Search results for: mathematical modelling
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3276

Search results for: mathematical modelling

636 Bird-Adapted Filter for Avian Species and Individual Identification Systems Improvement

Authors: Ladislav Ptacek, Jan Vanek, Jan Eisner, Alexandra Pruchova, Pavel Linhart, Ludek Muller, Dana Jirotkova

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One of the essential steps of avian song processing is signal filtering. Currently, the standard methods of filtering are the Mel Bank Filter or linear filter distribution. In this article, a new type of bank filter called the Bird-Adapted Filter is introduced; whereby the signal filtering is modifiable, based upon a new mathematical description of audiograms for particular bird species or order, which was named the Avian Audiogram Unified Equation. According to the method, filters may be deliberately distributed by frequency. The filters are more concentrated in bands of higher sensitivity where there is expected to be more information transmitted and vice versa. Further, it is demonstrated a comparison of various filters for automatic individual recognition of chiffchaff (Phylloscopus collybita). The average Equal Error Rate (EER) value for Linear bank filter was 16.23%, for Mel Bank Filter 18.71%, the Bird-Adapted Filter gave 14.29%, and Bird-Adapted Filter with 1/3 modification was 12.95%. This approach would be useful for practical use in automatic systems for avian species and individual identification. Since the Bird-Adapted Filter filtration is based on the measured audiograms of particular species or orders, selecting the distribution according to the avian vocalization provides the most precise filter distribution to date.

Keywords: avian audiogram, bird individual identification, bird song processing, bird species recognition, filter bank

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635 Teaching Behaviours of Effective Secondary Mathematics Teachers: A Study in Dhaka, Bangladesh

Authors: Asadullah Sheikh, Kerry Barnett, Paul Ayres

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Despite significant progress in access, equity and public examination success, poor student performance in mathematics in secondary schools has become a major concern in Bangladesh. A substantial body of research has emphasised the important contribution of teaching practices to student achievement. However, this has not been investigated in Bangladesh. Therefore, the study sought to find out the effectiveness of mathematics teaching practices as a means of improving secondary school mathematics in Dhaka Municipality City (DMC) area, Bangladesh. The purpose of this study was twofold, first, to identify the 20 highest performing secondary schools in mathematics in DMC, and second, to investigate the teaching practices of mathematics teachers in these schools. A two-phase mixed method approach was adopted. In the first phase, secondary source data were obtained from the Board of Intermediate and Secondary Education (BISE), Dhaka and value-added measures used to identify the 20 highest performing secondary schools in mathematics. In the second phase, a concurrent mixed method design, where qualitative methods were embedded within a dominant quantitative approach was utilised. A purposive sampling strategy was used to select fifteen teachers from the 20 highest performing secondary schools. The main sources of data were classroom teaching observations, and teacher interviews. The data from teacher observations were analysed with descriptive and nonparametric statistics. The interview data were analysed qualitatively. The main findings showed teachers adopt a direct teaching approach which incorporates orientation, structuring, modelling, practice, questioning and teacher-student interaction that creates an individualistic learning environment. The variation in developmental levels of teaching skill indicate that teachers do not necessarily use the qualitative (i.e., focus, stage, quality and differentiation) aspects of teaching behaviours effectively. This is the first study to investigate teaching behaviours of effective secondary mathematics teachers within Dhaka, Bangladesh. It contributes in an international dimension to the field of educational effectiveness and raise questions about existing constructivist approaches. Further, it contributes to important insights about teaching behaviours that can be used to inform the development of evidence-based policy and practice on quality teaching in Bangladesh.

Keywords: effective teaching, mathematics, secondary schools, student achievement, value-added measures

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634 Understanding the Effect of Material and Deformation Conditions on the “Wear Mode Diagram”: A Numerical Study

Authors: A. Mostaani, M. P. Pereira, B. F. Rolfe

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The increasing application of Advanced High Strength Steel (AHSS) in the automotive industry to fulfill crash requirements has introduced higher levels of wear in stamping dies and parts. Therefore, understanding wear behaviour in sheet metal forming is of great importance as it can help to reduce the high costs currently associated with tool wear. At the contact between the die and the sheet, the tips of hard tool asperities interact with the softer sheet material. Understanding the deformation that occurs during this interaction is important for our overall understanding of the wear mechanisms. For these reasons, the scratching of a perfectly plastic material by a rigid indenter has been widely examined in the literature; with finite element modelling (FEM) used in recent years to further understand the behaviour. The ‘wear mode diagram’ has been commonly used to classify the deformation regime of the soft work-piece during scratching, into three modes: ploughing, wedge formation, and cutting. This diagram, which is based on 2D slip line theory and upper bound method for perfectly plastic work-piece and rigid indenter, relates different wear modes to attack angle and interfacial strength. This diagram has been the basis for many wear studies and wear models to date. Additionally, it has been concluded that galling is most likely to occur during the wedge formation mode. However, there has been little analysis in the literature of how the material behaviour and deformation conditions associated with metal forming processes influence the wear behaviour. Therefore, the first aim of this work is first to use a commercial FEM package (Abaqus/Explicit) to build a 3D model to capture wear modes during scratching with indenters with different attack angles and different interfacial strengths. The second goal is to utilise the developed model to understand how wear modes might change in the presence of bulk deformation of the work-piece material as a result of the metal forming operation. Finally, the effect of the work-piece material properties, including strain hardening, will be examined to understand how these influence the wear modes and wear behaviour. The results show that both strain hardening and substrate deformation can change the critical attack angle at which the wedge formation regime is activated.

Keywords: finite element, pile-up, scratch test, wear mode

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633 Storm-Runoff Simulation Approaches for External Natural Catchments of Urban Sewer Systems

Authors: Joachim F. Sartor

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According to German guidelines, external natural catchments are greater sub-catchments without significant portions of impervious areas, which possess a surface drainage system and empty in a sewer network. Basically, such catchments should be disconnected from sewer networks, particularly from combined systems. If this is not possible due to local conditions, their flow hydrographs have to be considered at the design of sewer systems, because the impact may be significant. Since there is a lack of sufficient measurements of storm-runoff events for such catchments and hence verified simulation methods to analyze their design flows, German standards give only general advices and demands special considerations in such cases. Compared to urban sub-catchments, external natural catchments exhibit greatly different flow characteristics. With increasing area size their hydrological behavior approximates that of rural catchments, e.g. sub-surface flow may prevail and lag times are comparable long. There are few observed peak flow values and simple (mostly empirical) approaches that are offered by literature for Central Europe. Most of them are at least helpful to crosscheck results that are achieved by simulation lacking calibration. Using storm-runoff data from five monitored rural watersheds in the west of Germany with catchment areas between 0.33 and 1.07 km2 , the author investigated by multiple event simulation three different approaches to determine the rainfall excess. These are the modified SCS variable run-off coefficient methods by Lutz and Zaiß as well as the soil moisture model by Ostrowski. Selection criteria for storm events from continuous precipitation data were taken from recommendations of M 165 and the runoff concentration method (parallel cascades of linear reservoirs) from a DWA working report to which the author had contributed. In general, the two run-off coefficient methods showed results that are of sufficient accuracy for most practical purposes. The soil moisture model showed no significant better results, at least not to such a degree that it would justify the additional data collection that its parameter determination requires. Particularly typical convective summer events after long dry periods, that are often decisive for sewer networks (not so much for rivers), showed discrepancies between simulated and measured flow hydrographs.

Keywords: external natural catchments, sewer network design, storm-runoff modelling, urban drainage

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632 Overview of Environmental and Economic Theories of the Impact of Dams in Different Regions

Authors: Ariadne Katsouras, Andrea Chareunsy

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The number of large hydroelectric dams in the world has increased from almost 6,000 in the 1950s to over 45,000 in 2000. Dams are often built to increase the economic development of a country. This can occur in several ways. Large dams take many years to build so the construction process employs many people for a long time and that increased production and income can flow on into other sectors of the economy. Additionally, the provision of electricity can help raise people’s living standards and if the electricity is sold to another country then the money can be used to provide other public goods for the residents of the country that own the dam. Dams are also built to control flooding and provide irrigation water. Most dams are of these types. This paper will give an overview of the environmental and economic theories of the impact of dams in different regions of the world. There is a difference in the degree of environmental and economic impacts due to the varying climates and varying social and political factors of the regions. Production of greenhouse gases from the dam’s reservoir, for instance, tends to be higher in tropical areas as opposed to Nordic environments. However, there are also common impacts due to construction of the dam itself, such as, flooding of land for the creation of the reservoir and displacement of local populations. Economically, the local population tends to benefit least from the construction of the dam. Additionally, if a foreign company owns the dam or the government subsidises the cost of electricity to businesses, then the funds from electricity production do not benefit the residents of the country the dam is built in. So, in the end, the dams can benefit a country economically, but the varying factors related to its construction and how these are dealt with, determine the level of benefit, if any, of the dam. Some of the theories or practices used to evaluate the potential value of a dam include cost-benefit analysis, environmental impacts assessments and regressions. Systems analysis is also a useful method. While these theories have value, there are also possible shortcomings. Cost-benefit analysis converts all the costs and benefits to dollar values, which can be problematic. Environmental impact assessments, likewise, can be incomplete, especially if the assessment does not include feedback effects, that is, they only consider the initial impact. Finally, regression analysis is dependent on the available data and again would not necessarily include feedbacks. Systems analysis is a method that can allow more complex modelling of the environment and the economic system. It would allow a clearer picture to emerge of the impacts and can include a long time frame.

Keywords: comparison, economics, environment, hydroelectric dams

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631 Phosphorus Recovery Optimization in Microbial Fuel Cell

Authors: Abdullah Almatouq

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Understanding the impact of key operational variables on concurrent energy generation and phosphorus recovery in microbial fuel cell is required to improve the process and reduce the operational cost. In this study, full factorial design (FFD) and central composite designs (CCD) were employed to identify the effect of influent COD concentration and cathode aeration flow rate on energy generation and phosphorus (P) recovery and to optimise MFC power density and P recovery. Results showed that influent chemical oxygen demand (COD) concentration and cathode aeration flow rate had a significant effect on power density, coulombic efficiency, phosphorus precipitation efficiency and phosphorus precipitation rate at the cathode. P precipitation was negatively affected by the generated current during the batch duration. The generated energy was reduced due to struvite being precipitated on the cathode surface, which might obstruct the mass transfer of ions and oxygen. Response surface mathematical model was used to predict the optimum operating conditions that resulted in a maximum power density and phosphorus precipitation efficiency of 184 mW/m² and 84%, and this corresponds to COD= 1700 mg/L and aeration flow rate=210 mL/min. The findings highlight the importance of the operational conditions of energy generation and phosphorus recovery.

Keywords: energy, microbial fuel cell, phosphorus, struvite

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630 Modeling Floodplain Vegetation Response to Groundwater Variability Using ArcSWAT Hydrological Model, Moderate Resolution Imaging Spectroradiometer - Normalised Difference Vegetation Index Data, and Machine Learning

Authors: Newton Muhury, Armando A. Apan, Tek Maraseni

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This study modelled the relationships between vegetation response and available water below the soil surface using the Terra’s Moderate Resolution Imaging Spectroradiometer (MODIS) generated Normalised Difference Vegetation Index (NDVI) and soil water content (SWC) data. The Soil & Water Assessment Tool (SWAT) interface known as ArcSWAT was used in ArcGIS for the groundwater analysis. The SWAT model was calibrated and validated in SWAT-CUP software using 10 years (2001-2010) of monthly streamflow data. The average Nash-Sutcliffe Efficiency during the calibration and validation was 0.54 and 0.51, respectively, indicating that the model performances were good. Twenty years (2001-2020) of monthly MODIS NDVI data for three different types of vegetation (forest, shrub, and grass) and soil water content for 43 sub-basins were analysed using the WEKA, machine learning tool with a selection of two supervised machine learning algorithms, i.e., support vector machine (SVM) and random forest (RF). The modelling results show that different types of vegetation response and soil water content vary in the dry and wet season. For example, the model generated high positive relationships (r=0.76, 0.73, and 0.81) between the measured and predicted NDVI values of all vegetation in the study area against the groundwater flow (GW), soil water content (SWC), and the combination of these two variables, respectively, during the dry season. However, these relationships were reduced by 36.8% (r=0.48) and 13.6% (r=0.63) against GW and SWC, respectively, in the wet season. On the other hand, the model predicted a moderate positive relationship (r=0.63) between shrub vegetation type and soil water content during the dry season, which was reduced by 31.7% (r=0.43) during the wet season. Our models also predicted that vegetation in the top location (upper part) of the sub-basin is highly responsive to GW and SWC (r=0.78, and 0.70) during the dry season. The results of this study indicate the study region is suitable for seasonal crop production in dry season. Moreover, the results predicted that the growth of vegetation in the top-point location is highly dependent on groundwater flow in both dry and wet seasons, and any instability or long-term drought can negatively affect these floodplain vegetation communities. This study has enriched our knowledge of vegetation responses to groundwater in each season, which will facilitate better floodplain vegetation management.

Keywords: ArcSWAT, machine learning, floodplain vegetation, MODIS NDVI, groundwater

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629 Flood Mapping Using Height above the Nearest Drainage Model: A Case Study in Fredericton, NB, Canada

Authors: Morteza Esfandiari, Shabnam Jabari, Heather MacGrath, David Coleman

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Flood is a severe issue in different places in the world as well as the city of Fredericton, New Brunswick, Canada. The downtown area of Fredericton is close to the Saint John River, which is susceptible to flood around May every year. Recently, the frequency of flooding seems to be increased, especially after the fact that the downtown area and surrounding urban/agricultural lands got flooded in two consecutive years in 2018 and 2019. In order to have an explicit vision of flood span and damage to affected areas, it is necessary to use either flood inundation modelling or satellite data. Due to contingent availability and weather dependency of optical satellites, and limited existing data for the high cost of hydrodynamic models, it is not always feasible to rely on these sources of data to generate quality flood maps after or during the catastrophe. Height Above the Nearest Drainage (HAND), a state-of-the-art topo-hydrological index, normalizes the height of a basin based on the relative elevation along with the stream network and specifies the gravitational or the relative drainage potential of an area. HAND is a relative height difference between the stream network and each cell on a Digital Terrain Model (DTM). The stream layer is provided through a multi-step, time-consuming process which does not always result in an optimal representation of the river centerline depending on the topographic complexity of that region. HAND is used in numerous case studies with quite acceptable and sometimes unexpected results because of natural and human-made features on the surface of the earth. Some of these features might cause a disturbance in the generated model, and consequently, the model might not be able to predict the flow simulation accurately. We propose to include a previously existing stream layer generated by the province of New Brunswick and benefit from culvert maps to improve the water flow simulation and accordingly the accuracy of HAND model. By considering these parameters in our processing, we were able to increase the accuracy of the model from nearly 74% to almost 92%. The improved model can be used for generating highly accurate flood maps, which is necessary for future urban planning and flood damage estimation without any need for satellite imagery or hydrodynamic computations.

Keywords: HAND, DTM, rapid floodplain, simplified conceptual models

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628 Character Development Outcomes: A Predictive Model for Behaviour Analysis in Tertiary Institutions

Authors: Rhoda N. Kayongo

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As behavior analysts in education continue to debate on how higher institutions can continue to benefit from their social and academic related programs, higher education is facing challenges in the area of character development. This is manifested in the percentages of college completion rates, teen pregnancies, drug abuse, sexual abuse, suicide, plagiarism, lack of academic integrity, and violence among their students. Attending college is a perceived opportunity to positively influence the actions and behaviors of the next generation of society; thus colleges and universities have to provide opportunities to develop students’ values and behaviors. Prior studies were mainly conducted in private institutions and more so in developed countries. However, with the complexity of the nature of student body currently due to the changing world, a multidimensional approach combining multiple factors that enhance character development outcomes is needed to suit the changing trends. The main purpose of this study was to identify opportunities in colleges and develop a model for predicting character development outcomes. A survey questionnaire composed of 7 scales including in-classroom interaction, out-of-classroom interaction, school climate, personal lifestyle, home environment, and peer influence as independent variables and character development outcomes as the dependent variable was administered to a total of five hundred and one students of 3rd and 4th year level in selected public colleges and universities in the Philippines and Rwanda. Using structural equation modelling, a predictive model explained 57% of the variance in character development outcomes. Findings from the results of the analysis showed that in-classroom interactions have a substantial direct influence on character development outcomes of the students (r = .75, p < .05). In addition, out-of-classroom interaction, school climate, and home environment contributed to students’ character development outcomes but in an indirect way. The study concluded that in the classroom are many opportunities for teachers to teach, model and integrate character development among their students. Thus, suggestions are made to public colleges and universities to deliberately boost and implement experiences that cultivate character within the classroom. These may contribute tremendously to the students' character development outcomes and hence render effective models of behaviour analysis in higher education.

Keywords: character development, tertiary institutions, predictive model, behavior analysis

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627 Optoelectronic Hardware Architecture for Recurrent Learning Algorithm in Image Processing

Authors: Abdullah Bal, Sevdenur Bal

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This paper purposes a new type of hardware application for training of cellular neural networks (CNN) using optical joint transform correlation (JTC) architecture for image feature extraction. CNNs require much more computation during the training stage compare to test process. Since optoelectronic hardware applications offer possibility of parallel high speed processing capability for 2D data processing applications, CNN training algorithm can be realized using Fourier optics technique. JTC employs lens and CCD cameras with laser beam that realize 2D matrix multiplication and summation in the light speed. Therefore, in the each iteration of training, JTC carries more computation burden inherently and the rest of mathematical computation realized digitally. The bipolar data is encoded by phase and summation of correlation operations is realized using multi-object input joint images. Overlapping properties of JTC are then utilized for summation of two cross-correlations which provide less computation possibility for training stage. Phase-only JTC does not require data rearrangement, electronic pre-calculation and strict system alignment. The proposed system can be incorporated simultaneously with various optical image processing or optical pattern recognition techniques just in the same optical system.

Keywords: CNN training, image processing, joint transform correlation, optoelectronic hardware

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626 Implementation of Model Reference Adaptive Control in Tuning of Controller Gains for Following-Vehicle System with Fixed Time Headway

Authors: Fatemeh Behbahani, Rubiyah Yusof

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To avoid collision between following vehicles and vehicles in front, it is vital to keep appropriate, safe spacing between both vehicles over all speeds. Therefore, the following vehicle needs to have exact information regarding the speed and spacing between vehicles. This project is conducted to simulate the tuning of controller gain for a vehicle-following system through the selected control strategy, spacing control policy and fixed-time headway policy. In addition, the paper simulates and designs an adaptive gain controller for a road-vehicle-following system which uses information on the spacing, velocity and also acceleration of a preceding vehicle in the proposed one-vehicle look-ahead strategy. The mathematical model is implemented using Kirchhoff and Newton’s Laws, and stability simulated. The trial-error method was used to obtain a suitable value of controller gain. However, the adaptive-based controller system was able to optimize the gain value automatically. Model Reference Adaptive Control (MRAC) is designed and utilized and based on firstly the Gradient and secondly the Lyapunov approach. The Lyapunov approach considers stability. The Gradient approach was found to improve the best value of gain in the controller system with fixed-time headway.

Keywords: one-vehicle look-ahead, model reference adaptive, stability, tuning gain controller, MRAC

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625 Sustainability Assessment Tool for the Selection of Optimal Site Remediation Technologies for Contaminated Gasoline Sites

Authors: Connor Dunlop, Bassim Abbassi, Richard G. Zytner

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Life cycle assessment (LCA) is a powerful tool established by the International Organization for Standardization (ISO) that can be used to assess the environmental impacts of a product or process from cradle to grave. Many studies utilize the LCA methodology within the site remediation field to compare various decontamination methods, including bioremediation, soil vapor extraction or excavation, and off-site disposal. However, with the authors' best knowledge, limited information is available in the literature on a sustainability tool that could be used to help with the selection of the optimal remediation technology. This tool, based on the LCA methodology, would consider site conditions like environmental, economic, and social impacts. Accordingly, this project was undertaken to develop a tool to assist with the selection of optimal sustainable technology. Developing a proper tool requires a large amount of data. As such, data was collected from previous LCA studies looking at site remediation technologies. This step identified knowledge gaps or limitations within project data. Next, utilizing the data obtained from the literature review and other organizations, an extensive LCA study is being completed following the ISO 14040 requirements. Initial technologies being compared include bioremediation, excavation with off-site disposal, and a no-remediation option for a generic gasoline-contaminated site. To complete the LCA study, the modelling software SimaPro is being utilized. A sensitivity analysis of the LCA results will also be incorporated to evaluate the impact on the overall results. Finally, the economic and social impacts associated with each option will then be reviewed to understand how they fluctuate at different sites. All the results will then be summarized, and an interactive tool using Excel will be developed to help select the best sustainable site remediation technology. Preliminary LCA results show improved sustainability for the decontamination of a gasoline-contaminated site for each technology compared to the no-remediation option. Sensitivity analyses are now being completed on on-site parameters to determine how the environmental impacts fluctuate at other contaminated gasoline locations as the parameters vary, including soil type and transportation distances. Additionally, the social improvements and overall economic costs associated with each technology are being reviewed. Utilizing these results, the sustainability tool created to assist in the selection of the overall best option will be refined.

Keywords: life cycle assessment, site remediation, sustainability tool, contaminated sites

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624 Oryzanol Recovery from Rice Bran Oil: Adsorption Equilibrium Models Through Kinetics Data Approachments

Authors: A.D. Susanti, W. B. Sediawan, S.K. Wirawan, Budhijanto, Ritmaleni

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Oryzanol content in rice bran oil (RBO) naturally has high antioxidant activity. Its reviewed has several health properties and high interested in pharmacy, cosmetics, and nutrition’s. Because of the low concentration of oryzanol in crude RBO (0.9-2.9%) then its need to be further processed for practical usage, such as via adsorption process. In this study, investigation and adjustment of adsorption equilibrium models were conducted through the kinetic data approachments. Mathematical modeling on kinetics of batch adsorption of oryzanol separation from RBO has been set-up and then applied for equilibrium results. The size of adsorbent particles used in this case are usually relatively small then the concentration in the adsorbent is assumed to be not different. Hence, the adsorption rate is controlled by the rate of oryzanol mass transfer from the bulk fluid of RBO to the surface of silica gel. In this approachments, the rate of mass transfer is assumed to be proportional to the concentration deviation from the equilibrium state. The equilibrium models applied were Langmuir, coefficient distribution, and Freundlich with the values of the parameters obtained from equilibrium results. It turned out that the models set-up can quantitatively describe the experimental kinetics data and the adjustment of the values of equilibrium isotherm parameters significantly improves the accuracy of the model. And then the value of mass transfer coefficient per unit adsorbent mass (kca) is obtained by curve fitting.

Keywords: adsorption equilibrium, adsorption kinetics, oryzanol, rice bran oil

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623 Stability Analysis of Stagnation-Point Flow past a Shrinking Sheet in a Nanofluid

Authors: Amin Noor, Roslinda Nazar, Norihan Md. Arifin

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In this paper, a numerical and theoretical study has been performed for the stagnation-point boundary layer flow and heat transfer towards a shrinking sheet in a nanofluid. The mathematical nanofluid model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Numerical results are obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction Φ, the shrinking parameter λ and the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al2O3 and TiO2. It is found that solutions do not exist for larger shrinking rates and dual (upper and lower branch) solutions exist when λ < -1.0. A stability analysis has been performed to show which branch solutions are stable and physically realizable. It is also found that the upper branch solutions are stable while the lower branch solutions are unstable.

Keywords: heat transfer, nanofluid, shrinking sheet, stability analysis, stagnation-point flow

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622 Development of Advanced Linear Calibration Technique for Air Flow Sensing by Using CTA-Based Hot Wire Anemometry

Authors: Ming-Jong Tsai, T. M. Wu, R. C. Chu

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The purpose of this study is to develop an Advanced linear calibration Technique for air flow sensing by using CTA-based Hot wire Anemometry. It contains a host PC with Human Machine Interface, a wind tunnel, a wind speed controller, an automatic data acquisition module, and nonlinear calibration model. To improve the fitting error by using single fitting polynomial, this study proposes a Multiple three-order Polynomial Fitting Method (MPFM) for fitting the non-linear output of a CTA-based Hot wire Anemometry. The CTA-based anemometer with built-in fitting parameters is installed in the wind tunnel, and the wind speed is controlled by the PC-based controller. The Hot-Wire anemometer's thermistor resistance change is converted into a voltage signal or temperature differences, and then sent to the PC through a DAQ card. After completion measurements of original signal, the Multiple polynomial mathematical coefficients can be automatically calculated, and then sent into the micro-processor in the Hot-Wire anemometer. Finally, the corrected Hot-Wire anemometer is verified for the linearity, the repeatability, error percentage, and the system outputs quality control reports.

Keywords: flow rate sensing, hot wire, constant temperature anemometry (CTA), linear calibration, multiple three-order polynomial fitting method (MPFM), temperature compensation

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621 Algorithm Development of Individual Lumped Parameter Modelling for Blood Circulatory System: An Optimization Study

Authors: Bao Li, Aike Qiao, Gaoyang Li, Youjun Liu

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Background: Lumped parameter model (LPM) is a common numerical model for hemodynamic calculation. LPM uses circuit elements to simulate the human blood circulatory system. Physiological indicators and characteristics can be acquired through the model. However, due to the different physiological indicators of each individual, parameters in LPM should be personalized in order for convincing calculated results, which can reflect the individual physiological information. This study aimed to develop an automatic and effective optimization method to personalize the parameters in LPM of the blood circulatory system, which is of great significance to the numerical simulation of individual hemodynamics. Methods: A closed-loop LPM of the human blood circulatory system that is applicable for most persons were established based on the anatomical structures and physiological parameters. The patient-specific physiological data of 5 volunteers were non-invasively collected as personalized objectives of individual LPM. In this study, the blood pressure and flow rate of heart, brain, and limbs were the main concerns. The collected systolic blood pressure, diastolic blood pressure, cardiac output, and heart rate were set as objective data, and the waveforms of carotid artery flow and ankle pressure were set as objective waveforms. Aiming at the collected data and waveforms, sensitivity analysis of each parameter in LPM was conducted to determine the sensitive parameters that have an obvious influence on the objectives. Simulated annealing was adopted to iteratively optimize the sensitive parameters, and the objective function during optimization was the root mean square error between the collected waveforms and data and simulated waveforms and data. Each parameter in LPM was optimized 500 times. Results: In this study, the sensitive parameters in LPM were optimized according to the collected data of 5 individuals. Results show a slight error between collected and simulated data. The average relative root mean square error of all optimization objectives of 5 samples were 2.21%, 3.59%, 4.75%, 4.24%, and 3.56%, respectively. Conclusions: Slight error demonstrated good effects of optimization. The individual modeling algorithm developed in this study can effectively achieve the individualization of LPM for the blood circulatory system. LPM with individual parameters can output the individual physiological indicators after optimization, which are applicable for the numerical simulation of patient-specific hemodynamics.

Keywords: blood circulatory system, individual physiological indicators, lumped parameter model, optimization algorithm

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620 Prediction of Fluid Induced Deformation using Cavity Expansion Theory

Authors: Jithin S. Kumar, Ramesh Kannan Kandasami

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Geomaterials are generally porous in nature due to the presence of discrete particles and interconnected voids. The porosity present in these geomaterials play a critical role in many engineering applications such as CO2 sequestration, well bore strengthening, enhanced oil and hydrocarbon recovery, hydraulic fracturing, and subsurface waste storage. These applications involves solid-fluid interactions, which govern the changes in the porosity which in turn affect the permeability and stiffness of the medium. Injecting fluid into the geomaterials results in permeation which exhibits small or negligible deformation of the soil skeleton followed by cavity expansion/ fingering/ fracturing (different forms of instabilities) due to the large deformation especially when the flow rate is greater than the ability of the medium to permeate the fluid. The complexity of this problem increases as the geomaterial behaves like a solid and fluid under certain conditions. Thus it is important to understand this multiphysics problem where in addition to the permeation, the elastic-plastic deformation of the soil skeleton plays a vital role during fluid injection. The phenomenon of permeation and cavity expansion in porous medium has been studied independently through extensive experimental and analytical/ numerical models. The analytical models generally use Darcy's/ diffusion equations to capture the fluid flow during permeation while elastic-plastic (Mohr-Coulomb and Modified Cam-Clay) models were used to predict the solid deformations. Hitherto, the research generally focused on modelling cavity expansion without considering the effect of injected fluid coming into the medium. Very few studies have considered the effect of injected fluid on the deformation of soil skeleton. However, the porosity changes during the fluid injection and coupled elastic-plastic deformation are not clearly understood. In this study, the phenomenon of permeation and instabilities such as cavity and finger/ fracture formation will be quantified extensively by performing experiments using a novel experimental setup in addition to utilizing image processing techniques. This experimental study will describe the fluid flow and soil deformation characteristics under different boundary conditions. Further, a well refined coupled semi-analytical model will be developed to capture the physics involved in quantifying the deformation behaviour of geomaterial during fluid injection.

Keywords: solid-fluid interaction, permeation, poroelasticity, plasticity, continuum model

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619 Study on Natural Light Distribution Inside the Room by Using Sudare as an Outside Horizontal Blind in Tropical Country of Indonesia

Authors: Agus Hariyadi, Hiroatsu Fukuda

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In tropical country like Indonesia, especially in Jakarta, most of the energy consumption on building is for the cooling system, the second one is from lighting electric consumption. One of the passive design strategy that can be done is optimizing the use of natural light from the sun. In this area, natural light is always available almost every day around the year. Natural light have many effect on building. It can reduce the need of electrical lighting but also increase the external load. Another thing that have to be considered in the use of natural light is the visual comfort from occupant inside the room. To optimize the effectiveness of natural light need some modification of façade design. By using external shading device, it can minimize the external load that introduces into the room, especially from direct solar radiation which is the 80 % of the external energy load that introduces into the building. It also can control the distribution of natural light inside the room and minimize glare in the perimeter zone of the room. One of the horizontal blind that can be used for that purpose is Sudare. It is traditional Japanese blind that have been used long time in Japanese traditional house especially in summer. In its original function, Sudare is used to prevent direct solar radiation but still introducing natural ventilation. It has some physical characteristics that can be utilize to optimize the effectiveness of natural light. In this research, different scale of Sudare will be simulated using EnergyPlus and DAYSIM simulation software. EnergyPlus is a whole building energy simulation program to model both energy consumption—for heating, cooling, ventilation, lighting, and plug and process loads—and water use in buildings, while DAYSIM is a validated, RADIANCE-based daylighting analysis software that models the annual amount of daylight in and around buildings. The modelling will be done in Ladybug and Honeybee plugin. These are two open source plugins for Grasshopper and Rhinoceros 3D that help explore and evaluate environmental performance which will directly be connected to EnergyPlus and DAYSIM engines. Using the same model will maintain the consistency of the same geometry used both in EnergyPlus and DAYSIM. The aims of this research is to find the best configuration of façade design which can reduce the external load from the outside of the building to minimize the need of energy for cooling system but maintain the natural light distribution inside the room to maximize the visual comfort for occupant and minimize the need of electrical energy consumption.

Keywords: façade, natural light, blind, energy

Procedia PDF Downloads 322
618 Sensitivity Analysis of the Heat Exchanger Design in Net Power Oxy-Combustion Cycle for Carbon Capture

Authors: Hirbod Varasteh, Hamidreza Gohari Darabkhani

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The global warming and its impact on climate change is one of main challenges for current century. Global warming is mainly due to the emission of greenhouse gases (GHG) and carbon dioxide (CO2) is known to be the major contributor to the GHG emission profile. Whilst the energy sector is the primary source for CO2 emission, Carbon Capture and Storage (CCS) are believed to be the solution for controlling this emission. Oxyfuel combustion (Oxy-combustion) is one of the major technologies for capturing CO2 from power plants. For gas turbines, several Oxy-combustion power cycles (Oxyturbine cycles) have been investigated by means of thermodynamic analysis. NetPower cycle is one of the leading oxyturbine power cycles with almost full carbon capture capability from a natural gas fired power plant. In this manuscript, sensitivity analysis of the heat exchanger design in NetPower cycle is completed by means of process modelling. The heat capacity variation and supercritical CO2 with gaseous admixtures are considered for multi-zone analysis with Aspen Plus software. It is found that the heat exchanger design has a major role to increase the efficiency of NetPower cycle. The pinch-point analysis is done to extract the composite and grand composite curve for the heat exchanger. In this paper, relationship between the cycle efficiency and the minimum approach temperature (∆Tmin) of the heat exchanger has also been evaluated.  Increase in ∆Tmin causes a decrease in the temperature of the recycle flue gases (RFG) and an overall decrease in the required power for the recycled gas compressor. The main challenge in the design of heat exchangers in power plants is a tradeoff between the capital and operational costs. To achieve lower ∆Tmin, larger size of heat exchanger is required. This means a higher capital cost but leading to a better heat recovery and lower operational cost. To achieve this, ∆Tmin is selected from the minimum point in the diagrams of capital and operational costs. This study provides an insight into the NetPower Oxy-combustion cycle’s performance analysis and operational condition based on its heat exchanger design.

Keywords: carbon capture and storage, oxy-combustion, netpower cycle, oxy turbine cycles, zero emission, heat exchanger design, supercritical carbon dioxide, oxy-fuel power plant, pinch point analysis

Procedia PDF Downloads 182
617 Management and Evaluation of the Importance of Porous Media in Biomedical Engineering as Associated with Magnetic Resonance Imaging Besides Drug Delivery

Authors: Fateme Nokhodchi Bonab

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Studies related to magnetic resonance imaging (MRI) and drug delivery are reviewed in this study to demonstrate the role of transport theory in porous media in facilitating advances in biomedical applications. Diffusion processes are believed to be important in many therapeutic modalities such as: B. Delivery of drugs to the brain. We analyse the progress in the development of diffusion equations using the local volume average method and the evaluation of applications related to diffusion equations. Torsion and porosity have significant effects on diffusive transport. In this study, various relevant models of torsion are presented and mathematical modeling of drug release from biodegradable delivery systems is analysed. In this study, a new model of drug release kinetics from porous biodegradable polymeric microspheres under bulk and surface erosion of the polymer matrix is presented. Solute drug diffusion, drug dissolution from the solid phase, and polymer matrix erosion have been found to play a central role in controlling the overall drug release process. This work paves the way for MRI and drug delivery researchers to develop comprehensive models based on porous media theory that use fewer assumptions compared to other approaches.

Keywords: MRI, porous media, drug delivery, biomedical applications

Procedia PDF Downloads 62
616 Optimal Design of Step-Stress Partially Life Test Using Multiply Censored Exponential Data with Random Removals

Authors: Showkat Ahmad Lone, Ahmadur Rahman, Ariful Islam

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The major assumption in accelerated life tests (ALT) is that the mathematical model relating the lifetime of a test unit and the stress are known or can be assumed. In some cases, such life–stress relationships are not known and cannot be assumed, i.e. ALT data cannot be extrapolated to use condition. So, in such cases, partially accelerated life test (PALT) is a more suitable test to be performed for which tested units are subjected to both normal and accelerated conditions. This study deals with estimating information about failure times of items under step-stress partially accelerated life tests using progressive failure-censored hybrid data with random removals. The life data of the units under test is considered to follow exponential life distribution. The removals from the test are assumed to have binomial distributions. The point and interval maximum likelihood estimations are obtained for unknown distribution parameters and tampering coefficient. An optimum test plan is developed using the D-optimality criterion. The performances of the resulting estimators of the developed model parameters are evaluated and investigated by using a simulation algorithm.

Keywords: binomial distribution, d-optimality, multiple censoring, optimal design, partially accelerated life testing, simulation study

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615 Design and Control of a Knee Rehabilitation Device Using an MR-Fluid Brake

Authors: Mina Beheshti, Vida Shams, Mojtaba Esfandiari, Farzaneh Abdollahi, Abdolreza Ohadi

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Most of the people who survive a stroke need rehabilitation tools to regain their mobility. The core function of these devices is a brake actuator. The goal of this study is to design and control a magnetorheological brake which can be used as a rehabilitation tool. In fact, the fluid used in this brake is called magnetorheological fluid or MR that properties can change by variation of the magnetic field. The braking properties can be set as control by using this feature of the fluid. In this research, different MR brake designs are first introduced in each design, and the dimensions of the brake have been determined based on the required torque for foot movement. To calculate the brake dimensions, it is assumed that the shear stress distribution in the fluid is uniform and the fluid is in its saturated state. After designing the rehabilitation brake, the mathematical model of the healthy movement of a healthy person is extracted. Due to the nonlinear nature of the system and its variability, various adaptive controllers, neural networks, and robust have been implemented to estimate the parameters and control the system. After calculating torque and control current, the best type of controller in terms of error and control current has been selected. Finally, this controller is implemented on the experimental data of the patient's movements, and the control current is calculated to achieve the desired torque and motion.

Keywords: rehabilitation, magnetorheological fluid, knee, brake, adaptive control, robust control, neural network control, torque control

Procedia PDF Downloads 127
614 Drying Kinects of Soybean Seeds

Authors: Amanda Rithieli Pereira Dos Santos, Rute Quelvia De Faria, Álvaro De Oliveira Cardoso, Anderson Rodrigo Da Silva, Érica Leão Fernandes Araújo

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The study of the kinetics of drying has great importance for the mathematical modeling, allowing to know about the processes of transference of heat and mass between the products and to adjust dryers managing new technologies for these processes. The present work had the objective of studying the kinetics of drying of soybean seeds and adjusting different statistical models to the experimental data varying cultivar and temperature. Soybean seeds were pre-dried in a natural environment in order to reduce and homogenize the water content to the level of 14% (b.s.). Then, drying was carried out in a forced air circulation oven at controlled temperatures of 38, 43, 48, 53 and 58 ± 1 ° C, using two soybean cultivars, BRS 8780 and Sambaíba, until reaching a hygroscopic equilibrium. The experimental design was completely randomized in factorial 5 x 2 (temperature x cultivar) with 3 replicates. To the experimental data were adjusted eleven statistical models used to explain the drying process of agricultural products. Regression analysis was performed using the least squares Gauss-Newton algorithm to estimate the parameters. The degree of adjustment was evaluated from the analysis of the coefficient of determination (R²), the adjusted coefficient of determination (R² Aj.) And the standard error (S.E). The models that best represent the drying kinetics of soybean seeds are those of Midilli and Logarítmico.

Keywords: curve of drying seeds, Glycine max L., moisture ratio, statistical models

Procedia PDF Downloads 597
613 Quantum Graph Approach for Energy and Information Transfer through Networks of Cables

Authors: Mubarack Ahmed, Gabriele Gradoni, Stephen C. Creagh, Gregor Tanner

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High-frequency cables commonly connect modern devices and sensors. Interestingly, the proportion of electric components is rising fast in an attempt to achieve lighter and greener devices. Modelling the propagation of signals through these cable networks in the presence of parameter uncertainty is a daunting task. In this work, we study the response of high-frequency cable networks using both Transmission Line and Quantum Graph (QG) theories. We have successfully compared the two theories in terms of reflection spectra using measurements on real, lossy cables. We have derived a generalisation of the vertex scattering matrix to include non-uniform networks – networks of cables with different characteristic impedances and propagation constants. The QG model implicitly takes into account the pseudo-chaotic behavior, at the vertices, of the propagating electric signal. We have successfully compared the asymptotic growth of eigenvalues of the Laplacian with the predictions of Weyl law. We investigate the nearest-neighbour level-spacing distribution of the resonances and compare our results with the predictions of Random Matrix Theory (RMT). To achieve this, we will compare our graphs with the generalisation of Wigner distribution for open systems. The problem of scattering from networks of cables can also provide an analogue model for wireless communication in highly reverberant environments. In this context, we provide a preliminary analysis of the statistics of communication capacity for communication across cable networks, whose eventual aim is to enable detailed laboratory testing of information transfer rates using software defined radio. We specialise this analysis in particular for the case of MIMO (Multiple-Input Multiple-Output) protocols. We have successfully validated our QG model with both TL model and laboratory measurements. The growth of Eigenvalues compares well with Weyl’s law and the level-spacing distribution agrees so well RMT predictions. The results we achieved in the MIMO application compares favourably with the prediction of a parallel on-going research (sponsored by NEMF21.)

Keywords: eigenvalues, multiple-input multiple-output, quantum graph, random matrix theory, transmission line

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612 Comparison of Two Theories for the Critical Laser Radius in Thermal Quantum Plasma

Authors: Somaye Zare

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The critical beam radius is a significant factor that predicts the behavior of the laser beam in the plasma, so if the laser beam radius is adequately greater in comparison to it, the beam will experience stable focusing on the plasma; otherwise, the beam will diverge after entering into the plasma. In this work, considering the paraxial approximation and moment theories, the localization of a relativistic laser beam in thermal quantum plasma is investigated. Using the dielectric function obtained in the quantum hydrodynamic model, the mathematical equation for the laser beam width parameter is attained and solved numerically by the fourth-order Runge-Kutta method. The results demonstrate that the stouter focusing effect is occurred in the moment theory compared to the paraxial approximation. Besides, similar to the two theories, with increasing Fermi temperature, plasma density, and laser intensity, the oscillation rate of the beam width parameter growths and focusing length reduces which means improving the focusing effect. Furthermore, it is understood that behaviors of the critical laser radius are different in the two theories, in the paraxial approximation, the critical radius after a minimum value is enhanced with increasing laser intensity, but in the moment theory, with increasing laser intensity, the critical radius decreases until it becomes independent of the laser intensity.

Keywords: laser localization, quantum plasma, paraxial approximation, moment theory, quantum hydrodynamic model

Procedia PDF Downloads 48
611 A Comparative Evaluation of the SIR and SEIZ Epidemiological Models to Describe the Diffusion Characteristics of COVID-19 Polarizing Viewpoints on Online

Authors: Maryam Maleki, Esther Mead, Mohammad Arani, Nitin Agarwal

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This study is conducted to examine how opposing viewpoints related to COVID-19 were diffused on Twitter. To accomplish this, six datasets using two epidemiological models, SIR (Susceptible, Infected, Recovered) and SEIZ (Susceptible, Exposed, Infected, Skeptics), were analyzed. The six datasets were chosen because they represent opposing viewpoints on the COVID-19 pandemic. Three of the datasets contain anti-subject hashtags, while the other three contain pro-subject hashtags. The time frame for all datasets is three years, starting from January 2020 to December 2022. The findings revealed that while both models were effective in evaluating the propagation trends of these polarizing viewpoints, the SEIZ model was more accurate with a relatively lower error rate (6.7%) compared to the SIR model (17.3%). Additionally, the relative error for both models was lower for anti-subject hashtags compared to pro-subject hashtags. By leveraging epidemiological models, insights into the propagation trends of polarizing viewpoints on Twitter were gained. This study paves the way for the development of methods to prevent the spread of ideas that lack scientific evidence while promoting the dissemination of scientifically backed ideas.

Keywords: mathematical modeling, epidemiological model, seiz model, sir model, covid-19, twitter, social network analysis, social contagion

Procedia PDF Downloads 36
610 Simulation of Improving the Efficiency of a Fire-Tube Steam Boiler

Authors: Roudane Mohamed

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In this study we are interested in improving the efficiency of a steam boiler to 4.5T/h and minimize fume discharge temperature by the addition of a heat exchanger against the current in the energy system, the output of the boiler. The mathematical approach to the problem is based on the use of heat transfer by convection and conduction equations. These equations have been chosen because of their extensive use in a wide range of application. A software and developed for solving the equations governing these phenomena and the estimation of the thermal characteristics of boiler through the study of the thermal characteristics of the heat exchanger by both LMTD and NUT methods. Subsequently, an analysis of the thermal performance of the steam boiler by studying the influence of different operating parameters on heat flux densities, temperatures, exchanged power and performance was carried out. The study showed that the behavior of the boiler is largely influenced. In the first regime (P = 3.5 bar), the boiler efficiency has improved significantly from 93.03 to 99.43 at the rate of 6.47% and 4.5%. For maximum speed, the change is less important, it is of the order of 1.06%. The results obtained in this study of great interest to industrial utilities equipped with smoke tube boilers for the preheating air temperature intervene to calculate the actual temperature of the gas so the heat exchanged will be increased and minimize temperature smoke discharge. On the other hand, this work could be used as a model of computation in the design process.

Keywords: numerical simulation, efficiency, fire tube, heat exchanger, convection and conduction

Procedia PDF Downloads 197
609 The Impact of Research Anxiety on Research Orientation and Interest in Research Courses in Social Work Students

Authors: Daniel Gredig, Annabelle Bartelsen-Raemy

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Social work professionals should underpin their decisions with scientific knowledge and research findings. Hence, research is used as a framework for social work education and research courses have become a taken-for-granted component of study programmes. However, it has been acknowledged that social work students have negative beliefs and attitudes as well as frequently feelings of fear of research courses. Against this background, the present study aimed to establish the relationship between student’s fear of research courses, their research orientation and interest in research courses. We hypothesized that fear predicts the interest in research courses. Further, we hypothesized that research orientation (perceived importance and attributed usefulness for research for social work practice and perceived unbiased nature of research) was a mediating variable. In the years 2014, 2015 and 2016, we invited students enrolled for a bachelor programme in social work in Switzerland to participate in the study during their introduction day to the school taking place two weeks before their programme started. For data collection, we used an anonymous self-administered on-line questionnaire filled in on site. Data were analysed using descriptive statistics and structural equation modelling (generalized least squares estimates method). The sample included 708 students enrolled in a social work bachelor-programme, 501 being female, 184 male, and 5 intersexual, aged 19–56, having various entitlements to study, and registered for three different types of programme modes (full time programme; part time study with field placements in blocks; part time study involving concurrent field placement). Analysis showed that the interest in research courses was predicted by fear of research courses (β = -0.29) as well as by the perceived importance (β = 0.27), attributed usefulness of research (β = 0.15) and perceived unbiased nature of research (β = 0.08). These variables were predicted, in turn, by fear of research courses (β = -0.10, β = -0.23, and β = -0.13). Moreover, interest was predicted by age (β = 0.13). Fear of research courses was predicted by age (β = -0.10) female gender (β = 0.28) and having completed a general baccalaureate (β = -0.09). (GFI = 0.997, AGFI = 0.988, SRMR = 0.016, CMIN/df = 0.946, adj. R2 = 0.312). Findings evidence a direct as well as a mediated impact of fear on the interest in research courses in entering first-year students in a social work bachelor-programme. It highlights one of the challenges social work education in a research framework has to meet with. It seems, there have been considerable efforts to address the research orientation of students. However, these findings point out that, additionally, research anxiety in terms of fear of research courses should be considered and addressed by teachers when conceptualizing research courses.

Keywords: research anxiety, research courses, research interest, research orientation, social work students, teaching

Procedia PDF Downloads 163
608 Practical Design Procedures of 3D Reinforced Concrete Shear Wall-Frame Structure Based on Structural Optimization Method

Authors: H. Nikzad, S. Yoshitomi

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This study investigates and develops the structural optimization method. The effect of size constraints on practical solution of reinforced concrete (RC) building structure with shear wall is proposed. Cross-sections of beam and column, and thickness of shear wall are considered as design variables. The objective function to be minimized is total cost of the structure by using a simple and efficient automated MATLAB platform structural optimization methodology. With modification of mathematical formulations, the result is compared with optimal solution without size constraints. The most suitable combination of section sizes is selected as for the final design application based on linear static analysis. The findings of this study show that defining higher value of upper bound of sectional sizes significantly affects optimal solution, and defining of size constraints play a vital role in finding of global and practical solution during optimization procedures. The result and effectiveness of proposed method confirm the ability and efficiency of optimal solutions for 3D RC shear wall-frame structure.

Keywords: structural optimization, linear static analysis, ETABS, MATLAB, RC shear wall-frame structures

Procedia PDF Downloads 353
607 A Quantum Leap: Developing Quantum Semi-Structured Complex Numbers to Solve the “Division by Zero” Problem

Authors: Peter Jean-Paul, Shanaz Wahid

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The problem of division by zero can be stated as: “what is the value of 0 x 1/0?” This expression has been considered undefined by mathematicians because it can have two equally valid solutions either 0 or 1. Recently semi-structured complex number set was invented to solve “division by zero”. However, whilst the number set had some merits it was considered to have a poor theoretical foundation and did not provide a quality solution to “division by zero”. Moreover, the set lacked consistency in simple algebraic calculations producing contradictory results when dividing by zero. To overcome these issues this research starts by treating the expression " 0 x 1/0" as a quantum mechanical system that produces two tangled results 0 and 1. Dirac Notation (a tool from quantum mechanics) was then used to redefine the unstructured unit p in semi-structured complex numbers so that p represents the superposition of two results (0 and 1) and collapses into a single value when used in algebraic expressions. In the process, this paper describes a new number set called Quantum Semi-structured Complex Numbers that provides a valid solution to the problem of “division by zero”. This research shows that this new set (1) forms a “Field”, (2) can produce consistent results when solving division by zero problems, (3) can be used to accurately describe systems whose mathematical descriptions involve division by zero. This research served to provide a firm foundation for Quantum Semi-structured Complex Numbers and support their practical use.

Keywords: division by zero, semi-structured complex numbers, quantum mechanics, Hilbert space, Euclidean space

Procedia PDF Downloads 135