Search results for: Plastic equation of state

Authors: Nguyen Thi Thanh Truc, Chi-Hyeon Lee, Byeong-Kyu Lee, Srinivasa Reddy Mallampati

Abstract:

This study evaluated to facilitate separation of ABS plastics from other waste plastics by froth flotation after surface hydrophilization of ABS with heat treatment. The mild heat treatment at 100oC for 60s could selectively increase the hydrophilicity of the ABS plastics surface (i.e., ABS contact angle decreased from 79o to 65.8o) among other plastics mixture. The SEM and XPS results of plastic samples sufficiently supported the increase in hydrophilic functional groups and decrease contact angle on ABS surface, after heat treatment. As a result of the froth flotation (at mixing speed 150 rpm and airflow rate 0.3 L/min) after heat treatment, about 85% of ABS was selectively separated from other heavy plastics with 100% of purity. The effect of optimum treatment condition and detailed mechanism onto separation efficiency in the froth floatation was also investigated. This research is successful in giving a simple, effective, and inexpensive method for ABS separation from waste plastics.

Keywords: ABS, hydrophilic, heat treatment, froth flotation, contact angle.

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Authors: Abdul Rauf, Muhammad Irfan, Muhammad Nadeem, Ishtiaq Ahmed, Hafiz Muhammad Nasir Iqbal

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Rhizopus oligosporus was used in the present study for the production of protease enzyme under SSF. Sunflower meal was used as by-product of oil industry incorporated with organic salts was employed for the production of protease enzyme. The main purpose of the present was to study different parameters of protease productivity, its yields and to optimize basal fermentation conditions. The optimal conditions found for protease production using sunflower meal as a substrate in the present study were inoculum size (1%), substrate (Sunflower meal), substrate concentration (20 g), pH (3), cultivation period (72 h), incubation temperature (35oC), substrate to diluent-s ratio (1:2) and tween 81 (1 mL). The maximum production of protease in the presence of cheaper substrate at low concentration and stability at acidic pH, these characteristics make the strain and its enzymes useful in different industry.

Keywords: Acidic protease, Rhizopus oligosporus, Mediaoptimization, Solid state Fermentation

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Authors: Baoshan Wei, Shuai Han, Xing Zhang

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Local obstacle avoidance is critical for mobile robot navigation. It is a challenging task to ensure path optimality and safety in cluttered environments. We proposed an Environment Aware Dynamic Window Approach in this paper to cope with the issue. The method integrates environment characterization into Dynamic Window Approach (DWA). Two strategies are proposed in order to achieve the integration. The local goal strategy guides the robot to move through openings before approaching the final goal, which solves the local minima problem in DWA. The adaptive control strategy endows the robot to adjust its state according to the environment, which addresses path safety compared with DWA. Besides, the evaluation shows that the path generated from the proposed algorithm is safer and smoother compared with state-of-the-art algorithms.

Keywords: Adaptive control, dynamic window approach, environment aware, local obstacle avoidance, mobile robots.

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Authors: Melih Turgut, Süha Yılmaz

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In this paper, first, a characterization of spherical Pseudo null curves in Semi-Euclidean space is given. Then, to investigate position vector of a pseudo null curve, a system of differential equation whose solution gives the components of the position vector of a pseudo null curve on the Frenet axis is established by means of Frenet equations. Additionally, in view of some special solutions of mentioned system, characterizations of some special pseudo null curves are presented.

Keywords: Semi-Euclidean Space, Pseudo Null Curves, Position Vectors.

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Authors: Kayode A. Olaniyi, Adeola A. Ogunleye, Tola M. Osifeko

Abstract:

Electric Vehicles (EV) appear to be gaining increasing patronage as a feasible alternative to Internal Combustion Engine Vehicles (ICEVs) for having low emission and high operation efficiency. The EV energy storage systems are required to handle high energy and power density capacity constrained by limited space, operating temperature, weight and cost. The choice of strategies for energy storage evaluation, monitoring and control remains a challenging task. This paper presents review of various energy storage technologies and recent researches in battery evaluation techniques used in EV applications. It also underscores strategies for the hybrid energy storage management and control schemes for the improvement of EV stability and reliability. The study reveals that despite the advances recorded in battery technologies there is still no cell which possess both the optimum power and energy densities among other requirements, for EV application. However combination of two or more energy storages as hybrid and allowing the advantageous attributes from each device to be utilized is a promising solution. The review also reveals that State-of-Charge (SoC) is the most crucial method for battery estimation. The conventional method of SoC measurement is however questioned in the literature and adaptive algorithms that include all model of disturbances are being proposed. The review further suggests that heuristic-based approach is commonly adopted in the development of strategies for hybrid energy storage system management. The alternative approach which is optimization-based is found to be more accurate but is memory and computational intensive and as such not recommended in most real-time applications.

Keywords: Hybrid electric vehicle, hybrid energy storage, battery state estimation, ate of charge, state of health.

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Authors: Ha Thi Nguyen, Guangya Yang, Arne Hejde Nielsen, Peter Højgaard Jensen

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Automatic voltage regulator (AVR) plays an important role in volt/var control of synchronous condenser (SC) in power systems. Test AVR performance in steady-state and dynamic conditions in real grid is expensive, low efficiency, and hard to achieve. To address this issue, we implement hardware-in-the-loop (HiL) test for the AVR of SC to test the steady-state and dynamic performances of AVR in different operating conditions. Startup procedure of the system and voltage set point changes are studied to evaluate the AVR hardware response. Overexcitation, underexcitation, and AVR set point loss are tested to compare the performance of SC with the AVR hardware and that of simulation. The comparative results demonstrate how AVR will work in a real system. The results show HiL test is an effective approach for testing devices before deployment and is able to parameterize the controller with lower cost, higher efficiency, and more flexibility.

Keywords: Automatic voltage regulator, hardware-in-the-loop, synchronous condenser, real time digital simulator.

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Authors: Ping Liu, Yongkun Li

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This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.

Keywords: Enterprise cluster, permanence, extinction, impulsive, comparison theorem.

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Authors: Essam A. Al-Bahkali

Abstract:

A three-dimensional finite element modeling for austenitic stainless steel AISI 304 annealed condition sheets of 1.0 mm thickness are developed using ABAQUS® software. This includes spot welded and weld bonded joints models. Both models undergo thermal heat caused by spot welding process and then are subjected to axial load up to the failure point. The properties of elastic and plastic regions, modulus of elasticity, fracture limit, nugget and heat affected zones are determined. Complete loaddisplacement curve for each joining model is obtained and compared with the experiment data and with the finite element models without including the effect of thermal process. In general, the results obtained for both spot welded and weld-bonded joints affected by thermal process showed an excellent agreement with the experimental data.

Keywords: Heat Affected Zone, Spot Welded, Thermal Process, Weld-Bonded.

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Authors: Snehasis Kundu, Koeli Ghoshal

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In this paper, based on flume experimental data, the velocity distribution in open channel flows is re-investigated. From the analysis, it is proposed that the wake layer in outer region may be divided into two regions, the relatively weak outer region and the relatively strong outer region. Combining the log law for inner region and the parabolic law for relatively strong outer region, an explicit equation for mean velocity distribution of steady and uniform turbulent flow through straight open channels is proposed and verified with the experimental data. It is found that the sediment concentration has significant effect on velocity distribution in the relatively weak outer region.

Keywords: Inner and outer region, Log law, Parabolic law, Richardson number.

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Authors: R. C. Ferreira, H. H. C. De Lima, A. A. Cândido, O. M. Couto Junior, P. A. Arroyo, K. Q De Carvalho, G. F. Gauze, M. A. S. D. Barros

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Removal of the widespread used drug paracetamol from water was investigated using activated carbon originated from dende coconut mesocarp and babassu coconut mesocarp. Kinetic and equilibrium data were obtained at different values of pH. Both activated carbons showed high efficiency when pH ≤ pHPZC as the carbonil group of paracetamol molecule are adsorbed due to positively charged carbon surface. Microporosity also played an important role in such process. Pseudo-second order model was better adjusted to the kinetic results. Equilibrium data may be represented by Langmuir equation.

Keywords: Adsorption, activated carbon, babassu, dende.

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Authors: Abdelaziz Khernane, Naceur Khelil, Leila Djerou

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The aim of this work is to study the numerical implementation of the Hilbert Uniqueness Method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step, the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: Boundary control, exact controllability, finite difference methods, functional optimization.

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Authors: D. S. Vardar, A. S. Kipcak, F. T. Senberber, E. M. Derun, N. Tugrul, S. Piskin

Abstract:

Zinc borate is an important inorganic hydrate borate material, which can be used as a flame retardant agent and corrosion resistance material. This compound can loss its structural water content at higher than 290°C. Due to thermal stability; Zinc Borate can be used as flame retardant at high temperature process of plastic and gum. In this study, the ultrasonic reaction of zinc borates were studied using hydrozincite (Zn5(CO3)2·(OH)6) and boric acid (H3BO3) raw materials. Before the synthesis raw materials were characterized by X-Ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FT-IR). Ultrasonic method is a new application on the zinc borate synthesis. The synthesis parameters were set to 90°C reaction temperature and 55 minutes of reaction time, with 1:1, 1:2, 1:3, 1:4 and 1:5 molar ratio of starting materials (Zn5(CO3)2·(OH)6 : H3BO3). After the zinc borate synthesis, the products were analyzed by XRD and FT-IR. As a result, optimum molar ratio of 1:5 is determined for the synthesis of zinc borates with ultrasonic method.

Keywords: Borate, ultrasonic method, zinc borate, zinc borate synthesis.

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Authors: Kei Kawamorita, Ryouta Kasahara, Yuuki Mochizuki, Kenichiro Noguchi

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A separation-kernel-based operating system (OS) has been designed for use in secure embedded systems by applying formal methods to the design of the separation-kernel part. The separation kernel is a small OS kernel that provides an abstract distributed environment on a single CPU. The design of the separation kernel was verified using two formal methods, the B method and the Spin model checker. A newly designed semi-formal method, the extended state transition method, was also applied. An OS comprising the separation-kernel part and additional OS services on top of the separation kernel was prototyped on the Intel IA-32 architecture. Developing and testing of a prototype embedded application, a point-of-sale application, on the prototype OS demonstrated that the proposed architecture and the use of formal methods to design its kernel part are effective for achieving a secure embedded system having a high-assurance separation kernel.

Keywords: B method, embedded systems, extended state transition, formal methods, separation kernel, Spin.

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Authors: Oktay Emir

Abstract:

The objective of this study is to determine how entrepreneurs perceive the economic, social and physical impacts of tourism. The study was conducted in the city of Afyonkarahisar, Turkey, which is rich in thermal tourism resources and investments. A survey was used as the data collection method, and the questionnaire was applied to 472 entrepreneurs. A simple random sampling method was used to identify the sample. Independent sampling t-tests and ANOVA tests were used to analyse the data obtained. Additionally, some statistically significant differences (p<0.05) were found based on the participants’ demographic characteristics regarding their opinions about the social, economic and physical impacts of tourism activities.

Keywords: Tourism, perception, entrepreneurship, entrepreneurs, structural equation modelling.

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Authors: Maruful H. Mazumder, Raymond I. Gilbert, Zhen- T. Chang

Abstract:

A reliable estimate of the average bond stress within the anchorage of steel reinforcing bars in tension is critically important for the design of reinforced concrete member. This paper describes part of a recently completed experimental research program in the Centre for Infrastructure Engineering and Safety (CIES) at the University of New South Wales, Sydney, Australia aimed at assessing the effects of different factors on the anchorage requirements of modern high strength steel reinforcing bars. The study found that an increase in the anchorage length and bar diameter generally leads to a reduction of the average ultimate bond stress. By the extension of a well established analytical model of bond and anchorage, it is shown here that the differences in the average ultimate bond stress for different anchorage lengths is associated with the variable degree of plastic deformation in the tensile zone of the concrete surrounding the bar.

Keywords: Anchorage, Bond stress, Development length, Reinforced concrete.

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Authors: S. Cherif, M. Turki-Hadj Alouane

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In this paper, we propose a modified version of the Constant Modulus Algorithm (CMA) tailored for blind Decision Feedback Equalizer (DFE) of first order Markovian time varying channels. The proposed NonStationary CMA (NSCMA) is designed so that it explicitly takes into account the Markovian structure of the channel nonstationarity. Hence, unlike the classical CMA, the NSCMA is not blind with respect to the channel time variations. This greatly helps the equalizer in the case of realistic channels, and avoids frequent transmissions of training sequences. This paper develops a theoretical analysis of the steady state performance of the CMA and the NSCMA for DFEs within a time varying context. Therefore, approximate expressions of the mean square errors are derived. We prove that in the steady state, the NSCMA exhibits better performance than the classical CMA. These new results are confirmed by simulation. Through an experimental study, we demonstrate that the Bit Error Rate (BER) is reduced by the NSCMA-DFE, and the improvement of the BER achieved by the NSCMA-DFE is as significant as the channel time variations are severe.

Keywords: Time varying channel, Markov model, Blind DFE, CMA, NSCMA.

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Authors: T. Magrakvelidze, N. Bantsadze, N. Lekveishvili, Kh. Lomidze

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The results of an experimental study of the process of convective and boiling heat transfer in the vessel with stirrer for smooth and rough ring-shaped pipes are presented. It is established that creation of two-dimensional artificial roughness on the heated surface causes the essential (~100%) intensification of convective heat transfer. In case of boiling the influence of roughness appears on the initial stage of boiling and in case of fully developed nucleate boiling there was no intensification of heat transfer. The similitude equation for calculating convective heat transfer coefficient, which generalizes well experimental data both for the smooth and the rough surfaces is proposed.

Keywords: boiling, heat transfer, roughness.

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Authors: Ali Shojaei-Fard

Abstract:

In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations.

Keywords: Birkhoff Factorization, Connes-Kreimer Hopf Algebra of Rooted Trees, Integral Renormalization, Lax Pair Equation, Rota- Baxter Algebras.

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Authors: Thaniya Kaosol

Abstract:

General as well as the MSW management in Thailand is reviewed in this paper. Topics include the MSW generation, sources, composition, and trends. The review, then, moves to sustainable solutions for MSW management, sustainable alternative approaches with an emphasis on an integrated MSW management. Information of waste in Thailand is also given at the beginning of this paper for better understanding of later contents. It is clear that no one single method of MSW disposal can deal with all materials in an environmentally sustainable way. As such, a suitable approach in MSW management should be an integrated approach that could deliver both environmental and economic sustainability. With increasing environmental concerns, the integrated MSW management system has a potential to maximize the useable waste materials as well as produce energy as a by-product. In Thailand, the compositions of waste (86%) are mainly organic waste, paper, plastic, glass, and metal. As a result, the waste in Thailand is suitable for an integrated MSW management. Currently, the Thai national waste management policy starts to encourage the local administrations to gather into clusters to establish central MSW disposal facilities with suitable technologies and reducing the disposal cost based on the amount of MSW generated.

Keywords: MSW, management, sustainable, Thailand

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Authors: Djalal Hamed

Abstract:

The aim of this paper is to perform an analytic solution of steady state natural convection in a narrow rectangular channel between two vertical parallel MTR-type fuel plates, imposed under a cosine shape heat flux to determine the margin of the nuclear core power at which the natural convection cooling mode can ensure a safe core cooling, where the cladding temperature should not be reach the specific safety limits (90 °C). For this purpose, a simple computer program is developed to determine the principal parameter related to the nuclear core safety such as the temperature distribution in the fuel plate and in the coolant (light water) as a function of the reactor power. Our results are validated throughout a comparison against the results of another published work, which is considered like a reference of this study.

Keywords: Buoyancy force, friction force, friction factor, MTR-type fuel, natural convection, vertical heated rectangular channel.

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Authors: A. R. Nezamabadi, M. Karami Khorramabadi

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This paper studies dynamic stability of homogeneous beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Bernoulli-Euler beam theory. Applying the Hamilton's principle, the governing dynamic equation is established. The influences of applied voltage, foundation coefficient and piezoelectric thickness on the unstable regions are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Dynamic stability, Homogeneous graded beam-Piezoelectric layer, Harmonic balance method.

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Authors: Imen Mejri, Ahmed Mahmoudi, Mohamed A. Abbassi, Ahmed Omri

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The radiation effect within the solid anode, electrolyte, and cathode SOFC layers problem has been investigated in this paper. Energy equation is solved by the Lattice Boltzmann method (LBM). The Rosseland method is used to model the radiative transfer in the electrodes. The Schuster-Schwarzschild method is used to model the radiative transfer in the electrolyte. Without radiative effect, the found results are in good agreement with those published. The obtained results show that the radiative effect can be neglected.

Keywords: SOFC, lattice Boltzmann method, conduction, radiation.

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Authors: Y. J. Huang, C. H. Chang

Abstract:

In this paper, an intelligent automatic parking control method is proposed. First, the dynamical equation of the rear parking control is derived. Then a fuzzy logic control is proposed to perform the parking planning process. Further, a rear neural network is proposed for the steering control. Through the simulations and experiments, the intelligent auto-parking mode controllers have been shown to achieve the demanded goals with satisfactory control performance and to guarantee the system robustness under parametric variations and external disturbances. To improve some shortcomings and limitations in conventional parking mode control and further to reduce consumption time and prime cost.

Keywords: Auto-parking system, Fuzzy control, Neural network, Robust

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Authors: Guadalupe Pérez, Jorge Islas, Mirna Guevara, Raúl Suárez

Abstract:

Jatropha curcas is a perennial oleaginous plant that is currently considered an energy crop with high potential as an environmentally sustainable biofuel. During the last decades, research in biofuels has grown in tropical and subtropical regions in Latin America. However, as far we know, there are no reports on the growth and yield patterns of Jatropha curcas under the specific agro climatic scenarios of the State of Morelos, Mexico. This study presents the results of 52 months monitoring of 10 toxic and non-toxic ecotypes of Jatropha curcas (E1M, E2M, E3M, E4M, E5M, E6O, E7O, E8O, E9C, E10C) in an experimental plantation with minimum watering and fertilization resources. The main objective is to identify the ecotypes with the highest potential as biodiesel raw material in the select region, by developing experimental information. Specifically, we monitored biophysical and growth parameters, including plant survival and seed production (at the end of month 52), to study the performance of each ecotype and to establish differences among the variables of morphological growth, net seed oil content, and toxicity. To analyze the morphological growth, a statistical approach to the biophysical parameters was used; the net seed oil content -80 to 192 kg/ha- was estimated with the first harvest; and the toxicity was evaluated by examining the phorbol ester concentration (µg/L) in the oil extracted from the seeds. The comparison and selection of ecotypes was performed through a methodology developed based on the normalization of results. We identified four outstanding ecotypes (E1M, E2M, E3M, and E4M) that can be used to establish Jatropha curcas as energy crops in the state of Morelos for feasible agro-industrial production of biodiesel and other products related to the use of biomass.

Keywords: Biodiesel production, Jatropha curcas, morphologic growth, toxic and non-toxic ecotypes, seed oil content.

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Authors: Maisara Mohyeldin Gasim, A. K. Amirruddin, A. Shahrani

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This paper investigates the effect of replacing crankshaft with cam on the indicated torque during compression and power strokes in internal combustion engines. A Cycloidal cam profile was used in Revetec engine to calculate and compare the torque to a conventional engine, using a computational method. Firstly, the cylinder pressure was calculated using Ferguson equation, and then the torque calculated depending on cylinder pressure values in every crank angle. the results showed that by using Cycloidal cam profile in Revetec engine the torque can increased by 14% compared with conventional engines, which means an increase in engine efficiency.

Keywords: Revetec engine, indicated torque, cam profile.

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Keywords: Finite element model, model updating, modal data, optimal approximation.

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Authors: Ahmed N. Shmroukh, Ahmed Hamza H. Ali, Ali K. Abel-Rahman

Abstract:

Adsorption refrigeration working pair is a vital and is the main component in the adsorption refrigeration machine. Therefore the development key is laying on the adsorption pair that leads to the improvement of the adsorption refrigeration machine. In this study the state-of-the-art in the application of the adsorption refrigeration working pairs in both classical and modern adsorption pairs are presented, compared and summarized. It is found that the maximum adsorption capacity for the classical working pairs was 0.259kg/kg for activated carbon/methanol and that for the modern working pairs was 2kg/kg for maxsorb III/R-134a. The study concluded that, the performances of the adsorption working pairs of adsorption cooling systems are still need further investigations as well as developing adsorption pairs having higher sorption capacity with low or no impact on environmental, to build compact, efficient, reliable and long life performance adsorption chillier. Also, future researches need to be focused on designing the adsorption system that provide efficient heating and cooling for the adsorbent materials through distributing the adsorbent material over heat exchanger surface, to allow good heat and mass transfer between the adsorbent and the refrigerant.

Keywords: Adsorption, Adsorbent/Adsorbate Pairs, Refrigeration.

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Authors: Kee-Young Kwahk

Abstract:

Cognizant of the fact that enterprise systems involve organizational change and their implementation is over shadowed by a high failure rate, it is argued that there is the need to focus attention on employees- perceptions of such organizational change when explaining adoption behavior of enterprise systems. For this purpose, the research incorporates a conceptual constructo fattitude toward change that captures views about the need for organizational change. Centered on this conceptual construct, the research model includes beliefs regarding the system and behavioral intention as its consequences, and the personal characteristics of organizational commitment and perceived personal competence as its antecedents. Structural equation analysis using LISREL provides significant support for the proposed relationships. Theoretical and practical implications are discussed along with limitations.

Keywords: Sociotechnical changes, organizational change, attitude toward change, enterprise information systems.

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Authors: Nour Aljafari, Mariam, S. Maani, Serter Atabay, Tarig Ali, Said Daker, Lara Daher, Hamad Bukhammas, Mohammed Abou Shakra

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This paper aims at determining the soil characteristics that influence the irrigation process of green landscapes and deciding on the optimum amount of water needed for irrigation. The laboratory experiments were conducted using the constant head methodology to determine the soil infiltration rates. The steady state infiltration rate was reached after 10 minutes of infiltration at a rate of 200 mm/hr. The effects of different water heads on infiltration rates were also investigated, and the head of 11 cm was found to be the optimum head for the test. The experimental results showed consistent infiltration results for the range between 11 cm and 15 cm. The study also involved finding the initial moisture content, which ranged between 5% and 25%, and finding the organic content, which occupied 1% to 2% of the soil. These results will be later utilized, using the water balance approach, to estimate the optimum amount of water needed for irrigation for changing weather conditions.

Keywords: Infiltration rate, moisture content, grass type, organic content.

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Authors: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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