Search results for: quantile modelling

Authors: Zied Guidara, Alexander Morgenstern, Aref Younes Maalej

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In this paper, a desiccant solar unit for air conditioning and desalination is presented first. Secondly, a dynamic modelling study of the desiccant wheel is developed. After that, a simulation study and an experimental investigation of the behaviour of desiccant wheel are developed. The experimental investigation is done in the chamber of commerce in Freiburg-Germany. Indeed, the variations of calculated and measured temperatures and specific humidity of dehumidified and rejected air are presented where a good agreement is found when comparing the model predictions with experimental data under the considered range of operating conditions. Finally, the study of the compartments of desalination and water condensation shows that the unit can produce an acceptable quantity of water at the same time of the air conditioning operation.

Keywords: air conditioning, desalination, condensation, design, desiccant wheel

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Authors: Osama A. Terfas, Abdelhakim A. Hameda, Abdusalam A. Alktiwi

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An investigation on ductile crack growth of shallow semi-elliptical surface cracks with a/w=0.2, a/c=0.33 under bending was carried out, where a is the crack depth, w is the plate thickness and c is the crack length at surface. Finite element analysis and experiments were modelling and the crack growth model were verified with experimental data. The results showed that the initial crack shape was no longer maintained as the crack developed under ductile tearing. The maximum growth at the deepest point at early stages was stopped when the crack depth reached half thickness and growth occurred beneath surface. Excellent agreement in the crack shape patterns was observed between the experiments and the crack growth model.

Keywords: crack growth, ductile tearing, mean stress, surface cracks

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Authors: Krishna Kistan Govender, Alex Masianoga

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The aim of this explanatory study was to critically understand how ethical leadership impacts employee creative behaviour, as well as the creative behaviour dimensions, in a South African transport and logistics SOE. A quantitative study was conducted using a pre-developed questionnaire, and data for 160 middle and executive managers was analysed through structural equation modelling and multiple regression techniques conducted with the Smart PLS statistical software. All five hypothesized relationships were supported, and it was confirmed that ethical leadership has a significant positive influence on employee creative behaviour, as well as on each of the creative behaviour dimensions, namely: idea exploration, idea generation, idea championing, and idea implementation.

Keywords: ethical leaders, employee creative behaviour, state-owned enterprises, South Africa

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Authors: Javier Fernandez De Canete, Alvaro Fernandez-Quintero

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Nowadays, adaptive control schemes are being used when model based control schemes are applied in presence of uncertainty and model mismatches. Artificial neural networks have been employed both in modelling and control of non-linear dynamic systems with unknown dynamics. In fact, these are powerful tools to solve this control problem when only input-output operational data are available. A neural network controller under SIMULINK together with the ARDUINO hardware platform has been used to perform real-time speed control of a computer case fan. Comparison of performance with a PID controller has also been presented in order to show the efficacy of neural control under different command signals tracking and also when disturbance signals are present in the speed control loops.

Keywords: neural networks, ARDUINO platform, SIMULINK, adaptive speed control

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Authors: Georgia Pozoukidou

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TELUM software is a land use model designed specifically to help metropolitan planning organizations (MPOs) prepare their transportation improvement programs and fulfill their numerous planning responsibilities. In this context obtaining, preparing, and validating socioeconomic forecasts are becoming fundamental tasks for an MPO in order to ensure that consistent population and employment data are provided to travel demand models. Chittenden County Metropolitan Planning Organization of Vermont State was used as a case study to test the applicability of TELUM land use model. The technical insights and lessons learned from the land use model application have transferable value for all MPOs faced with land use forecasting development and transportation modelling.

Keywords: calibration data requirements, land use models, land use planning, metropolitan planning organizations

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Authors: Huseyin Gokberk, Shian Gao

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CFD analysis of the relationship between the coefficients of lift and drag with respect to the angle of attack on a NACA 2412 wing section of an RC plane is conducted. Both the 2D and 3D models are investigated with the turbulence model. The 2D analysis has a free stream velocity of 10m/s at different AoA of 0°, 2°, 5°, 10°, 12°, and 15°. The induced drag and drag coefficient increased throughout the changes in angles even after the critical angle had been exceeded, whereas the lift force and coefficient of lift increased but had a limit at the critical stall angle, which results in values to reduce sharply. Turbulence flow characteristics are analysed around the aerofoil with the additions caused due to a finite 3D model. 3D results highlight how wing tip vortexes develop and alter the flow around the wing with the effects of the tapered configuration.

Keywords: CFD, turbulence modelling, aerofoil, angle of attack

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Authors: Gerardo Ayala-Jaimes, Gilberto Gonzalez-Avalos, Allen A. Castillo, Alejandra Jimenez

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The modeling of a single-phase cycloconverter in Bond Graph is presented, which includes an alternating current power supply, hybrid dynamics, switch control, and resistive load; this approach facilitates the integration of systems across different energy domains and structural analysis. Cycloconverters, used in motor control, demonstrate the viability of graphical modeling. The use of Bonds is proposed to model the hybrid interaction of the system, and the results are displayed through simulations using 20Sim and Multisim software. The motivation behind developing these models with a graphical approach is to design and build low-cost energy converters, thereby making the main contribution of this document the modeling and simulation of a single-phase cycloconverter.

Keywords: bond graph, hybrid system, rectifier, cycloconverter, modelling

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Authors: Ruwaida Abdul Rasid, Kevin J. Hughes, Peter J. Henggs, Mohamed Pourkashanian

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Heightened concerns over the amount of carbon emitted from coal-related processes are generating shifts to the application of biomass. In co-gasification, where coal is gasified along with biomass, the biomass may be fed together with coal (co-feeding) or an independent biomass gasifier needs to be integrated with the coal gasifier. The main aim of this work is to evaluate the biomass introduction methods in coal co-gasification. This includes the evaluation of biomass concentration input (B0 to B100) and its gasification performance. A process model is developed and simulated in Aspen HYSYS, where both coal and biomass are modeled according to its ultimate analysis. It was found that the syngas produced increased with increasing biomass content for both co-feeding and independent schemes. However, the heating values and heat duties decreases with biomass concentration as more CO2 are produced from complete combustion.

Keywords: aspen HYSYS, biomass, coal, co-gasification modelling, simulation

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Authors: R. Abdulrahman, A. Eardley, A. Soliman

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The proliferation in the development of mobile learning (m-learning) has played a vital role in the rapidly growing electronic learning market. This relatively new technology can help to encourage the development of in learning and to aid knowledge transfer a number of areas, by familiarizing students with innovative information and communications technologies (ICT). M-learning plays a substantial role in the deployment of learning methods for nursing students by using the Internet and portable devices to access learning resources ‘anytime and anywhere’. However, acceptance of m-learning by students is critical to the successful use of m-learning systems. Thus, there is a need to study the factors that influence student’s intention to use m-learning. This paper addresses this issue. It outlines the outcomes of a study that evaluates the unified theory of acceptance and use of technology (UTAUT) model as applied to the subject of user acceptance in relation to m-learning activity in nurse education. The model integrates the significant components across eight prominent user acceptance models. Therefore, a standard measure is introduced with core determinants of user behavioural intention. The research model extends the UTAUT in the context of m-learning acceptance by modifying and adding individual innovativeness (II) and quality of service (QoS) to the original structure of UTAUT. The paper goes on to add the factors of previous experience (of using mobile devices in similar applications) and the nursing students’ readiness (to use the technology) to influence their behavioural intentions to use m-learning. This study uses a technique called ‘convenience sampling’ which involves student volunteers as participants in order to collect numerical data. A quantitative method of data collection was selected and involves an online survey using a questionnaire form. This form contains 33 questions to measure the six constructs, using a 5-point Likert scale. A total of 42 respondents participated, all from the Nursing Institute at the Armed Forces Hospital in Saudi Arabia. The gathered data were then tested using a research model that employs the structural equation modelling (SEM), including confirmatory factor analysis (CFA). The results of the CFA show that the UTAUT model has the ability to predict student behavioural intention and to adapt m-learning activity to the specific learning activities. It also demonstrates satisfactory, dependable and valid scales of the model constructs. This suggests further analysis to confirm the model as a valuable instrument in order to evaluate the user acceptance of m-learning activity.

Keywords: mobile learning, nursing institute students’ acceptance of m-learning activity in Saudi Arabia, unified theory of acceptance and use of technology model (UTAUT), structural equation modelling (SEM)

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Authors: N. Benmebarek, F. Berrabah, S. Benmebarek

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This paper is interested by numerical analysis using PLAXIS code of geosynthetic reinforced embankment crossing a section about 11 km on sabkha soil of Chott El Hodna in Algeria. The site observations indicated that the surface soil of this sabkha is very sensitive to moisture and complicated by the presence of locally weak zones. Therefore, serious difficulties were encountered during building the first embankment layer. This paper focuses on the use of geosynthetic to mitigate the difficulty encountered. Due to the absence of an accepted design methods, parametric studies are carried out to assess the effect of basal embankment reinforcement on both the bearing capacity and compaction conditions. The results showed the contribution conditions of geosynthetics to improve the bearing capacity of sabkha soil.

Keywords: reinforced embankment, numerical modelling, geosynthetics, weak bearing capacity

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Authors: Lan Yang, Kathryn Cormican, Ming Yu

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ISO/IEC/IEEE 15288: 2015, Systems and Software Engineering - System Life Cycle Processes is an international standard that provides generic top-level process descriptions to support systems engineering (SE). However, the processes defined in the standard needs improvement to lift integrity and consistency. The goal of this research is to explore the way by building an ontology model for the SE standard to manage the knowledge of SE. The ontology model gives a whole picture of the SE knowledge domain by building connections between SE concepts. Moreover, it creates a hierarchical classification of the concepts to fulfil different requirements of displaying and analysing SE knowledge.

Keywords: knowledge management, model-based systems engineering, ontology modelling, systems engineering ontology

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Authors: Hari Govindmishra, Sarabjot Singh

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The study offers an approach to understand different determinants of shopping behaviour, and the effect of ethnicity on shopping behaviour. The results reveal that the Indian culture is composite in nature and because of which there is no difference between different ethnic groups in their preference for three shopping behaviour determinants, viz., status consciousness, need for touch and companion opinion. The research model investigates the relevant relationship between these constructs by using a structural equation modelling approach, which reveals that status consciousness, need for touch and companion opinion are significant determinants of shopping behaviour. Consequently, the shopping behaviour managers have to understand the collective nature of Indian ethnic consumers in their shopping behaviour.

Keywords: ethnic groups, status consciousness, companion opinion, need for touch, shopping behaviour

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Authors: Mohamed A. Abou-Shouk, Mahamoud M. Hewedi

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This study extends technology acceptance model (TAM) to investigate the antecedents and consequences of social media adoption by tourists and travel agents. It compares their perceptions on social media adoption and its consequences. Online survey was addressed to tourists and travel agents for data collection purposes. Structural equation modelling was employed for analysis purposes. The findings revealed that the majority of tourists and travel agents involved in the study believe in the usefulness of social media adoption for travel planning and marketing purposes. They agree that adopting social media could change the attitude of tourists towards specific destination or attraction and influence their purchasing decisions. This study contributes to knowledge by extending TAM and provides some managerial implication to marketers.

Keywords: TAM, social media, travel and tourism, travel agents

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Authors: Tudor Deaconescu, Andrea Deaconescu

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Deployment of pneumatic muscles in various industrial applications is still in its early days, considering the relative newness of these components. The field of robotics holds particular future potential for pneumatic muscles, especially in view of their specific behaviour known as compliance. The paper presents and discusses an innovative constructive solution for a gripper system mountable on an industrial robot, based on actuation by a linear pneumatic muscle and transmission of motion by gear and rack mechanism. The structural, operational and constructive models of the new gripper are presented, along with some of the experimental results obtained subsequently to the testing of a prototype. Further presented are two control variants of the gripper system, one by means of a 3/2-way fast-switching solenoid valve, the other by means of a proportional pressure regulator. Advantages and disadvantages are discussed for both variants.

Keywords: gripper system, pneumatic muscle, structural modelling, robotics

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Authors: N. M. Amin, W. N. A. W. Sulaiman

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The effectiveness of the seismic response between 3D solid elements model and simplified beam elements model has been investigated. At present, the studies of the numerical modelling using 3D solid element are minimal due to numerical software constraint. The finite element analysis using 3D solid element was chosen to study displacement response of laminated rubber bearing (LRB) during high intensity Kobe earthquake. In this research a simply supported bridge (single span), fixed at support was analysed by using transient analysis subjected to real time history loading of Kobe earthquake.

Keywords: laminated rubber bearing, solid element, simplified beam element, transient analysis

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Authors: Ivo Zution Goncalves, Christopher M. U. Neale, Hiran Medeiros, Everardo Mantovani, Natalia Souza

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Multispectral and thermal infrared imagery from satellite sensors coupled with climate and soil datasets were used to estimate evapotranspiration and biomass in center pivots planted to maize in Brazil during the 2016 season. The hybrid remote sensing based model named Spatial EvapoTranspiration Modelling Interface (SETMI) was applied using multispectral and thermal infrared imagery from the Landsat Thematic Mapper instrument. Field data collected by the IRRIGER center pivot management company included daily weather information such as maximum and minimum temperature, precipitation, relative humidity for estimating reference evapotranspiration. In addition, soil water content data were obtained every 0.20 m in the soil profile down to 0.60 m depth throughout the season. Early season soil samples were used to obtain water-holding capacity, wilting point, saturated hydraulic conductivity, initial volumetric soil water content, layer thickness, and saturated volumetric water content. Crop canopy development parameters and irrigation application depths were also inputs of the model. The modeling approach is based on the reflectance-based crop coefficient approach contained within the SETMI hybrid ET model using relationships developed in Nebraska. The model was applied to several fields located in Minas Gerais State in Brazil with approximate latitude: -16.630434 and longitude: -47.192876. The model provides estimates of real crop evapotranspiration (ET), crop irrigation requirements and all soil water balance outputs, including biomass estimation using multi-temporal satellite image inputs. An interpolation scheme based on the growing degree-day concept was used to model the periods between satellite inputs, filling the gaps between image dates and obtaining daily data. Actual and accumulated ET, accumulated cold temperature and water stress and crop water requirements estimated by the model were compared with data measured at the experimental fields. Results indicate that the SETMI modeling approach using data assimilation, showed reliable daily ET and crop water requirements for maize, interpolated between remote sensing observations, confirming the applicability of the SETMI model using new relationships developed in Nebraska for estimating mainly ET and water requirements in Brazil under tropical conditions.

Keywords: basal crop coefficient, irrigation, remote sensing, SETMI

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Authors: C. Patrascioiu

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The paper describes the modeling and simulation of the heat pumps domain processes. The main objective of the study is the use of the heat pump in propene–propane distillation processes. The modeling and simulation instrument is the Unisim^® Design simulator. The paper is structured in three parts: An overview of the compressing gases, the modeling and simulation of the freezing systems, and the modeling and simulation of the heat pumps. For each of these systems, there are presented the Unisim^® Design simulation diagrams, the input–output system structure and the numerical results. Future studies will consider modeling and simulation of the propene–propane distillation process with heat pump.

Keywords: distillation, heat pump, simulation, unisim design

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Authors: Ezrah Kipkirui Tonui, George Otieno Orwa

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A survey of 138 farmers was conducted in Rift valley, Kenya, in November and December 2013 in three counties (Uasin-gishu, Elgeyo-marakwet, and Tranzoia) to determine public knowledge and attitude towards genetically modified (GM) maize. Above two third (70%) of the respondents had knowledge of GM maize, mostly those educated and male. Female was found to be having low knowledge on GM maize. Public acknowledged the technology’s potential positive impacts, with more than 90% willing to adopt and more than 98% willing to buy GM seedlings at any given price. A small percentage less than 3% were of a negative opinion about willing to buy and adopt GM seeds. We conclude that GM technology has a role to play in food security in Kenya. However, the public needs more information about the technology, which can be provided through established sources of information and training. Finally, public knowledge and attitude on GM maize should be studied on a regular basis, and the survey population broadened to 47 counties.

Keywords: public, knowledge, attitudes, GM maize, Kenya

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Authors: Farnaz Fotovvatikhah, Javad Akbari

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Test time of a test architecture is an important factor which depends on the architecture's delay and test patterns. Here a new architecture to store the test results based on network on chip is presented. In addition, simple analytical model is proposed to calculate link test time for built in self-tester (BIST) and external tester (Ext) in multiprocessor systems. The results extracted from the model are verified using FPGA implementation and experimental measurements. Systems consisting 16, 25, and 36 processors are implemented and simulated and test time is calculated. In addition, BIST and Ext are compared in terms of test time at different conditions such as at different number of test patterns and nodes. Using the model the maximum frequency of testing could be calculated and the test structure could be optimized for high speed testing.

Keywords: test, nano on-chip network, JTAG, modelling

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Authors: M. Wigwe, J. G Akpa, E. N Wami

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Mathematical models of the absorber of a glycol dehydration facility was developed using the principles of conservation of mass and energy. Models which predict variation of the water content of gas in mole fraction, variation of gas and liquid temperatures across the parking height were developed. These models contain contributions from bulk and diffusion flows. The effect of diffusion on the process occurring in the absorber was studied in this work. The models were validated using the initial conditions in the plant data from Company W TEG unit in Nigeria. The results obtained showed that the effect of diffusion was noticed between z=0 and z=0.004 m. A deviation from plant data of 0% was observed for the gas water content at a residence time of 20 seconds, at z=0.004 m. Similarly, deviations of 1.584% and 2.844% were observed for the gas and TEG temperatures.

Keywords: separations, absorption, simulation, dehydration, water content, triethylene glycol

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Authors: Tizi Hayet, Berrama Tarek, Bounif Nadia

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Phenol and its derivatives are organic compounds utilized in the chemical industry. They are introduced into the environment by accidental spills and illegal release of industrial and municipal wastewater. Phenols are organic intermediaries that considered as potential pollutants. Adsorption is one of the purification and separation techniques used in this area. Algeria produces annually 131000 tones of fig; therefore, a large amount of fig leaves is generated, and the conversion of this waste into adsorbent allows the valorization of agricultural residue. The main purpose of this present work is to describe an application of the statistical method for modeling and optimization of the conditions of the phenol (Ph) adsorption from agricultural by-product locally available (fig leaves). The best experimental performance of Ph elimination on the adsorbent was obtained with: Adsorbent concentration (X2) = 0.2 g L-1; Initial concentration (X3) = 150 mg L-1; Speed agitation (X1) = 300 rpm.

Keywords: low-cost adsorbents, fig leaves, full factorial design, phenol, biosorption

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Authors: Juan Manuel Sanchez-Cartas, Gonzalo Leon

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A price competition algorithm for ABMs based on game theory principles is proposed to deal with the simulation of theoretical market models. The algorithm is applied to the classical Hotelling’s model and to a two-sided market model to show it leads to the optimal behavior predicted by theoretical models. However, when theoretical models fail to predict the equilibrium, the algorithm is capable of reaching a feasible outcome. Results highlight that the algorithm can be implemented in other simulation models to guarantee rational users and endogenous optimal behaviors. Also, it can be applied as a tool of verification given that is theoretically based.

Keywords: agent-based models, algorithmic game theory, multi-sided markets, price optimization

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Authors: Dewi Selvia Fardhyanti, Astrilia Damayanti

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Coal tar is a liquid by-product of the process of coal gasification and carbonation, also in some industries such as steel, power plant, cement, and others. This liquid oil mixture contains various kinds of useful compounds such as aromatic compounds and phenolic compounds. These compounds are widely used as raw material for insecticides, dyes, medicines, perfumes, coloring matters, and many others. This research investigates thermodynamic modelling of liquid-liquid equilibria (LLE) in solvent extraction of o-Cresol from the coal tar. The equilibria are modeled by ternary components of Wohl, Van Laar, and Three-Suffix Margules models. The values of the parameters involved are obtained by curve-fitting to the experimental data. Based on the comparison between calculated and experimental data, it turns out that among the three models studied, the Three-Suffix Margules seems to be the best to predict the LLE of o-Cresol for those system.

Keywords: coal tar, o-Cresol, Wohl, Van Laar, three-suffix margules

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Authors: Oulad Naoui Noureddine, Cherif ELAmine, Djehiche Abdelkader

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Water resources management includes several disciplines; the modeling of rainfall-runoff relationship is the most important discipline to prevent natural risks. There are several models to study rainfall-runoff relationship in watersheds. However, the majority of these models are not applicable in all basins of the world.  In this study, a new stochastic method called The Only Corresponding Competitor method (OCC) was used for the hydrological modeling of M’ZAB   Watershed (South East of Algeria) to adapt a few empirical models for any hydrological regime.  The results obtained allow to authorize a certain number of visions, in which it would be interesting to experiment with hydrological models that improve collectively or separately the data of a catchment by the OCC method.

Keywords: modelling, optimization, rainfall-runoff relationship, empirical model, OCC

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Authors: Akash K. Walunj, Dipendu Bhunia, Samarth Gupta, Prabhat Gupta

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Coupled shear walls consist of two shear walls connected intermittently by beams along the height. The behavior of coupled shear walls is mainly governed by the coupling beams. The coupling beams are designed for ductile inelastic behavior in order to dissipate energy. The base of the shear walls may be designed for elastic or ductile inelastic behavior. The amount of energy dissipation depends on the yield moment capacity and plastic rotation capacity of the coupling beams. In this paper, an analytical model of coupling beam was developed to calculate the rotations and moment capacities of coupling beam with conventional reinforcement.

Keywords: design studies, computational model(s), case study/studies, modelling, coupling beam

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Authors: M. Mosaad, J. H. Almutairi, A. S. Almutairi

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In this paper, saturated-vapour film condensation on a vertical wall with the backside cooled by forced convection is analyzed as a conjugate problem. In the analysis, the temperature and heat flux at the wall sides are assumed unknown and determined from the solution. The model is presented in a dimensionless form to take a broad view of the solution. The dimensionless variables controlling this coupled heat transfer process are discovered from the analysis. These variables explain the relative impact of the interactive heat transfer mechanisms of forced convection and film condensation. The study shows that the conjugate treatment of film condensation process yields results different from that predicted by a non-conjugate Nusselt-type solution, wherein the effect of the cooling fluid is neglected.

Keywords: film condensation, forced convection, coupled heat transfer, analytical modelling

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Authors: S. Jakšić, B. Žmuk

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The paper investigates the key factors of export dynamics for a set of Central and Southeast European (CSEE) countries in the context of current economic and financial crisis. In order to model the export dynamics a Global Vector Auto Regressive (GVAR) model is defined. As opposed to models which model each country separately, the GVAR combines all country models in a global model which enables obtaining important information on spill-over effects in the context of globalization and rising international linkages. The results of the study indicate that for most of the CSEE countries, exports are mainly driven by domestic shocks, both in the short run and in the long run. This study is the first application of the GVAR model to studying the export dynamics in the CSEE countries and therefore the results of the study present an important empirical contribution.

Keywords: export, GFEVD, global VAR, international trade, weak exogeneity

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Authors: Jadwiga Królikowska, Andrzej Królikowski, Jarosław Bajer

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The work delineates the threats of maladjustment of the capacity of rain canals, designed and built in the early 20th century, in connection to heavy rainfall, especially in summer. This is the cause of the so called 'urban floods.' It directly relates to fierce raise of paving in the cities. Resolving this problem requires a change in philosophy of draining the rainfall by wider use of retention, infiltration and usage of rainwater. In systemic approach to managing the safety of urban drainage systems the risk, which is directly connected to safety failures, has been accepted as a measure. The risk level defines the probability of occurrence of losses greater than the ones forecast for a given time frame. The procedure of risk modelling, enabling its numeric analysis by using appropriate weights, is a significant issue in this paper.

Keywords: risk management, drainage system, urban areas, urban floods

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Authors: Olga V. Korotkaya

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This article is devoted to an important problem of calculation of deflected mode of the combustion chamber and the nozzle end of a new liquid-propellant rocket cruise engine. A special attention is given to the methodology of calculation. Three operating modes are considered. The analysis has been conducted in ANSYS software. The methods of conducted research are mathematical modelling, substructure method, cyclic symmetry, and finite element method. The calculation has been carried out to order of S. P. Korolev Rocket and Space Corporation «Energia». The main results are practical. Proposed methodology and created models would be able to use for a wide range of strength problems.

Keywords: combustion chamber, cyclic symmetry, finite element method, liquid-propellant rocket engine, nozzle end, substructure

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Authors: Divij Gupta

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Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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