Search results for: solution density.

Authors: Imad Chaddad, Andrei A. Kolyshkin

Abstract:

Linear and weakly nonlinear analysis of shallow wake flows is presented in the present paper. The evolution of the most unstable linear mode is described by the complex Ginzburg-Landau equation (CGLE). The coefficients of the CGLE are calculated numerically from the solution of the corresponding linear stability problem for a one-parametric family of shallow wake flows. It is shown that the coefficients of the CGLE are not so sensitive to the variation of the base flow profile.

Keywords: Ginzburg-Landau equation, shallow wake flow, weakly nonlinear theory.

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Authors: Commander Sunil Tyagi

Abstract:

Effectiveness of Artificial Neural Networks (ANN) and Support Vector Machines (SVM) classifiers for fault diagnosis of rolling element bearings are presented in this paper. The characteristic features of vibration signals of rotating driveline that was run in its normal condition and with faults introduced were used as input to ANN and SVM classifiers. Simple statistical features such as standard deviation, skewness, kurtosis etc. of the time-domain vibration signal segments along with peaks of the signal and peak of power spectral density (PSD) are used as features to input the ANN and SVM classifier. The effect of preprocessing of the vibration signal by Discreet Wavelet Transform (DWT) prior to feature extraction is also studied. It is shown from the experimental results that the performance of SVM classifier in identification of bearing condition is better then ANN and pre-processing of vibration signal by DWT enhances the effectiveness of both ANN and SVM classifier

Keywords: ANN, Artificial Intelligence, Fault Diagnosis, Pattern Recognition, Rolling Element Bearing, SVM. Wavelet Transform

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Authors: R. R. Ali, W. A. W. A. Rahman, R. M. Kasmani, H. Hasbullah, N. Ibrahim, A. N. Sadikin, U. A. Asli

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In this study, tapioca starch, which acts as natural polymer, was added in the blend in order to produce biodegradable product. Low density polyethylene (LDPE) and tapioca starch blends were prepared by extrusion and the test sample by injection moulding process. Ethylene vinyl acetate (EVA) acts as compatibilizer while glycerol as processing aid was added in the blend. The blends were characterized by using melt flow index (MFI), fourier transform infrared (FTIR) and the effects of water absorption to the sample. As the starch content increased, MFI of the blend was decreased. Tensile testing were conducted shows the tensile strength and elongation at break decreased while the modulus increased as the starch increased. For the biodegradation, soil burial test was conducted and the loss in weight was studied as the starch content increased. Morphology studies were conducted in order to show the distribution between LDPE and starch.

Keywords: Biofilms, degradable polymers, starch based polyethylene, injection moulding.

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Authors: S. Hachemi, A. Ounis, S. Chabi

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This paper presents the results of an experimental  study on the effects of elevated temperature on compressive and  flexural strength of Normal Strength Concrete (NSC), High Strength  Concrete (HSC) and High Performance Concrete (HPC). In addition,  the specimen mass and volume were measured before and after  heating in order to determine the loss of mass and volume during the  test. In terms of non-destructive measurement, ultrasonic pulse  velocity test was proposed as a promising initial inspection method  for fire damaged concrete structure. 100 Cube specimens for three  grades of concrete were prepared and heated at a rate of 3°C/min up  to different temperatures (150, 250, 400, 600, and 900°C). The results  show a loss of compressive and flexural strength for all the concretes  heated to temperature exceeding 400°C. The results also revealed that  mass and density of the specimen significantly reduced with an  increase in temperature.

 

Keywords: High temperature, Compressive strength, Mass loss, Ultrasonic pulse velocity.

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Authors: S. Yessengabulov, A. Uyzbayeva

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Residential buildings fund of Kazakhstan was built in the Soviet time about 35-60 years ago without considering energy efficiency measures. Currently, most of these buildings are in a rundown condition and fail to meet the minimum of hygienic, sanitary and comfortable living requirements. The paper aims to examine the reports of recent building energy survey activities in the country and provide a possible solution for retrofitting existing housing stock built before 1989 which could be applicable for building envelope in cold climate. Methodology also includes two-dimensional modeling of possible practical solutions and further recommendations.

Keywords: Energy audit, energy efficient buildings in Kazakhstan, retrofit, two-dimensional conduction heat transfer analysis

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Authors: Hamoud Al-Hadrami, Hossein Emadi, Athar Hussain

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Green hydrogen is quickly emerging as a new source of the renewable energy for the world. Hydrogen production using water electrolysis is deemed as an environmentally friendly and safe source of energy for transportation and other industries. However, storing high volumes of hydrogen seems to be a significant challenge. Abandoned hydrocarbon reservoirs are considered as viable hydrogen storage options because of the availability of the required infrastructure such as wells and surface facilities. However, long-term wellbore integrity in these wells could be a serious challenge. The aim of this research is to investigate the effect of stored hydrogen on the wellbore integrity such as casing cement. The methodology is to experimentally expose hydrogen to wet and dry cement and measure the impact on cement rheological and mechanical properties. Hydrogen reduces the compressive strength of a set cement if it gets in contact with the cement slurry. Also, mixing hydrogen with cement slurry slightly increases its density and rheological properties which need to be considered to have a successful primary cementing operation.

Keywords: Green hydrogen, underground storage, wellbore integrity, cement, compressive strength.

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Authors: S. R. Kumar, Shashikant Rajpal

Abstract:

A nanocrystalline thin film of ZnSe was successfully electrodeposited on copper substrate using a non-aqueous solution and subsequently annealed in air at 400°C. XRD analysis indicates the polycrystalline deposit of (111) plane in both the cases. The sharpness of the peak increases due to annealing of the film and average grain size increases to 20 nm to 27nm. SEM photograph indicate that grains are uniform and densely distributed over the surface. Annealing increases the average grain size by 20%. The EDS spectroscopy shows the ratio of Zn & Se is 1.1 in case of annealed film. AFM analysis indicates the average roughness of the film reduces from 181nm to 165nm due to annealing of the film. The bandgap also decreases from 2.71eV to 2.62eV.

Keywords: Electrodeposition, Non-aqueous medium, SEM, XRD.

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Authors: Muammer Ozkan, Orkun Ozener, Irfan Yavasliol

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The fuel cost of the motor vehicle operating on its common route is an important part of the operating cost. Therefore, the importance of the fuel saving is increasing day by day. One of the parameters which improve fuel saving is the regulation of driving characteristics. The number and duration of stop is increased by the heavy traffic load. It is possible to improve the fuel saving with regulation of traffic flow and driving characteristics. The researches show that the regulation of the traffic flow decreases fuel consumption, but it is not enough to improve fuel saving without the regulation of driving characteristics. This study analyses the fuel consumption of two trips of city bus operating on its common route and determines the effect of traffic density and driving characteristics on fuel consumption. Finally it offers some suggestions about regulation of driving characteristics to improve the fuel saving. Fuel saving is determined according to the results obtained from simulation program. When experimental and simulation results are compared, it has been found that the fuel saving was reached up the to 40 percent ratios.

Keywords: Fuel Consumption, Fuel Economy, Driving Characteristics, Optimization

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Authors: May Phyo Thwal, Khin Htay Kyi, Kyaw Swar Soe

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According to the density of the chips, designers are trying to put so any facilities of computational and storage on single chips. Along with the complexity of computational and storage circuits, the designing, testing and debugging become more and more complex and expensive. So, hardware design will be built by using very high speed hardware description language, which is more efficient and cost effective. This paper will focus on the implementation of 32-bit ALU design based on Verilog hardware description language. Adder and subtracter operate correctly on both unsigned and positive numbers. In ALU, addition takes most of the time if it uses the ripple-carry adder. The general strategy for designing fast adders is to reduce the time required to form carry signals. Adders that use this principle are called carry look- ahead adder. The carry look-ahead adder is to be designed with combination of 4-bit adders. The syntax of Verilog HDL is similar to the C programming language. This paper proposes a unified approach to ALU design in which both simulation and formal verification can co-exist.

Keywords: Addition, arithmetic logic unit, carry look-ahead adder, Verilog HDL.

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Authors: Said Laachir, Aziz Laaribi

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The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.

Keywords: Helmholtz equation, Nikiforov-Uvarov method, exact solutions, eigenfunctions.

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Authors: Omid Jadidi, Fatemeh Firouzi, Enzo Bagliery

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Supplier selection, in real situation, is affected by several qualitative and quantitative factors and is one of the most important activities of purchasing department. Since at the time of evaluating suppliers against the criteria or factors, decision makers (DMS) do not have precise, exact and complete information, supplier selection becomes more difficult. In this case, Grey theory helps us to deal with this problem of uncertainty. Here, we apply Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and select the best supplier by using interval fuzzy numbers. Through this article, we compare TOPSIS with some other approaches and afterward demonstrate that the concept of TOPSIS is very important for ranking and selecting right supplier.

Keywords: TOPSIS, fuzzy number, MADM, Supplier selection

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Authors: Antonio Carlos Marques Alvim, Fernando Carvalho da Silva, Aquilino Senra Martinez

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For a quick and accurate calculation of spatial neutron distribution in nuclear power reactors 3D nodal codes are usually used aiming at solving the neutron diffusion equation for a given reactor core geometry and material composition. These codes use a second order polynomial to represent the transverse leakage term. In this work, a nodal method based on the well known nodal expansion method (NEM), developed at COPPE, making use of this polynomial expansion was modified to treat the transverse leakage term for the external surfaces of peripheral reflector nodes. The proposed method was implemented into a computational system which, besides solving the diffusion equation, also solves the burnup equations governing the gradual changes in material compositions of the core due to fuel depletion. Results confirm the effectiveness of this modified treatment of peripheral nodes for practical purposes in PWR reactors.

Keywords: Transverse leakage, nodal expansion method, power density, PWR reactors

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Authors: Baha Tulu Tanju, Kamil Kahveci

Abstract:

Buoyancy driven heat transfer of nanofluids in a cylindrical enclosure used as a control unit in the subsea hydrocarbon injection wells is investigated in this study. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. The base fluid is water and CuO is used as nanoparticles. Solution is obtained for nanoparticle solid volume fraction of 8% and for Rayleigh number in the range of 105-107. The results show that nanoparticle usage in the cylindrical electronic control unit has a significant effect on the flow and heat transfer.

Keywords: CuO, enclosure, nanofluid, natural convection

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Authors: Ya Hong Dong, Conrad T.C. Wong, S. Thomas Ng, James M.W. Wong

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Precast concrete has been widely adopted in public housing construction of Hong Kong since the mid-1980s. While pre-casting is considered an environmental friendly solution, there is lack of study to investigate the life cycle performance of precast concrete units. This study aims to bridge the knowledge gap by providing a comprehensive life cycle assessment (LCA) study for two precast elements namely façade and bathroom. The results show that raw material is the most significant contributor of environmental impact accounting for about 90% to the total impact. Furthermore, human health is more affected by the production of precast concrete than the ecosystems.

Keywords: Environment, green, LCA, LCIA, precast.

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Authors: Siddegowda, Y. A. Sathish, G. Krishnegowda, T. M. Mohan Kumar

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Road accidents are a human tragedy. They involve high human suffering and monetary costs in terms of untimely death, injuries and social problems. India had earned the dubious distinction of having more number of fatalities due to road accidents in the world. Road safety is emerging as a major social concern around the world especially in India because of infrastructure project works. A case study was taken on NH – 07 which connects to various major cities and industries. The study shows that major cases of fatalities are due to bus, trucks and high speed vehicles. The main causes of accidents are due to high density, non-restriction of speed, use of mobile phones, lack of board signs on road parking, visibility restriction, improper geometric design, road use characteristics, environmental aspects, social aspects etc. Data analysis and preventive measures are enlightened in this paper.

Keywords: Accidents, environmental aspects, fatalities, geometric design, road user characteristics.

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Authors: Débora C. G. Oliveira, Julio D. Salles, Bruna A. Moriy, João A. Rossignolo, Holmer Savastano JR.

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The objective of this study was to identify the optimal level of partial replacement of Portland cement by the ashes originating from burning straw and bagasse from sugar cane (ASB). Order to this end, were made five series of flat plates and cylindrical bodies: control and others with the partial replacement in 20, 30, 40 and 50% of ASB in relation to the mass of the Ordinary Portland cement, and conducted a mechanical testing of simple axial compression (cylindrical bodies) and the four-point bending (flat plates) and determined water absorption (WA), bulk density (BD) and apparent void volume (AVV) on both types of specimens. Based on the data obtained, it may be noted that the control treatment containing only Portland cement, obtained the best results. However, the cylindrical bodies with 20% ashes showed better results compared to the other treatments. And in the formulations plates, the treatment which showed the best results was 30% cement replacement by ashes.

Keywords: Modulus of rupture, simple axial compression, waste.

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Authors: Kleiner Marques Marra, Tércio Pedrosa

Abstract:

This paper reports the production of uranium-molybdenum alloys, which have been considered promising fuel for test and research nuclear reactors. U-Mo alloys were produced in three molybdenum contents: 5 wt.%, 7 wt.%, and 10 wt.%, using an electric vacuum induction furnace. A boron nitride-coated graphite crucible was employed in the production of the alloys and, after melting, the material was immediately poured into a boron nitride-coated graphite mold. The incorporation of carbon was observed, but it happened in a lower intensity than in the case of the non-coated crucible/mold. It is observed that the carbon incorporation increased and alloys density decreased with Mo addition. It was also noticed that the increase in the carbon or molybdenum content did not seem to change the as-cast structure in terms of granulation. The three alloys presented body-centered cubic crystal structure (g phase), after solidification, besides a seeming negative microsegregation of molybdenum, from the center to the periphery of the grains. There were signs of macrosegregation, from the base to the top of the ingots.

Keywords: Incorporation of carbon, macrosegregation and microsegregation, solidification, uranium-molybdenum alloys.

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Authors: Gábor Szűcs, Gyula Sallai

Abstract:

The goal of this paper is to find Wardrop equilibrium in transport networks at case of uncertainty situations, where the uncertainty comes from lack of information. We use simulation tool to find the equilibrium, which gives only approximate solution, but this is sufficient for large networks as well. In order to take the uncertainty into account we have developed an interval-based procedure for finding the paths with minimal cost using the Dempster-Shafer theory. Furthermore we have investigated the users- behaviors using game theory approach, because their path choices influence the costs of the other users- paths.

Keywords: Dempster-Shafer theory, S-O and U-Otransportation network, uncertainty of information, Wardropequilibrium.

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Authors: A. Traidia, F. Roger, A. Chidley, J. Schroeder, T. Marlaud

Abstract:

A transient finite element model has been developed to study the heat transfer and fluid flow during spot Gas Tungsten Arc Welding (GTAW) on stainless steel. Temperature field, fluid velocity and electromagnetic fields are computed inside the cathode, arc-plasma and anode using a unified MHD formulation. The developed model is then used to study the influence of different helium-argon gas mixtures on both the energy transferred to the workpiece and the time evolution of the weld pool dimensions. It is found that the addition of helium to argon increases the heat flux density on the weld axis by a factor that can reach 6.5. This induces an increase in the weld pool depth by a factor of 3. It is also found that the addition of only 10% of argon to helium decreases considerably the weld pool depth, which is due to the electrical conductivity of the mixture that increases significantly when argon is added to helium.

Keywords: GTAW, Thermal plasmas, Fluid flow, Marangoni effect, Shielding Gases.

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Authors: M. A. Rubio, A. Urquia

Abstract:

Genetic algorithms (GA) are applied to the solution of high-dimensional optimization problems. Additionally, sensitivity analysis (SA) is usually carried out to determine the effect on optimal solutions of changes in parameter values of the objective function. These two analyses (i.e., optimization and sensitivity analysis) are computationally intensive when applied to high-dimensional functions. The approach presented in this paper consists in performing the SA during the GA execution, by statistically analyzing the data obtained of running the GA. The advantage is that in this case SA does not involve making additional evaluations of the objective function and, consequently, this proposed approach requires less computational effort than conducting optimization and SA in two consecutive steps.

Keywords: Optimization, sensitivity, genetic algorithms, model calibration.

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Authors: Abdelouahab Moussaoui, Nabila Ferahta, Victor Chen

Abstract:

The development of aid's systems for the medical diagnosis is not easy thing because of presence of inhomogeneities in the MRI, the variability of the data from a sequence to the other as well as of other different source distortions that accentuate this difficulty. A new automatic, contextual, adaptive and robust segmentation procedure by MRI brain tissue classification is described in this article. A first phase consists in estimating the density of probability of the data by the Parzen-Rozenblatt method. The classification procedure is completely automatic and doesn't make any assumptions nor on the clusters number nor on the prototypes of these clusters since these last are detected in an automatic manner by an operator of mathematical morphology called skeleton by influence zones detection (SKIZ). The problem of initialization of the prototypes as well as their number is transformed in an optimization problem; in more the procedure is adaptive since it takes in consideration the contextual information presents in every voxel by an adaptive and robust non parametric model by the Markov fields (MF). The number of bad classifications is reduced by the use of the criteria of MPM minimization (Maximum Posterior Marginal).

Keywords: Clustering, Automatic Classification, SKIZ, MarkovFields, Image segmentation, Maximum Posterior Marginal (MPM).

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Authors: Bin Su

Abstract:

The draft Auckland Unitary Plan outlines the future land used for new housing and businesses with Auckland population growth over the next thirty years. According to Auckland Unitary Plan, over the next 30 years, the population of Auckland is projected to increase by one million, and up to 70% of total new dwellings occur within the existing urban area. Intensification will not only increase the number of median or higher density houses such as terrace house, apartment building, etc. within the existing urban area but also change mean housing design data that can impact building thermal performance under the local climate. Based on mean energy consumption and building design data, and their relationships of a number of Auckland sample houses, this study is to estimate the future mean housing energy consumption associated with the change of mean housing design data and evaluate housing energy efficiency with the Auckland Unitary Plan.

Keywords: Auckland Unitary Plan, Building thermal design, Housing design, Housing energy efficiency.

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Authors: Markéta Gregušová, Vladimíra Schindlerová, Ivana Šajdlerová, Petr Mohyla, Jan Kedroň

Abstract:

Company managers are always looking for more and more opportunities to succeed in today's fiercely competitive market. To maintain your place among the successful companies on the market today or to come up with a revolutionary business idea is much more difficult than before. Each new or improved method, tool, or approach that can improve the functioning of business processes or even of the entire system is worth checking and verification. The use of simulation in the design of manufacturing systems and their management in practice is one of the ways without increased risk, which makes it possible to find the optimal parameters of manufacturing processes and systems. The paper presents an example of use of simulation for solution of the bottleneck problem in the concrete company.

Keywords: Practical applications, business processes, systems, simulation.

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Authors: L. S. Chuah, Z. Hassan, C. W. Chin, H. Abu Hassan

Abstract:

This article reports on the studies of porous GaN prepared by ultra-violet (UV) assisted electrochemical etching in a solution of 4:1:1 HF: CH3OH:H2O2 under illumination of an UV lamp with 500 W power for 10, 25 and 35 minutes. The optical properties of porous GaN sample were compared to the corresponding as grown GaN. Porosity induced photoluminescence (PL) intensity enhancement was found in these samples. The resulting porous GaN displays blue shifted PL spectra compared to the as-grown GaN. Appearance of the blue shifted emission is correlated with the development of highly anisotropic structures in the morphology. An estimate of the size of the GaN nanostructure can be obtained with the help of a quantized state effective mass theory.

Keywords: Photoluminescence, porous GaN, electrochemical etching, Si, RF-MBE.

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Authors: Y. Alqaheem, A. Alomair, F. Altarkait, F. Alswaileh, Nusrat Tanoli

Abstract:

Helium market is continuously growing due to its essential uses in the electronic and healthcare sectors. Currently, helium is produced by cryogenic distillation but the process is uneconomical especially for low production volumes. On the other hand, polymeric membranes can provide a cost-effective solution for helium purification due to their low operating energy. However, the preparation of membranes involves the use of very toxic solvents such as chloroform. In this work, polyetherimide membranes were prepared using a less toxic solvent, n-methylpyrrolidone with a polymer-to-solvent ratio of 27 wt%. The developed membrane showed a superior helium permeability of 15.9 Barrer that surpassed the permeability of membranes made by chloroform.

Keywords: Helium separation, polyetherimide, dense membrane, gas permeability, solvent.

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Authors: Magdi M. E. Zumrawi, Mohamed Awad

Abstract:

Determination of Resilient Modulus (M_R) is quite important for characterizing materials in pavement design and evaluation. The main focus of this study is to develop a correlation that predict the resilient modulus of subgrade soils from simple and easy measured soil index properties. To achieve this objective, three subgrade soils representing typical Khartoum soils were selected and tested in the laboratory for measuring resilient modulus. Other basic laboratory tests were conducted on the soils to determine their physical properties. Several soil samples were prepared and compacted at different moisture contents and dry densities and then tested using resilient modulus testing machine. Based on experimental results, linear relationship of M_R with the consistency factor ‘F_c’ which is a combination of dry density, void ratio and consistency index had been developed. The results revealed that very good linear relationship found between the M_R and the consistency factor with a coefficient of linearity (R²) more than 0.9. The consistency factor could be used for the prediction of the M_R of compacted subgrade soils with precise and reliable results.

Keywords: Consistency factor, resilient modulus, subgrade soil, properties.

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Authors: Omar M. Sallabi, Younis El-Haddad

Abstract:

The Genetic Algorithm (GA) is one of the most important methods used to solve many combinatorial optimization problems. Therefore, many researchers have tried to improve the GA by using different methods and operations in order to find the optimal solution within reasonable time. This paper proposes an improved GA (IGA), where the new crossover operation, population reformulates operation, multi mutation operation, partial local optimal mutation operation, and rearrangement operation are used to solve the Traveling Salesman Problem. The proposed IGA was then compared with three GAs, which use different crossover operations and mutations. The results of this comparison show that the IGA can achieve better results for the solutions in a faster time.

Keywords: AI, Genetic algorithms, TSP.

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Authors: Nor-Edine Abriak, Mahfoud Benzerzour, Mouhamadou Amar, Abdeljalil Zri

Abstract:

In this work, firstly we have studied the potential of raw sediments and sediments treated with lime or cement for use in a foundation layer and the base layer of a roadway. Secondly, we have examined mineral changes caused by the addition of lime or cement in order to explain the mechanical performance of stabilized sediments. After determining the amount of lime and cement required stabilizing the sediments, the compaction characteristics and Immediate Bearing Capacity (IBI) were studied using the Modified Proctor method. Then, the evolution of the three parameters, which are optimum water content, maximum dry density and IBI, were determined. Mechanical performances can be evaluated through resistance to compression, resistance under traction and the elasticity modulus. The resistances of the formulations treated with ROLAC®645 increase with the amount of ROLAC®645. Traction resistance and the elastic modulus were used to evaluate the potential of the formulations as road construction materials using the classification diagram. The results show that all the other formulations with ROLAC®645 can be used in subgrades and foundation layers for roads.

Keywords: Sediment, lime, cement, roadway.

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Authors: L. Menaa, A. Cherifi, K. Tigouirat, M. Choura

Abstract:

Analyse of locally manufactured Low Density Polyethylene (LDPE) durability, used within lining systems at bottom of Municipal Solid Waste (landfill), is done in the present work. For this end, short and middle time creep behavior under tension of the analyzed material is carried out. The locally manufactured material is tested and compared to the European one (LDPE-CE). Both materials was tested in 03 various mediums: ambient and two aggressive (salty water and foam water), using three specimens in each case. A testing campaign is carried out using an especially designed and achieved testing bench. Moreover, characterisation tests were carried out to evaluate the medium effect on the mechanical properties of the tested material (LDPE). Furthermore, experimental results have been used to establish a law regression which can be used to predict creep behaviour of the analyzed material. As a result, the analyzed LDPE material has showed a good stability in different ambient and aggressive mediums; as well, locally manufactured LDPE seems more flexible, compared with the European one. This makes it more useful to the desired application.

Keywords: LDPE membrane, solid waste, aggressive mediums, durability

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Authors: Miloš Šeda

Abstract:

In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented.

Keywords: Flow shop, job shop, mixed integer model, representation scheme.

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