Search results for: shallow water equations

Authors: Ali A. Sayadi, Thomas R. Neitzert, G. Charles Clifton

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Lightweight concrete is being used in the construction industry as a building material in its own right. Ultra-lightweight concrete can be applied as a filler and support material for the manufacturing of composite building materials. This paper is about the development of a stable and reproducible ultra-lightweight concrete with the inclusion of poly-lactic acid (PLA) beads and assessing the feasibility of PLA as a lightweight aggregate that will deliver advantages such as a more eco-friendly concrete and a non-petroleum polymer aggregate. In total, sixty-three samples were prepared and the effectiveness of mineral admixture, curing conditions, water-cement ratio, PLA ratio, EPS ratio and perlite ratio on compressive strength of perlite concrete are studied. The results show that PLA particles are sensitive to alkali environment of cement paste and considerably shrank and lost their strength. A higher compressive strength and a lower density was observed when expanded polystyrene (EPS) particles replaced PLA beads. In addition, a set of equations is proposed to estimate the water-cement ratio, cement content and compressive strength of perlite concrete.

Keywords: Perlite concrete, poly-lactic acid, expanded polystyrene, concrete.

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Authors: Atamas N. A., Atamas A. A.

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Energetic and structural results for ethanol-water mixtures as a function of the mole fraction were calculated using Monte Carlo methodology. Energy partitioning results obtained for equimolar water-ethanol mixture and ether organic liquids are compared. It has been shown that at xet=0.22 the RDFs for waterethanol and ethanol-ethanol interactions indicated strong hydrophobic interactions between ethanol molecules and the local structure of solution is less structured at this concentration as at ether ones. Results obtained for ethanol-water mixture as a function of concentration are in good agreement with the experimental data.

Keywords: Ethanol, molecular liquids, Monte Carlo, water, thermodynamics.

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Authors: Changjin Xu

Abstract:

In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: Carrie Ho, Choo Bo Quan

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Urban non-point source (NPS) pollution for a residential catchment in Miri, Sarawak was investigated for two storm events in 2011. Runoff from two storm events were sampled and tested for water quality parameters including TSS, BOD5, COD, NH3-N, NO3-N, NO2-N, P and Pb. Concentration of the water quality parameters was found to vary significantly between storms and the pollutant of concern was found to be NO3-N, TSS, COD and Pb. Results were compared to the Interim National Water Quality Standards for Malaysia (INWQS),and the stormwater runoff from the study can be classified as polluted, exceeding class III water quality, especially in terms of TSS, COD, and NH3-N with maximum EMCs of 158, 135, and 2.17 mg/L, respectively.

Keywords: Residential land-use, urban runoff, water quality.

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Authors: Nasri M., Soleimani A.

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Since water resources of desert Naein City are very limited, a approach which saves water resources and meanwhile meets the needs of the greenspace for water is to use city-s sewage wastewater. Proper treatment of Naein-s sewage up to the standards required for green space uses may solve some of the problems of green space development of the city. The present paper closely examines available statistics and information associated with city-s sewage system, and determines complementary stages of sewage treatment facilities of the city. In the present paper, population, per capita water use, and required discharge for various greenspace pieces including different plants are calculated. Moreover, in order to facilitate the application of water resources, a Crude water distribution network apart from drinking water distribution network is designed, and a plan for mixing municipal wells- water with sewage wastewater in proposed mixing tanks is suggested. Hence, following greenspace irrigation reform and complementary plan, per capita greenspace of the city will be increased from current amount of 13.2 square meters to 32 square meters.

Keywords: Sewage Treatment Facility, Wastewater, Greenspace, Distribution Network, Naein City

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Authors: Ashwin Bala, K. Panthalaraja Kumaran, S. Prithviraj, R. Pradeep, J. Udhayakumar, S. Ajith

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In this paper comprehensive studies have been carried out for the design optimization of a waste heat recovery system for effectively utilizing the domestic air conditioner heat energy for producing hot water. Numerical studies have been carried for the geometry optimization of a waste heat recovery system for domestic air conditioners. Numerical computations have been carried out using a validated 2d pressure based, unsteady, 2nd-order implicit, SST k-ω turbulence model. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-Averaged, Navier- Stokes equations is employed. At identical inflow and boundary conditions various geometries were tried and effort has been taken for proposing the best design criteria. Several combinations of pipe line shapes viz., straight and spiral with different number of coils for the radiator have been attempted and accordingly the design criteria has been proposed for the waste heat recovery system design. We have concluded that, within the given envelope, the geometry optimization is a meaningful objective for getting better performance of waste heat recovery system for air conditioners.

Keywords: Air-conditioning system, Energy conversion system, Hot water production from waste heat, Waste heat recovery system.

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Authors: S. Wechmongkhonkon, N.Poomtong, S. Areerachakul

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Water quality is a subject of ongoing concern. Deterioration of water quality has initiated serious management efforts in many countries. This study endeavors to automatically classify water quality. The water quality classes are evaluated using 6 factor indices. These factors are pH value (pH), Dissolved Oxygen (DO), Biochemical Oxygen Demand (BOD), Nitrate Nitrogen (NO3N), Ammonia Nitrogen (NH3N) and Total Coliform (TColiform). The methodology involves applying data mining techniques using multilayer perceptron (MLP) neural network models. The data consisted of 11 sites of canals in Dusit district in Bangkok, Thailand. The data is obtained from the Department of Drainage and Sewerage Bangkok Metropolitan Administration during 2007-2011. The results of multilayer perceptron neural network exhibit a high accuracy multilayer perception rate at 96.52% in classifying the water quality of Dusit district canal in Bangkok Subsequently, this encouraging result could be applied with plan and management source of water quality.

Keywords: artificial neural network, classification, surface water quality

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Authors: Daniel Beysens, Imad Lekouch, Marina Mileta, Iryna Milimouk, Marc Muselli

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Dew harvesting needs only weak investment and exploits a free, clean and inexhaustible energy. This study aims to measure the relative contributions of dew and rain water in the Mediterranean Dalmatian coast and islands of Croatia and determine whether dew water is potable. Two sites were chosen, an open site on the coast favourable to dew formation (Zadar) and a less favourable site in a circus of mountains in Komiža (Vis Island). Between July 1st, 2003 and October 31st, 2006, dew hasbeen daily collected on a 1 m2 tilted (30°) test dew condenser together with ordinary meteorological data (air temperature and relative humidity, cloud coverage, windspeed and direction). The mean yearly cumulative dew yields were found to be 20 mm (Zadar) and 9.3 mm (Komiža ). During the dry season (May to October), monthly cumulative dew water yield can represent up to 38% of water collected by rain fall. In July 2003 and 2006, dew water represented about 120% of the monthly cumulative rain water. Dew and rain water were analyzed in Zadar. The corresponding parameters were measured: pH, electrical conductivity, major anions (HCO3 -, Cl-, SO4 2- , NO3 - , ,) and major cations (NH4 +, Na+, K+, Ca2+, Mg2+. Both dew and rain water are in conformity with the WHO directives for potability except Mg2+. Using existing roofs and refurbishing the abandoned impluviums to permit dew collection could then provide a useful supplementary amount of water, especially during the dry season.

Keywords: atmospheric water, dew chemistry, dew collection, radiative cooling, rain chemistry.

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Authors: Akbar H. Borzabadi, Omid S. Fard

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In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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Authors: Amir Gandomkar

Abstract:

Kish Islands in South of Iran is located in coastal water near Hormozgan Province. Based on the wind 3-hour statistics in Kish station, the mean annual windspeed in this Island is 8.6 knot (4.3 m/s). The maximum windspeed recorded in this stations 47 knot (23.5 m/s). In 45.7 percent of recorded times, windspeed has been Zero or less than 8 knot which is not suitable to use the wind energy. But in 54.3 percent of recorded times, windspeed has been more than 8 knot and suitable to use wind energy to run turbines. In 40.2 percent of recorded times, windspeed has been between 8 to 16 knot, in 13 percent of times between 16 to 24 knot and in 1 percent of times it has been higher than 24 knot. In this station, the direction of winds higher than 8 is west and wind direction in Kish station is stable in most times of the year.With regard to high – speed and stable direction winds during the year and also shallow coasts near this is land, it is possible to build offshore wind farms near Kish Island and utilize wind energy produce the electricity required in this Island during most of the year.

Keywords: Kish Island, Wind energy, Offshore wind farm, Windspeed, Wind direction

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Authors: A. J. Nazari, S. Honma

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This paper evaluates oil displacement by water in Hauterivian sandstone reservoir of Kashkari oil field in North of Afghanistan. The core samples of this oil field were taken out from well No-21^st, and the relative permeability and fractional flow are analyzed. Steady state flow laboratory experiments are performed to empirically obtain the fractional flow curves and relative permeability in different water saturation ratio. The relative permeability represents the simultaneous flow behavior in the reservoir. The fractional flow approach describes the individual phases as fractional of the total flow. The fractional flow curve interprets oil displacement by water, and from the tangent of fractional flow curve can find out the average saturation behind the water front flow saturation. Therefore, relative permeability and fractional flow curves are suitable for describing the displacement of oil by water in a petroleum reservoir. The effects of irreducible water saturation, residual oil saturation on the displaceable amount of oil are investigated through Buckley-Leveret analysis.

Keywords: Fractional flow, oil displacement, relative permeability, simultaneously flow.

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Authors: Ali Reza Rahmani, Mohamad Taghi Samadi, Maryam Khodadadi

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A laboratory set-up was designed to survey the effectiveness of UV/O3 advanced oxidation process (AOP) for the removal of Carbaryl from polluted water in batch reactor. The study was carried out by UV/O3 process for water samples containing 1 to 20 mg/L of Carbaryl in distilled water. Also the range of drinking water resources adjusted in synthetic water and effects of contact time, pH and Carbaryl concentration were studied. The residual pesticide concentration was determined by applying high performance liquid chromatography (HPLC). The results indicated that increasing of retention time and pH, enhances pesticide removal efficiency. The removal efficiency has been affected by pesticide initial concentration. Samples with low pesticide concentration showed a remarkable removal efficiency compared to the samples with high pesticide concentration. AOP method showed the removal efficiencies of 80% to 100%. Although process showed high performance for removal of pesticide from water samples, this process has different disadvantages including complication, intolerability, difficulty of maintenance and equipmental and structural requirements.

Keywords: AOP, Carbaryl, Pesticides, Water treatment.

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Authors: C. Recommandé, J.C. Blind, A. Clavel, R. Gourichon, V. Le Gal

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Simulations are developed in this paper with usual DSGE model equations. The model is based on simplified version of Smets-Wouters equations in use at European Central Bank which implies 10 macro-economic variables: consumption, investment, wages, inflation, capital stock, interest rates, production, capital accumulation, labour and credit rate, and allows take into consideration the banking system. Throughout the simulations, this model will be used to evaluate the impact of rate shocks recounting the actions of the European Central Bank during 2008.

Keywords: CC-LM, Central Bank, DSGE, Liquidity Shock, Non-standard Intervention.

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Authors: Nemat Abazari, Reza Abazari

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In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.

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Authors: Daniela Ocipova, Zuzana Vranayova, Ondrej Sikula

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Safe drinking water is one of the biggest issues facing the planet this century. The primary aim of this paper is to present our research focused on theoretical and experimental analysis of potable water and in-building water distribution systems from the point of view of microbiological risk on the basis of confrontation between the theoretical analysis and synthesis of gathered information in conditions of the Slovak Republic. The presence of the bacteria Legionella in water systems, especially in hot water distribution system, represents in terms of health protection of inhabitants the crucial problem which cannot be overlooked. Legionella pneumophila discovery, its classification and its influence on installations inside buildings are relatively new. There are a lot of guidelines and regulations developed in many individual countries for the design, operation and maintenance for tap water systems to avoid the growth of bacteria Legionella pneumophila, but in Slovakia we don-t have any. The goal of this paper is to show the necessity of prevention and regulations for installations inside buildings verified by simulation methods.

Keywords: Legionella pneumophila, water temperature, distribution system, risk analysis, simulations.

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Authors: A. Junaid, M. A. Z. Raja, I. M. Qureshi

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An evolutionary computing technique for solving initial value problems in Ordinary Differential Equations is proposed in this paper. Neural network is used as a universal approximator while the adaptive parameters of neural networks are optimized by genetic algorithm. The solution is achieved on the continuous grid of time instead of discrete as in other numerical techniques. The comparison is carried out with classical numerical techniques and the solution is found with a uniform accuracy of MSE ≈ 10-9 .

Keywords: Neural networks, Unsupervised learning, Evolutionary computing, Numerical methods, Fitness evaluation function.

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Authors: T. Manzur, S. Iffat, M. A. Noor

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In this paper, relationship between different properties of IC concrete and water cement ratio, obtained from a comprehensive experiment conducted on IC using local materials (Burnt clay chips- BC) is presented. In addition, saturated SAP was used as an IC material in some cases. Relationships have been developed through regression analysis. The focus of this analysis is on developing relationship between a dependent variable and an independent variable. Different percent replacements of BC and water cement ratios were used. Compressive strength, modulus of elasticity, water permeability and chloride permeability were tested and variations of these parameters were analyzed with respect to water cement ratio.

Keywords: Compressive strength, concrete, curing, lightweight, aggregate, superabsorbent polymer, internal curing.

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Authors: Shishen Xie

Abstract:

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.

Keywords: Competitive system, periodic solution, discrete time delay, topological degree.

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Authors: H. Elomari, M. Fallah, A. Elmousadik

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This work was conducted in the Souss region, known by severe water scarcity and a high agricultural activity dominated by the citrus (representing 40% of the area of Morocco's citrus). The objective of this work is to diagnose the current situation of the water efficiency in citrus irrigation and analyze the impact of various production factors on water productivity and its sustainability in the context of climate change. A field survey was conducted on 65 farms with areas varying from 0.5 to 350 ha. The stratification method was adopted as a sampling frame. Initial result indicates that the use of water shows a huge shortfall, since 31% of farms in the region are still using the surface irrigation system and 67% of farms are still using only the experience of the manager to control and adjust irrigation. The assessment of water productivity showed a value of 1.2 kg/m³ for surface irrigation and 3.8 kg/m³ for drip irrigation. The use of tools for control and adjustment of irrigation increases the water productivity of drip irrigation by 25%. The availability of the technical staff (internal or external) allows an increase in productivity of 172.4% compared to farms without technical advice.

Keywords: Citrus, irrigation efficiency, water productivity, drip irrigation.

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Authors: Frantisek Bozek, Alexandr Bozek, Eduard Bakos, Jiri Dvorak, Alena Bumbova, Lenka Jesonkova

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The case study deals with the semi-quantitative risk assessment of water resource earmarked for the emergency supply of population with drinking water. The risk analysis has been based on previously identified hazards/sensitivities of the elements of hydrogeological structure and technological equipment of ground water resource as well as on the assessment of the levels of hazard, sensitivity and criticality of individual resource elements in the form of point indexes. The following potential sources of hazard have been considered: natural disasters caused by atmospheric and geological changes, technological hazards, and environmental burdens. The risk analysis has proved that the assessed risks are acceptable and the water resource may be integrated into a crisis plan of a given region.

Keywords: Crisis, emergency, frequency, ground water, hazard, point index, risk, sensitivity, water supply.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, H. N. Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, Gauss-Seidel, Jacobi, algorithm

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Authors: Ekin Kıpçak, Yağmur Karakuş, Mesut Akgün

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Hydrogen is an important chemical in many industries and it is expected to become one of the major fuels for energy generation in the future. Unfortunately, hydrogen does not exist in its elemental form in nature and therefore has to be produced from hydrocarbons, hydrogen-containing compounds or water.

Above its critical point (374.8^oC and 22.1MPa), water has lower density and viscosity, and a higher heat capacity than those of ambient water. Mass transfer in supercritical water (SCW) is enhanced due to its increased diffusivity and transport ability. The reduced dielectric constant makes supercritical water a better solvent for organic compounds and gases. Hence, due to the aforementioned desirable properties, there is a growing interest toward studies regarding the gasification of organic matter containing biomass or model biomass solutions in supercritical water.

In this study, hydrogen and biofuel production by the catalytic gasification of 2-Propanol in supercritical conditions of water was investigated. Ru/Al₂O₃ was the catalyst used in the gasification reactions. All of the experiments were performed under a constant pressure of 25 MPa. The effects of five reaction temperatures (400, 450, 500, 550 and 600^oC) and five reaction times (10, 15, 20, 25 and 30 s) on the gasification yield and flammable component content were investigated.

Keywords: 2-Propanol, Gasification, Ru/Al2O3, Supercritical water.

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Authors: H. Shahabi

Abstract:

since in natural accidents, facilities that relate to this vita element are underground so, it is difficult to find quickly some right, exact and definite information about water utilities. There fore, this article has done operationally in Boukan city in Western Azarbaijan of Iran and it tries to represent operation and capabilities of Geographical Information system (GIS) in urban water management at the time of natural accidents. Structure of this article is that firstly it has established a comprehensive data base related to water utilities by collecting, entering, saving and data management, then by modeling water utilities we have practically considered its operational aspects related to water utility problems in urban regions.

Keywords: Natural Disaster, Geographical Information system (GIS), Modeling and network analysis, Boukan city in Western Azerbaijan, Iran

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Authors: N. Abbas, S. Lagomarsino, S. Cattari

Abstract:

Examining existing experimental results for shallow rigid foundations subjected to vertical centric load (N), accompanied or not with a bending moment (M), two main non-linear mechanisms governing the cyclic response of the soil-foundation system can be distinguished: foundation uplift and soil yielding. A soil-foundation failure limit, is defined as a domain of resistance in the two dimensional (2D) load space (N, M) inside of which lie all the admissible combinations of loads; these latter correspond to a pure elastic, non-linear elastic or plastic behavior of the soil-foundation system, while the points lying on the failure limit correspond to a combination of loads leading to a failure of the soil-foundation system. In this study, the proposed resistance domain is constructed analytically based on mechanics. Original elastic limit, uplift initiation limit and iso-uplift limits are constructed inside this domain. These limits give a prediction of the mechanisms activated for each combination of loads applied to the foundation. A comparison of the proposed failure limit with experimental tests existing in the literature shows interesting results. Also, the developed uplift initiation limit and iso-uplift curves are confronted with others already proposed in the literature and widely used due to the absence of other alternatives, and remarkable differences are noted, showing evident errors in the past proposals and relevant accuracy for those given in the present work.

Keywords: Foundation uplift, Iso-uplift curves, Resistance domain, Soil yield.

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Authors: Inom Sh. Normatov, Nurmakhmad Shermatov, Rajabali Barotov, Rano Eshankulova

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The results of the studies for the hydrogen production by the application of water electrolysis and plasma-chemical processing of gas condensate-waste of natural gas production methods are presented. Thin coating covers the electrode surfaces in the process of water electrolysis. Therefore, water for electrolysis was first exposed to electrosedimentation. The threshold voltage is shifted to a lower value compared with the use of electrodes made of stainless steel. At electrolysis of electrosedimented water by use of electrodes from stainless steel, a significant amount of hydrogen is formed. Pyrolysis of gas condensates in the atmosphere of a nitrogen was followed by the formation of acetylene (3-7 vol.%), ethylene (4-8 vol.%), and pyrolysis carbon (10-15 wt.%).

Keywords: Electrolyze, gas condensate, hydrogen, pyrolysis.

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Authors: Rahul Bansal, Sudipta Majumdar

Abstract:

This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: O. I. Nkwonta, G. M. Ochieng

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Surface water pollution is one of the serious environmental problems in rural areas of South Africa due to discharge of household waste into the streams, turning them into open sewers. In this study, samples of water were collected from a stream in Soshanguve and analysed. The result showed that pollution in the area was caused by man and its activities. The water quality in the area was found to have deterioted significantly after water runoff from farms and household wastes. The result shows, fertilizer runoff contributes 50% of the pollution while pesticides and sediments contribute up to 10% respectively in the streams, while household waste contributes up to 30%. This study gives an outline of the sources of water pollution in the area and provides a process of creating a clean and unpolluted environment for Soshanguve community in Pretoria north in order to achieve the 7th aim of the millennium development goals by 2015, which is ensuring environmental sustainability.

Keywords: Fertilizer, Household waste, Pollution, Roughing filters.

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Authors: Dennis Corbett

Abstract:

The city of Melbourne in Victoria, Australia, provides a number of examples of how a growing city can integrate urban planning and water planning to achieve sustainable urban development, environmental protection, liveability and integrated water management outcomes, and move towards becoming a “Water Sensitive City". Three examples are provided - the development at Botanic Ridge, where a 318 hectare residential development is being planned and where integrated water management options are being implemented using a “triple bottom line" sustainability investment approach; the Toolern development, which will capture and reuse stormwater and recycled water to greatly reduce the suburb-s demand for potable water, and the development at Kalkallo where a 1,200 hectare industrial precinct development is planned which will merge design of the development's water supply, sewerage services and stormwater system. The Paper argues that an integrated urban planning and water planning approach is fundamental to creating liveable, vibrant communities which meet social and financial needs while being in harmony with the local environment. Further work is required on developing investment frameworks and risk analysis frameworks to ensure that all possible solutions can be assessed equally.

Keywords: Integrated water management, stormwater management, sustainable urban development.

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Authors: A. Pereira, S. Haffner, L. V. Gasperin

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This paper presents two simplified models to determine nodal voltages in power distribution networks. These models allow estimating the impact of the installation of reactive power compensations equipments like fixed or switched capacitor banks. The procedure used to develop the models is similar to the procedure used to develop linear power flow models of transmission lines, which have been widely used in optimization problems of operation planning and system expansion. The steady state non-linear load flow equations are approximated by linear equations relating the voltage amplitude and currents. The approximations of the linear equations are based on the high relationship between line resistance and line reactance (ratio R/X), which is valid for power distribution networks. The performance and accuracy of the models are evaluated through comparisons with the exact results obtained from the solution of the load flow using two test networks: a hypothetical network with 23 nodes and a real network with 217 nodes.

Keywords: Distribution network models, distribution systems, optimization, power system planning.

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