Search results for: multiple-lump-type solution

Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: B. Chetti, W. A. Crosby

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The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: two-lobe bearing, thermal effect, static, dynamic characteristics

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Authors: K. A. D. D. Kuruppu, R. M. De Silva, K. M. N. De Silva

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This research work was based on developing a solar responsive aircraft window panel which can be used as a self-cleaning surface and also a surface which degrade Volatile Organic compounds (VOC) available in the aircraft cabin areas. Further, this surface has the potential of harvesting energy from Solar. The transparent inorganic nano sol solution was prepared. The obtained sol solution was characterized using X-ray diffraction, Particle size analyzer and FT-IR. The existing nano material which shows the similar characteristics was also used to compare the efficiencies with the newly prepared nano sol. Nano sol solution was coated on cleaned four aircraft window pieces separately using a spin coater machine. The existing nano material was dissolved and prepared a solution having the similar concentration as nano sol solution. Pre-cleaned four aircraft window pieces were coated with this solution and the rest cleaned four aircraft window pieces were considered as control samples. The control samples were uncoated from anything. All the window pieces were allowed to dry at room temperature. All the twelve aircraft window pieces were uniform in all the factors other than the type of coating. The surface morphologies of the samples were analyzed using SEM. The photocatalytic degradation of VOC was determined after incorporating gas of Toluene to each sample followed by the analysis done by UV-VIS spectroscopy. The self- cleaning capabilities were analyzed after adding of several types of stains on the window pieces. The self-cleaning property of each sample was analyzed using UV-VIS spectroscopy. The highest photocatalytic degradation of Volatile Organic compound and the highest photocatalytic degradation of stains were obtained for the samples which were coated by the nano sol solution. Therefore, the experimental results clearly show that there is a potential of using this nano sol in aircraft window pieces which favors the self-cleaning property as well as efficient photocatalytic degradation of VOC gases. This will ensure safer environment inside aircraft cabins.

Keywords: aircraft, nano, smart windows, solar

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Authors: Yendo Hu, Xu-Yu Wu, Dylan Oh

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GPS-Denied drones open the possibility of indoor applications, including dynamic arial surveillance, inspection, safety enforcement, and discovery. Indoor swarming further enhances these applications in accuracy, robustness, operational time, and coverage. For micro-drones, power management becomes a critical issue, given the battery payload restriction. This paper proposes an application enabling battery replacement solution that extends the micro-drone active phase without human intervention. First, a framework to quantify the effectiveness of a power management solution for a drone fleet is proposed. The operation-to-non-operation ratio, ONR, gives one a quantitative benchmark to measure the effectiveness of a power management solution. Second, a survey was carried out to evaluate the ONR performance for the various solutions. Third, through analysis, this paper proposes a solution tailored to the indoor micro-drone, suitable for swarming applications. The proposed automated battery replacement solution, along with a modified micro-drone architecture, was implemented along with the associated micro-drone. Fourth, the system was tested and compared with the various solutions within the industry. Results show that the proposed solution achieves an ONR value of 31, which is a 1-fold improvement of the best alternative option. The cost analysis shows a manufacturing cost of $25, which makes this approach viable for cost-sensitive markets (e.g., consumer). Further challenges remain in the area of drone design for automated battery replacement, landing pad/drone production, high-precision landing control, and ONR improvements.

Keywords: micro-drone, battery swap, battery replacement, battery recharge, landing pad, power management

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Authors: Muhammad Umair, Yuri Nikolaev, Denis Artemov, Ighor Uzhinsky

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A flexible manufacturing system is an integral part of a smart factory of industry 4.0 in which every machine is interconnected and works autonomously. Robots are in the process of replacing humans in every industrial sector. As the cyber-physical-system (CPS) and artificial intelligence (AI) are advancing, the manufacturing industry is getting more dependent on computers than human brains. This modernization has boosted the production with high quality and accuracy and shifted from classic production to smart manufacturing systems. However, material handling for such automated productions is a challenge and needs to be addressed with the best possible solution. Conventional clamping systems are designed for manual work and not suitable for highly automated production systems. Researchers and engineers are trying to find the most economical solution for loading/unloading and transportation workpieces from a warehouse to a machine shop for machining operations and back to the warehouse without human involvement. This work aims to propose an advanced multi-shape tooling solution for highly automated manufacturing systems. The currently obtained result shows that it could function well with automated guided vehicles (AGVs) and modern conveyor belts. The proposed solution is following requirements to be automation-friendly, universal for different part geometry and production operations. We used a bottom-up approach in this work, starting with studying different case scenarios and their limitations and finishing with the general solution.

Keywords: artificial intelligence, cyber physics system, Industry 4.0, material handling, smart factory, flexible manufacturing system

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Authors: Yang Zhong, Heng Liu

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

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

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Authors: N. Hatraf, L. Merabti, Z. Neffah, W. Taane

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The excessive consumption of fossil energies (electrical energy) during summer caused by the technological development involves more and more climate warming. In order to reduce the worst impact of gas emissions produced from classical air conditioning, heat driven solar absorption chiller is pretty promising; it consists on using solar as motive energy which is clean and environmentally friendly to provide cold. Solar absorption machine is composed by four components using Lithium Bromide /water as a refrigerating couple. LiBr- water is the most promising in chiller applications due to high safety, high volatility ratio, high affinity, high stability and its high latent heat. The lithium bromide solution is constitute by the salt lithium bromide which absorbs water under certain conditions of pressure and temperature however if the concentration of the solution is high in the absorption chillers; which exceed 70%, the solution will crystallize. The main aim of this article is to study the phenomena of the crystallization and to evaluate how the dependence between the electric conductivity and the concentration which should be controlled.

Keywords: absorption, crystallization, experimental results, lithium bromide solution

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: N. Tugrul, E. Sariburun, F. T. Senberber, A. S. Kipcak, E. Moroydor Derun, S. Piskin

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Boron-gypsum is a waste which occurs in the boric acid production process. In this study, the boron content of this waste is evaluated for the use in synthesis of magnesium borates and such evaluation of this kind of waste is useful more than storage or disposal. Magnesium borates, which are a sub-class of boron minerals, are useful additive materials for the industries due to their remarkable thermal and mechanical properties. Magnesium borates were obtained hydrothermally at different temperatures. Novelty of this study is the search of the solution density effects to magnesium borate synthesis process for the increasing the possibility of boron-gypsum usage as a raw material. After the synthesis process, products are subjected to XRD and FT-IR to identify and characterize their crystal structure, respectively.

Keywords: boron-gypsum, hydrothermal synthesis, magnesium borate, solution density

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Authors: Reza Ziaie Moayed, Hamidreza Rahmani

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Today, with developments in science and technology, there is an excessive potential for the use of nanomaterials in various fields of geotechnical project such as soil stabilization. This study investigates the effect of Nano-SiO₂ solution on the unconfined compression strength and Young's elastic modulus of Kaolinite. For this purpose, nano-SiO₂ was mixed with kaolinite in five different contents: 1, 2, 3, 4 and 5% by weight of the dry soil and a series of the unconfined compression test with curing time of one-day was selected as laboratory test. Analyses of the tests results show that stabilization of kaolinite with Nano-SiO₂ solution can improve effectively the unconfined compression strength of modified soil up to 1.43 times compared to  the pure soil.

Keywords: kaolinite, Nano-SiO2, stabilization, unconfined compression test, Young's modulus

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Authors: Ayat N. El-Shazly, Dina Magdy Abdo, Hamdy Maamoun Abdel-Ghafar, Xiangju Song, Heqing Jiang

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Product water recovery and draw solution (DS) reuse is the most energy-intensive stage in forwarding osmosis (FO) technology. Sucrose solution is the most suitable DS for FO application in food and beverages. However, sucrose DS recovery by conventional pressure-driven or thermal-driven concentration techniques consumes high energy. Herein, we developed a spontaneous and sustainable solar-driven evaporation process based on a photothermal membrane for the concentration and recovery of sucrose solution. The photothermal membrane is composed of multi-walled carbon nanotubes (f-MWCNTs)photothermal layer on a hydrophilic polyvinylidene fluoride (PVDF) substrate. The f-MWCNTs photothermal layer with a rough surface and interconnected network structures not only improves the light-harvesting and light-to-heat conversion performance but also facilitates the transport of water molecules. The hydrophilic PVDF substrate can promote the rapid transport of water for adequate water supply to the photothermal layer. As a result, the optimized f-MWCNTs/PVDF photothermal membrane exhibits an excellent light absorption of 95%, and a high surface temperature of 74 °C at 1 kW m−2 . Besides, it realizes an evaporation rate of 1.17 kg m−2 h−1 for 5% (w/v) of sucrose solution, which is about 5 times higher than that of the natural evaporation. The designed photothermal evaporation process is capable of concentrating sucrose solution efficiently from 5% to 75% (w/v), which has great potential in FO process and juice concentration.

Keywords: solar, pothothermal, membrane, MWCNT

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Authors: Sen Yung Lee, Chih Cheng Huang, Te Wen Tu

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A solution methodology without using integral transformation is proposed to develop analytical solutions for transient heat conduction in nonuniform hollow cylinders with time-dependent boundary condition at the outer surface. It is shown that if the thermal conductivity and the specific heat of the medium are in arbitrary polynomial function forms, the closed solutions of the system can be developed. The influence of physical properties on the temperature distribution of the system is studied. A numerical example is given to illustrate the efficiency and the accuracy of the solution methodology.

Keywords: analytical solution, nonuniform hollow cylinder, time-dependent boundary condition, transient heat conduction

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Authors: M. Al Nur, M. S. Kaiser

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Corrosion behaviour of hypereutectic Al-19Si automotive alloy in different pH=1, 3, 5, 7, 9, 11, and 13 environments was carried out using conventional gravimetric measurements and was complemented by resistivity, optical micrograph, scanning electron microscopy (SEM) and X-ray analyzer (EDX) investigations. Gravimetric analysis confirmed that the highest corrosion rate is shown at pH 13 followed by pH 1. Minimum corrosion occurs in the pH range of 3.0 to 11 due to establishment of passive layer on the surface. The highest corrosion rate at pH 13 is due to the presence of sodium hydroxide in the solution which dissolves the surface oxide film at a steady rate. At pH 1, it can be attributed that the presence of aggressive chloride ions serves to pick up the damage of the passive films at localized regions. With varying exposure periods by both, the environment complies with the normal corrosion rate profile that is an initial steep rise followed by a nearly constant value of corrosion rate. Resistivity increases in case of pH 1 solution for the higher pit formation and decreases at pH 13 due to formation of thin film. The SEM image of corroded samples immersed in pH 1 solution clearly shows pores on the surface and in pH 13 solution, and the corrosion layer seems more compact and homogenous and not porous.

Keywords: Al-Si alloy, corrosion, pH, resistivity, scanning electron microscopy (SEM)

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Authors: Roli Saini, Pradeep Kumar

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A coagulation/flocculation process was adopted for the reduction of carbamate insecticide (carbofuran) from aqueous solution. Ferric chloride (FeCl₃) was used as a coagulant to treat the carbofuran. To exploit the reduction efficiency of pesticide concentration and COD, the jar-test experiments were carried out and process was optimized through response surface methodology (RSM). The effects of two independent factors; i.e., FeCl₃ dosage and pH on the reduction efficiency were estimated by using central composite design (CCD). The initial COD of the 30 mg/L concentrated solution was found to be 510 mg/L. Results exposed that the maximum reduction occurred at an optimal condition of FeCl₃ = 80 mg/L, and pH = 5.0, from which the reduction of concentration and COD 75.13% and 65.34%, respectively. The present study also predicted that the obtained regression equations could be helpful as the theoretical basis for the coagulation process of pesticide wastewater.

Keywords: carbofuran, coagulation, optimization, response surface methodology

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Authors: S. Vasailor, C. Rattanakawin

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Electro-winning of copper metal from dilute sulfate solution (13.7 g/L) was performed in a lab electrolytic cell with stainless-steel cathode and lead-alloy anode. The effects of various parameters including cell voltage, electro-winning temperature and time were studied in order to acquire an appropriate current efficiency of copper deposition. The highest efficiency is about 95% obtaining from electro-winning condition of 3V, 55°C and 3,600 s correspondingly. The cathode copper with 95.5% Cu analyzed using atomic absorption spectrometry can be obtained from this single-winning condition. In order to increase the copper grade, solvent extraction should be used to increase the sulfate concentration, say 50 g/L, prior to winning the cathode copper effectively.

Keywords: copper metal, current efficiency, dilute sulfate solution, electro-winning

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Authors: M. S. Ashraf, Raja Rizwan Hussain, A. M. Alhozaimy, A. I. Al-Negheimish

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The effect of supplementary cementitious materials (SCMs) with concrete pore solution on the protective properties of the oxide films that form on reinforcing steel bars has been experimentally investigated using electrochemical impedance spectroscopy (EIS) and Tafel Scan. The tests were conducted on oxide films grown in saturated calcium hydroxide solutions that included different representative amounts of NaOH and KOH which are the compounds commonly observed in ordinary portland cement concrete pore solution. In addition to that, commonly used mineral admixtures (silica fume, natural pozzolan and fly ash) were also added to the simulated concrete pore solution. The results of electrochemical tests show that supplementary cementitious materials do have an effect on the protective properties of the passive oxide film. In particular, silica fume has been shown to have a negative influence on the film quality though it has positive effect on the concrete properties. Fly ash and natural pozzolan increase the protective qualities of the passive film. The research data in this area is very limited in the past and needed further investigation.

Keywords: supplementary cementitious materials (SCMs), passive film, EIS, Tafel scan, rebar, concrete, simulated concrete pore solution (SPS)

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Authors: A. Amiri Delouei

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In the current study, two-dimensional unsteady heat conduction in a functionally graded cylinder is studied analytically. The temperature distribution is in radial and longitudinal directions. Heat conduction coefficients are considered a power function of radius both in radial and longitudinal directions. The proposed solution can exactly satisfy the boundary conditions. Analytical unsteady temperature distribution for different parameters of functionally graded cylinder is investigated. The achieved exact solution is useful for thermal stress analysis of functionally graded cylinders. Regarding the analytical approach, this solution can be used to understand the concepts of heat conduction in functionally graded materials.

Keywords: functionally graded materials, unsteady heat conduction, cylinder, temperature distribution

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Authors: N. Guruprasad

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This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

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Authors: Kimia Kiaei, Mohammad Hasan Golpayegani

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The extraction of copper from a pregnant leach solution obtained through leaching was investigated in this study. Chemorex CP-150 was utilized as an organic extractant, while kerosene served as a diluent. The study focused on determining the optimal ratios of extractant to diluent, as well as the pH of the aqueous phase. Isotherm curves of extraction were generated, and Mc. Cabe-Thiele diagrams were constructed separately for an optimized experimental pH of 3.17 and a typical industrial pH of 2. Additionally, the sulfuric acid-to-PLS ratio and concentrations of interfering ions comprising Mn²⁺ and Fe³⁺ in the strip solution were evaluated during the stripping stage. The results indicated that the optimized values for the extractant-to-diluent ratio and pH were 5% and 3.17, respectively. The Mc. Cabe-Thiele diagrams revealed that at an aqueous-to-organic ratio of 1, the theoretical stages of solvent extraction at pH levels of 3.17 and 2 were one and two, respectively. Moreover, a sulfuric acid-to-PLS ratio of 20% was employed in the stripping stage, and it was observed that the concentrations of interfering ions fell within the acceptable range.

Keywords: copper, solvent extraction, heap leaching, Chemorex CP-150, pregnant leach solution

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Authors: K. Sever, Y. Seki, Z. Yenier, İ. Şen, M. Sarikanat

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It is known that Chitosan, as a natural polymer, has many excellent properties such as bicompotability, biodegradability and nontoxicity. Besides it has some limitations such as poor solubility in water and low conductivity in electrical devices and sensor applications. In order to improve electrical conductivity properties grapheme loading was conducted into chitosan. For this aim, chitosan solution was prepared in acidic condition and Graphene at different ratios was mixed with chitosan solution by the help of homogenizator. After film formation electrical conductivity values of chitosan and graphene loaded chitosan were determined. After grapheme loading into chitosan,solution significant increases in surface resistivity value of chitosan were observed. Besides variations on viscoeleastic properties with graphene loading was determined by dynamic mechanical analysis. Storage and Loss moduli were obtained for chitosan and grapheme loaded chitosan samples.

Keywords: chitosan, graphene, viscoelastic properties, electrical conductivity

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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: Mohammed A. Al-Ajmi, Reem S. Al-Kandari

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This study is concerned with the behavior of engineering students in Kuwait University which became a concern due to the global issues of education in all levels. A survey has been conducted to identify academic and societal issues that affect the engineering student performance through. The study is drawing major conclusions with regard to private tutoring and the online availability of textbooks’ solution manuals.

Keywords: solution manual, engineering, textbook, ethics

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Authors: S. Aizikovich, L. Krenev, Y. Tokovyy, Y. C. Wang

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An approximate analytical-numerical solution to the axisymmetric problem on thermo-mechanical indentation of a flat cylindrical punch into an arbitrarily non-homogeneous elastic half-space is constructed by making use of the bilateral asymptotic method. The key point of this method lies in evaluation of the ker¬nels in the obtained integral equations by making use of a numerical technique. Once the structure of the kernel is defined, it then is approximated by an analytical expression of special kind so that the solution of the integral equation can be achieved analytically. This fact allows for construction of the solution in an analytical form, which is convenient for analysis of the mechanical effects concerned with arbitrarily presumed non-homogeneity of the material.

Keywords: contact problem, circular punch, arbitrarily-nonhomogeneous halfspace

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Authors: H. Abchiche, M. Mellal

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The aim of this work is to study the parameters that influence the rheological behavior of a complex fluid (sodium Carboxyméthylcellulose solution), on a capillary rheometer. An installation has been made to be able to vary the diameter of trial conducts. The obtained results allowed us to deduce that: the diameter of trial conducts have a remarkable effect on the rheological responds.

Keywords: bingham’s fluid, CMC, cylindrical conduit, rheological behavior

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Authors: Su-Thing Ho, Shiao-Shing Chen, Hung-Te Hsu, Saikat Sinha Ray

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Forward osmosis (FO) is an emerging technology for direct and indirect potable water reuse application. However, successful implementation of FO is still hindered by the lack of draw solution recovery with high efficiency. Membrane distillation (MD) is a thermal separation process by using hydrophobic microporous membrane that is kept in sandwich mode between warm feed stream and cold permeate stream. Typically, temperature difference is the driving force of MD which attributed by the partial vapor pressure difference across the membrane. In this study, the direct contact membrane distillation (DCMD) system was used to recover diluted draw solution of FO. Na3PO4 at pH 9 and EDTA-2Na at pH 8 were used as the feed solution for MD since it produces high water flux and minimized salt leakage in FO process. At high pH, trivalent and tetravalent ions are much easier to remain at draw solution side in FO process. The result demonstrated that PTFE with pore size of 1 μm could achieve the highest water flux (12.02 L/m2h), followed by PTFE 0.45 μm (10.05 L/m2h), PTFE 0.1 μm (7.38 L/m2h) and then PP (7.17 L/m2h) while using 0.1 M Na3PO4 draw solute. The concentration of phosphate and conductivity in the PTFE (0.45 μm) permeate were low as 1.05 mg/L and 2.89 μm/cm respectively. Although PTFE with the pore size of 1 μm could obtain the highest water flux, but the concentration of phosphate in permeate was higher than other kinds of MD membranes. This study indicated that four kinds of MD membranes performed well and PTFE with the pore size of 0.45 μm was the best among tested membranes to achieve high water flux and high rejection of phosphate (99.99%) in recovery of diluted draw solution. Besides that, the results demonstrate that it can obtain high water flux and high rejection of phosphate when operated with cross flow velocity of 0.103 m/s with Tfeed of 60 ℃ and Tdistillate of 20 ℃. In addition to that, the result shows that Na3PO4 is more suitable for recovery than EDTA-2Na. Besides that, while recovering the diluted Na3PO4, it can obtain the high purity of permeate water. The overall performance indicates that, the utilization of DCMD is a promising technology to recover the diluted draw solution for FO process.

Keywords: membrane distillation, forward osmosis, draw solution, recovery

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Authors: Manojkumar Sabanayagam

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The Riemann hypothesis is an unsolved millennium problem and the search for a solution to the Riemann hypothesis is to study the pattern of prime number distribution. The scope of this paper is to identify the solution for the critical strip and the critical line axis, which has the non-trivial zero solutions using complex plane functions. The Riemann graphical plot is constructed using a linear complex variable function (X+iY) and is applicable only when X>1. But the investigation shows that complex variable behavior has two zones. The first zone is the transformation zone, where the definition of the complex plane should be a non-linear variable which is the critical strip zone in the graph (X=0 to 1). The second zone is the transformed zone (X>1) defined using linear variables conventionally. This paper deals with the Non-linear function in the transformation zone derived using cosine and sinusoidal time lag w.r.t imaginary number ‘i’. The alternate complex variable (Cosθ+i Sinθ) is used to understand the variables in the critical strip zone. It is concluded that the non-trivial zeros present in the Real part 0.5 are because the linear function is not the correct approach in the critical strip. This paper provides the solution to Reimann's hypothesis.

Keywords: Reimann hypothesis, critical strip, complex plane, transformation zone

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Authors: M. Chavez, H. Juarez, M. Pacio, O. Portillo

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PbS chemical bath heterojunction sollar cells have shown significant improvements in performance. Here we demonstrate a solar cell based on the heterojunction formed between PbS layer and PbS:Bi3+ thin films that are deposited via solution process at 40°C. The device achieve an current density of 4 mA/cm2. The simple and low-cost deposition method of PbS:Bi3+ films is promising for the fabrication.

Keywords: PbS doped, Bismuth, solar cell, thin films

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Authors: Ehsan Yadegari

Abstract:

While there are several metaheuristics and exact approaches to solving the Supply Chain Network Design (SCND) problem, there still remains an unfilled gap in using the Teaching-Learning-Based Optimization (TLBO) algorithm. The algorithm has demonstrated desirable results with problems with complicated combinational optimization. The present study introduces a Discrete Self-Study TLBO (DSS-TLBO) with priority-based solution representation that can solve a supply chain network configuration model to lower the total expenses of establishing facilities and the flow of materials. The network features four layers, namely suppliers, plants, distribution centers (DCs), and customer zones. It is designed to meet the customer’s demand through transporting the material between layers of network and providing facilities in the best economic Potential locations. To have a higher quality of the solution and increase the speed of TLBO, a distinct operator was introduced that ensures self-adaptation (self-study) in the algorithm based on the four types of local search. In addition, while TLBO is used in continuous solution representation and priority-based solution representation is discrete, a few modifications were added to the algorithm to remove the solutions that are infeasible. As shown by the results of experiments, the superiority of DSS-TLBO compared to pure TLBO, genetic algorithm (GA) and firefly Algorithm (FA) was established.

Keywords: supply chain network design, teaching–learning-based optimization, improved metaheuristics, discrete solution representation

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Authors: Tomer Gans-Or, Shmulik Pinkert

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The determination of lateral pile capacity per unit length is a key aspect in geotechnical engineering. Traditional approaches for assessing piles lateral capacity in cohesive soils involve the application of upper-bound and lower-bound plasticity theorems. However, a comprehensive solution encompassing the entire spectrum of soil strength parameters, particularly in frictional soils with or without cohesion, is still lacking. This research introduces an innovative implementation of the slice method limit equilibrium solution for lateral capacity assessment. For any given numerical discretization of the soil's domain around the pile, the lateral capacity evaluation is based on mobilized strength concept. The critical failure geometry is then found by a unique optimization procedure which includes both factor of safety minimization and geometrical optimization. The robustness of this suggested methodology is that the solution is independent of any predefined assumptions. Validation of the solution is accomplished through a comparison with established plasticity solutions for cohesive soils. Furthermore, the study demonstrates the applicability of the limit equilibrium method to address unresolved cases related to frictional and cohesive-frictional soils. Beyond providing capacity values, the method enables the utilization of the mobilized strength concept to generate safety-factor distributions for scenarios representing pre-failure states.

Keywords: lateral pile capacity, slice method, limit equilibrium, mobilized strength

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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