Search results for: soil modelling.

Authors: Martin Rozanek, Karel Roubik

Abstract:

The study deals with the modelling of the gas flow during heliox therapy. A special model has been developed to study the effect of the helium upon the gas flow in the airways during the spontaneous breathing. Lower density of helium compared with air decreases the Reynolds number and it allows improving the flow during the spontaneous breathing. In the cases, where the flow becomes turbulent while the patient inspires air the flow is still laminar when the patient inspires heliox. The use of heliox decreases the work of breathing and improves ventilation. It allows in some cases to prevent the intubation of the patients.

Keywords: Gas flow, heliox, Reynolds number, turbulent flow.

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Authors: Priti Bajpai, Mohammed Shibil

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This paper utilizes a comparative case study design to examine a regional onion market. The particular case of onion markets is used to understand perishable product supply chains. The site for the study is Dubai, United Arab Emirates. Results from a six-month field study are outlined. In particular, the findings suggest that firms should examine adding additional destinations to their supply chain. Further, we argue that utilizing Dubai as a supply chain hub is in certain cases counterproductive. Implications for food supply chains and regional trade are discussed.

Keywords: Supply chains, Food markets, Onion trade, Field study.

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Authors: Amit Kumar Gautam, Sudipta Majumdar

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This paper presents parameter estimation of a single-phase rectifier using extended Kalman filter (EKF). The state space model has been obtained using Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL). The capacitor voltage and diode current of the circuit have been estimated using EKF. Simulation results validate the better accuracy of the proposed method as compared to the least mean square method (LMS). Further, EKF has the advantage that it can be used for nonlinear systems.

Keywords: Extended Kalman filter, parameter estimation, single phase rectifier, state space modelling.

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Authors: Arkadiusz Biernacki

Abstract:

In this paper we present a statistical analysis of Voice over IP (VoIP) packet streams produced by the G.711 voice coder with voice activity detection (VAD). During telephone conversation, depending whether the interlocutor speaks (ON) or remains silent (OFF), packets are produced or not by a voice coder. As index of dispersion for both ON and OFF times distribution was greater than one, we used hyperexponential distribution for approximation of streams duration. For each stage of the hyperexponential distribution, we tested goodness of our fits using graphical methods, we calculated estimation errors, and performed Kolmogorov-Smirnov test. Obtained results showed that the precise VoIP source model can be based on the five-state Markov process.

Keywords: VoIP source modelling, distribution approximation, hyperexponential distribution.

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Authors: Ali K. M. Al-Nasrawi, Uday A. Al-Hamdany, Sarah M. Hamylton, Brian G. Jones, Yasir M. Alyazichi

Abstract:

Surface elevation dynamics have always responded to disturbance regimes. Creating Digital Elevation Models (DEMs) to detect surface dynamics has led to the development of several methods, devices and data clouds. DEMs can provide accurate and quick results with cost efficiency, in comparison to the inherited geomatics survey techniques. Nowadays, remote sensing datasets have become a primary source to create DEMs, including LiDAR point clouds with GIS analytic tools. However, these data need to be tested for error detection and correction. This paper evaluates various DEMs from different data sources over time for Apple Orchard Island, a coastal site in southeastern Australia, in order to detect surface dynamics. Subsequently, 30 chosen locations were examined in the field to test the error of the DEMs surface detection using high resolution global positioning systems (GPSs). Results show significant surface elevation changes on Apple Orchard Island. Accretion occurred on most of the island while surface elevation loss due to erosion is limited to the northern and southern parts. Concurrently, the projected differential correction and validation method aimed to identify errors in the dataset. The resultant DEMs demonstrated a small error ratio (≤ 3%) from the gathered datasets when compared with the fieldwork survey using RTK-GPS. As modern modelling approaches need to become more effective and accurate, applying several tools to create different DEMs on a multi-temporal scale would allow easy predictions in time-cost-frames with more comprehensive coverage and greater accuracy. With a DEM technique for the eco-geomorphic context, such insights about the ecosystem dynamic detection, at such a coastal intertidal system, would be valuable to assess the accuracy of the predicted eco-geomorphic risk for the conservation management sustainability. Demonstrating this framework to evaluate the historical and current anthropogenic and environmental stressors on coastal surface elevation dynamism could be profitably applied worldwide.

Keywords: DEMs, eco-geomorphic-dynamic processes, geospatial information science. Remote sensing, surface elevation changes.

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Authors: Panagiotis Kyratsis, Dr. Ing. Nikolaos Bilalis, Dr. Ing. Aristomenis Antoniadis

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Twist drills are geometrical complex tools and thus various researchers have adopted different mathematical and experimental approaches for their simulation. The present paper acknowledges the increasing use of modern CAD systems and using the API (Application Programming Interface) of a CAD system, drilling simulations are carried out. The developed DRILL3D software routine, creates parametrically controlled tool geometries and using different cutting conditions, achieves the generation of solid models for all the relevant data involved (drilling tool, cut workpiece, undeformed chip). The final data derived, consist a platform for further direct simulations regarding the determination of cutting forces, tool wear, drilling optimizations etc.

Keywords: Drilling, CAD based simulation, 3D-modelling.

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Authors: M. Almeshal, M. O. Tokhi, K. M. Goher

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A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.

Keywords: double inverted pendulum, modelling, robust control, simulation,

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Authors: U. Chattaraj, K. Dhusiya, M. Raviteja

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Perception reaction time of drivers is an outcome of human thought process, which is vague and approximate in nature and also varies from driver to driver. So, in this study a fuzzy logic based model for prediction of the same has been presented, which seems suitable. The control factors, like, age, experience, intensity of driving of the driver, speed of the vehicle and distance of stimulus have been considered as premise variables in the model, in which the perception reaction time is the consequence variable. Results show that the model is able to explain the impacts of the control factors on perception reaction time properly.

Keywords: Driver, fuzzy logic, perception reaction time, premise variable.

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Authors: Adel Smeda, Adel Alti, Mourad Oussalah, Abdallah Boukerram

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A key aspect of the design of any software system is its architecture. An architecture description provides a formal model of the architecture in terms of components and connectors and how they are composed together. COSA (Component-Object based Software Structures), is based on object-oriented modeling and component-based modeling. The model improves the reusability by increasing extensibility, evolvability, and compositionality of the software systems. This paper presents the COSA modelling tool which help architects the possibility to verify the structural coherence of a given system and to validate its semantics with COSA approach.

Keywords: Software Architecture, Architecture Description Languages, UML, Components, Connectors.

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Authors: James D. Clark, Bernard H. Stark

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The paper presents a modelling methodology for small scale multi-source renewable energy systems. Using historical site-specific weather data, the relationships of cost, availability and energy form are visualised as a function of the sizing of photovoltaic arrays, wind turbines, and battery capacity. The specific dependency of each site on its own particular weather patterns show that unique solutions exist for each site. It is shown that in certain cases the capital component cost can be halved if the desired theoretical demand availability is reduced from 100% to 99%.

Keywords: Energy Analysis, Forecasting, Distributed powergeneration.

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Authors: Ivana Scidà, Francesco Alotto, Anna Osello

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Due to the importance given today to innovation, the education sector is evolving thanks digital technologies. Virtual Reality (VR) can be a potential teaching tool offering many advantages in the field of training and education, as it allows to acquire theoretical knowledge and practical skills using an immersive experience in less time than the traditional educational process. These assumptions allow to lay the foundations for a new educational environment, involving and stimulating for students. Starting from the objective of strengthening the innovative teaching offer and the learning processes, the case study of the research concerns the digitalization of MastrLAB, High Quality Laboratory (HQL) belonging to the Department of Structural, Building and Geotechnical Engineering (DISEG) of the Polytechnic of Turin, a center specialized in experimental mechanical tests on traditional and innovative building materials and on the structures made with them. The MastrLAB-VR has been developed, a revolutionary innovative training tool designed with the aim of educating the class in total safety on the techniques of use of machinery, thus reducing the dangers arising from the performance of potentially dangerous activities. The virtual laboratory, dedicated to the students of the Building and Civil Engineering Courses of the Polytechnic of Turin, has been projected to simulate in an absolutely realistic way the experimental approach to the structural tests foreseen in their courses of study: from the tensile tests to the relaxation tests, from the steel qualification tests to the resilience tests on elements at environmental conditions or at characterizing temperatures. The research work proposes a methodology for the virtualization of technical laboratories through the application of Building Information Modelling (BIM), starting from the creation of a digital model. The process includes the creation of an independent application, which with Oculus Rift technology will allow the user to explore the environment and interact with objects through the use of joypads. The application has been tested in prototype way on volunteers, obtaining results related to the acquisition of the educational notions exposed in the experience through a virtual quiz with multiple answers, achieving an overall evaluation report. The results have shown that MastrLAB-VR is suitable for both beginners and experts and will be adopted experimentally for other laboratories of the University departments.

Keywords: Building Information Modelling, digital learning, education, virtual laboratory, virtual reality.

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Authors: Avita K. Marihal, K.S. Jagadeesh, Sarita Sinha

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Pentachlorophenol (PCP) is a polychlorinated aromatic compound that is widespread in industrial effluents and is considered to be a serious pollutant. Among the variety of industrial effluents encountered, effluents from tanning industry are very important and have a serious pollution potential. PCP is also formed unintentionally in effluents of paper and pulp industries. It is highly persistent in soils and is lethal to a wide variety of beneficial microorganisms and insects, human beings and animals. The natural processes that breakdown toxic chemicals in the environment have become the focus of much attention to develop safe and environmentfriendly deactivation technologies. Microbes and plants are among the most important biological agents that remove and degrade waste materials to enable their recycling in the environment. The present investigation was carried out with the aim of developing a microbial system for bioremediation of PCP polluted soils. A number of plant species were evaluated for their ability to tolerate different concentrations of pentachlorophenol (PCP) in the soil. The experiment was conducted for 30 days under pot culture conditions. The toxic effect of PCP on plants was studied by monitoring seed germination, plant growth and biomass. As the concentration of PCP was increased to 50 ppm, the inhibition of seed germination, plant growth and biomass was also increased. Although PCP had a negative effect on all plant species tested, maize and groundnut showed the maximum tolerance to PCP. Other tolerating crops included wheat, safflower, sunflower, and soybean. From the rhizosphere soil of the tolerant seedlings, as many as twenty seven PCP tolerant bacteria were isolated. From soybean, 8; sunflower, 3; safflower 8; maize 2; groundnut and wheat, 3 each isolates were made. They were screened for their PCP degradation potentials. HPLC analyses of PCP degradation revealed that the isolate MAZ-2 degraded PCP completely. The isolate MAZ-1 was the next best isolate with 90 per cent PCP degradation. These strains hold promise to be used in the bioremediation of PCP polluted soils.

Keywords: Biodegradation, pentachlorophenol, rhizobacteria.

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Authors: H. Bouadi, M. Bouchoucha, M. Tadjine

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In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. After, the use of Backstepping approach for the synthesis of tracking errors and Lyapunov functions, a sliding mode controller is developed in order to ensure Lyapunov stability, the handling of all system nonlinearities and desired tracking trajectories. Finally simulation results are also provided in order to illustrate the performances of the proposed controller.

Keywords: Dynamic modeling, nonholonomic constraints, Backstepping, sliding mode.

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Authors: James A Foster, Guglielmo S Aglietti

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Multifunctional structures are a potentially disruptive technology that allows for significant mass savings on spacecraft. The specific concept addressed herein is that of a multifunctional power structure. In this paper, a parametric optimisation of the design of such a structure that uses commercially available battery cells is presented. Using numerical modelling, it was found that there exists several trade-offs aboutthe conflict between the capacity of the panel and its mechanical properties. It was found that there is no universal optimal location for the cells. Placing them close to the mechanical interfaces increases loading in the mechanically weak cells whereas placing them at the centre of the panel increases the stress inthe panel and reduces the stiffness of the structure.

Keywords: Design Optimization, Multifunctional Structures, Power Storage.

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Authors: Hossein Abbasi

Abstract:

The stability is an important topic to plan and manage the energy in the microgrids as the same as the conventional power systems. The voltage and frequency stability is one of the most important issues recently studied in microgrids. The objectives of this paper are the modelling and designing of the components and optimal controllers for the voltage and frequency control of the AC/DC hybrid microgrid under the different disturbances. Since the PI controllers have the advantages of simple structure and easy implementation, so they are designed and modeled in this paper. The harmony search (HS) algorithm is used to optimize the controllers’ parameters. According to the achieved results, the PI controllers have a good performance in voltage and frequency control of the microgrid.

Keywords: Frequency control, HS algorithm, microgrid, PI controller, voltage control.

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Authors: Gilberto Gonzalez-A, Noe Barrera-G

Abstract:

An analysis of a synchronous generator in a bond graph approach is proposed. This bond graph allows to determine the simplified models of the system by using singular perturbations. Firstly, the nonlinear bond graph of the generator is linearized. Then, the slow and fast state equations by applying singular perturbations are obtained. Also, a bond graph to get the quasi-steady state of the slow dynamic is proposed. In order to verify the effectiveness of the singularly perturbed models, simulation results of the complete system and reduced models are shown.

Keywords: Bond graph modelling, synchronous generator, singular perturbations

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Authors: M. Sedighizadeh, A. Rezazadeh

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A method has been developed for preparing load models for power flow and stability. The load modeling (LOADMOD) computer software transforms data on load class mix, composition, and characteristics into the from required for commonly–used power flow and transient stability simulation programs. Typical default data have been developed for load composition and characteristics. This paper defines LOADMOD software and describes the dynamic and static load modeling techniques used in this software and results of initial testing for BAKHTAR power system.

Keywords: Load Modelling, Static, Power Flow.

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Authors: Neil Bar, Andrew Heweston

Abstract:

Probability of failure (PF) often appears alongside factor of safety (FS) in design acceptance criteria for rock slope, underground excavation and open pit mine designs. However, the design acceptance criteria generally provide no guidance relating to how PF should be calculated for homogeneous and heterogeneous rock masses, or what qualifies a ‘reasonable’ PF assessment for a given slope design. Observational and kinematic methods were widely used in the 1990s until advances in computing permitted the routine use of numerical modelling. In the 2000s and early 2010s, PF in numerical models was generally calculated using the point estimate method. More recently, some limit equilibrium analysis software offer statistical parameter inputs along with Monte-Carlo or Latin-Hypercube sampling methods to automatically calculate PF. Factors including rock type and density, weathering and alteration, intact rock strength, rock mass quality and shear strength, the location and orientation of geologic structure, shear strength of geologic structure and groundwater pore pressure influence the stability of rock slopes. Significant engineering and geological judgment, interpretation and data interpolation is usually applied in determining these factors and amalgamating them into a geotechnical model which can then be analysed. Most factors are estimated ‘approximately’ or with allowances for some variability rather than ‘exactly’. When it comes to numerical modelling, some of these factors are then treated deterministically (i.e. as exact values), while others have probabilistic inputs based on the user’s discretion and understanding of the problem being analysed. This paper discusses the importance of understanding the key aspects of slope design for homogeneous and heterogeneous rock masses and how they can be translated into reasonable PF assessments where the data permits. A case study from a large open pit gold mine in a complex geological setting in Western Australia is presented to illustrate how PF can be calculated using different methods and obtain markedly different results. Ultimately sound engineering judgement and logic is often required to decipher the true meaning and significance (if any) of some PF results.

Keywords: Probability of failure, point estimate method, Monte-Carlo simulations, sensitivity analysis, slope stability.

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Authors: Farnaz G. Nezami, Mir B. Aryanezhad, Seyed J. Sadjadi

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In this paper a nonlinear model is presented to demonstrate the relation between production and marketing departments. By introducing some functions such as pricing cost and market share loss functions it will be tried to show some aspects of market modelling which has not been regarded before. The proposed model will be a constrained signomial geometric programming model. For model solving, after variables- modifications an iterative technique based on the concept of geometric mean will be introduced to solve the resulting non-standard posynomial model which can be applied to a wide variety of models in non-standard posynomial geometric programming form. At the end a numerical analysis will be presented to accredit the validity of the mentioned model.

Keywords: Geometric programming, marketing, nonlinear optimization, production.

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Authors: Konstantinos C. Giotopoulos, Christos E. Alexakos, Grigorios N. Beligiannis, Spiridon D.Likothanassis

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In this contribution a newly developed elearning environment is presented, which incorporates Intelligent Agents and Computational Intelligence Techniques. The new e-learning environment is constituted by three parts, the E-learning platform Front-End, the Student Questioner Reasoning and the Student Model Agent. These parts are distributed geographically in dispersed computer servers, with main focus on the design and development of these subsystems through the use of new and emerging technologies. These parts are interconnected in an interoperable way, using web services for the integration of the subsystems, in order to enhance the user modelling procedure and achieve the goals of the learning process.

Keywords: E-learning environments, intelligent agents, user modeling, Bayesian Networks, computational intelligence.

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Authors: Oleksandr Poliakov, Genadiy Olinichenko, Yevgen Pashkov, Vadym Kramar, Mykhaylo Kalinin

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For maintenance of a spine stability during the postoperative period a transpedicular fixing of its elements is often used. Usually the transpedicular systems are formed of rods which as a result form a design of the frame type, fastening by screws to vertebras. Such design should be rigid and perceive loadings operating from the spine without essential deformations. From the perfection point of view of known designs their stress whole, and each of elements, in particular is of interest. In this study the modeling of the transpedicular screw is performed and estimation of its deformations taking into account interaction with a vertebra body having variable structure is made.

Keywords: Spine, screw, stress-strain state, transpedicular fixation system, vertebra

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Authors: Bogdan Walek, Jiri Bartos, Cyril Klimes, Jaroslav Prochazka, Pavel Smolka, Juraj Masar, Martin Pesl

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This paper focuses on creating a component model of information system under uncertainty. The paper identifies problem in current approach of component modeling and proposes fuzzy tool, which will work with vague customer requirements and propose components of the resulting component model. The proposed tool is verified on specific information system and results are shown in paper. After finding suitable sub-components of the resulting component model, the component model is visualised by tool.

Keywords: Component, component model, fuzzy, fuzzy rules, fuzzy sets, information system, modelling, tool.

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Authors: Md. Sharif Imam Ibne Amir, Mohammad Masud Kamal khan, Mohammad Golam Rasul, Raj H Sharma, Fatema Akram

Abstract:

Future flood can be predicted using the probable maximum flood (PMF). PMF is calculated using the historical discharge or rainfall data considering the other climatic parameters remaining stationary. However climate is changing globally and the key climatic variables are temperature, evaporation, rainfall and sea level rise are likely to change. To develop scenarios to a basin or catchment scale these important climatic variables should be considered. Nowadays scenario based on climatic variables is more suitable than PMF. Six scenarios were developed for a large Fitzroy basin and presented in this paper.

Keywords: Climate change, rainfall, potential evaporation, scenario, sea level rise (SLR), sub-catchment.

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Authors: Jonas Engqvist, Per Hard af Segerstad, Birger Bring, Mathias Wallin

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A macroscopic constitutive equation is developed for a high-density cellulose insulation material with emphasis on the outof- plane stress relaxation behavior. A hypothesis is proposed where the total stress is additively composed by an out-of-plane visco-elastic isotropic contribution and an in-plane elastic orthotropic response. The theory is validated against out-of-plane stress relaxation, compressive experiments and in-plane tensile hysteresis, respectively. For large scale finite element simulations, the presented model provides a balance between simplicity and capturing the materials constitutive behaviour.

Keywords: Cellulose insulation materials, constitutive modelling, material characterisation, pressboard.

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Authors: Disciglio G., Lops F., Carlucci A., Gatta G., Tarantino A., Frabboni L., Carriero F., Cibelli F., Raimondo M. L., Tarantino E.

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The tomato is a very important crop, whose cultivation in the Mediterranean basin is severely affected by the phytoparasitic weed Phelipanche ramosa. The semiarid regions of the world are considered the main areas where this parasitic weed is established causing heavy infestation as it is able to produce high numbers of seeds (up to 500,000 per plant), which remain viable for extended period (more than 20 years). In this paper the results obtained from eleven treatments in order to control this parasitic weed including chemical, agronomic, biological and biotechnological methods compared with the untreated test under two plowing depths (30 and 50 cm) are reported. The split-plot design with 3 replicates was adopted. In 2014 a trial was performed in Foggia province (southern Italy) on processing tomato (cv Docet) grown in the field infested by Phelipanche ramosa. Tomato seedlings were transplant on May 5, on a clay-loam soil. During the growing cycle of the tomato crop, at 56-78 and 92 days after transplantation, the number of parasitic shoots emerged in each plot was detected. At tomato harvesting, on August 18, the major quantity-quality yield parameters were determined (marketable yield, mean weight, dry matter, pH, soluble solids and color of fruits). All data were subjected to analysis of variance (ANOVA) and the means were compared by Tukey's test. Each treatment studied did not provide complete control against Phelipanche ramosa. However, among the different methods tested, some of them which Fusarium, gliphosate, radicon biostimulant and Red Setter tomato cv (improved genotypes obtained by Tilling technology) under deeper plowing (50 cm depth) proved to mitigate the virulence of the Phelipanche ramose attacks. It is assumed that these effects can be improved combining some of these treatments each other, especially for a gradual and continuing reduction of the “seed bank” of the parasite in the soil.

Keywords: Control methods, Phelipanche ramosa, tomato crop.

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Authors: Ya-Fen Lee, Yun-Yao Chi, Cing-Hong Hung

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Because of the global warming and the rising sea level, residents living in southwestern coastland, Taiwan are faced with the submerged land and may move to higher elevation area. It is desirable to discuss the key consideration factor for selecting the migration location under five dimensions of ಯ security”, “health”, “convenience”, “comfort” and “socio-economic” based on the document reviews. This paper uses the Structural Equation Modeling (SEM) and the questionnaire survey. The analysis results show that the convenience is the most key factor for residents in Taiwan. 

Keywords: Global warming, migration, structural equation modelling, questionnaire survey.

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Authors: Mahbub C. Mishu, Venketesh N. Dubey, Tamas Hickish, Jonathan Cole

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Pressure ulcer is a common problem for today’s healthcare industry. It occurs due to external load applied to the skin. Also when the subject is immobile for a longer period of time and there is continuous load applied to a particular area of human body, blood flow gets reduced and as a result pressure ulcer develops. Body support surface has a significant role in preventing ulceration so it is important to know the characteristics of support surface under loading conditions. In this paper we have presented mathematical models of different types of viscoelastic materials and also we have shown the validation of our simulation results with experiments.

Keywords: Pressure ulcer, viscoelastic material, mathematical model, experimental validation.

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Authors: Amin Chegenizadeh, Mahdi Keramatikerman, Hamid Nikraz

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Pavement engineering plays a significant role to develop cost effective and efficient highway and road networks. In general, pavement regarding structure is categorized in two core group namely flexible and rigid pavements. There are various benefits in application of rigid pavement. For instance, they have a longer life and lower maintenance costs in compare with the flexible pavement. In rigid pavement designs, temperature and thickness are two effective parameters that could widely affect the total cost of the project. In this study, a numerical modeling using Kenpave-Kenslab was performed to investigate the effect of these two important parameters in the rigid pavement.   

Keywords: Rigid pavement, Kenpave, Kenslab, thickness, temperature.

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Authors: Alicia Y. C. Tang, Rukaini Hj. Abdullah, Sharifuddin M. Zain

Abstract:

This paper discusses the development of a qualitative simulator (abbreviated QRiOM) for predicting the behaviour of organic chemical reactions. The simulation technique is based on the qualitative process theory (QPT) ontology. The modelling constructs of QPT embody notions of causality which can be used to explain the behaviour of a chemical system. The major theme of this work is that, in a qualitative simulation environment, students are able to articulate his/her knowledge through the inspection of explanations generated by software. The implementation languages are Java and Prolog. The software produces explanation in various forms that stresses on the causal theories in the chemical system which can be effectively used to support learning.

Keywords: Chemical reactions, explanation, qualitative processtheory, simulation

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Authors: Marzieh Dosti, Alireza Nazemi

Abstract:

Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this paper, a numerical solution for the one-dimensional hyperbolic telegraph equation by using the collocation method using the septic splines is proposed. The scheme works in a similar fashion as finite difference methods. Test problems are used to validate our scheme by calculate L2-norm and L∞-norm. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.

Keywords: B-spline, collocation method, second-order hyperbolic telegraph equation, difference schemes.

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