigated and optimized. The numerical method has been validated with experimental results. Also, in order to evaluate the effectiveness of the present method, the nozzles compared with the previous studies. The comparisons show that the nozzles obtained through this method are sufficiently better in some conditions, such as the flow uniformity, size of the boundary layer, and obtained an axial length of the nozzle. Designing the convergent nozzle part affects by flow uniformity through changing its axial length and input diameter. The results show that increasing the length of the convergent part improves the output flow uniformity.

Keywords: nozzle, supersonic, optimization, characteristic method, CFD

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