Search results for: mathematical physics

Authors: Zahid Ullah, Atlas Khan

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In today's data-driven world, the role of mathematics in bridging the gap between theory and applications is becoming increasingly vital. This abstract highlights the significance of mathematics as a powerful tool for analyzing, interpreting, and extracting meaningful insights from vast amounts of data. By integrating mathematical principles with real-world applications, researchers can unlock the full potential of data-driven decision-making processes. This abstract delves into the various ways mathematics acts as a bridge connecting theoretical frameworks to practical applications. It explores the utilization of mathematical models, algorithms, and statistical techniques to uncover hidden patterns, trends, and correlations within complex datasets. Furthermore, it investigates the role of mathematics in enhancing predictive modeling, optimization, and risk assessment methodologies for improved decision-making in diverse fields such as finance, healthcare, engineering, and social sciences. The abstract also emphasizes the need for interdisciplinary collaboration between mathematicians, statisticians, computer scientists, and domain experts to tackle the challenges posed by the data-driven landscape. By fostering synergies between these disciplines, novel approaches can be developed to address complex problems and make data-driven insights accessible and actionable. Moreover, this abstract underscores the importance of robust mathematical foundations for ensuring the reliability and validity of data analysis. Rigorous mathematical frameworks not only provide a solid basis for understanding and interpreting results but also contribute to the development of innovative methodologies and techniques. In summary, this abstract advocates for the pivotal role of mathematics in bridging theory and applications in a data-driven world. By harnessing mathematical principles, researchers can unlock the transformative potential of data analysis, paving the way for evidence-based decision-making, optimized processes, and innovative solutions to the challenges of our rapidly evolving society.

Keywords: mathematics, bridging theory and applications, data-driven world, mathematical models

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Authors: Carlos Alberto Carvalho Castro, Nancy Del Ducca Barbedo, Edmilsom Otoni Côrrea

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With increase the production oil and lines transmission gases that are in ample expansion, the industries medium and great transport they had to adapt itself to supply the demand manufacture in this fabrication segment. In this context, two welding processes have been more extensively used: the GMAW (Gas Metal Arc Welding) and the FCAW (Flux Cored Arc Welding). In this work, welds using these processes were carried out in flat position on ASTM A-36 carbon steel plates in order to make a comparative evaluation between them concerning to mechanical and metallurgical properties. A statistical tool based on technical analysis and design of experiments, DOE, from the Minitab software was adopted. For these analyses, the voltage, current, and welding speed, in both processes, were varied. As a result, it was observed that the welds in both processes have different characteristics in relation to the metallurgical properties and performance, but they present good weldability, satisfactory mechanical strength e developed mathematical models.

Keywords: Flux Cored Arc Welding (FCAW), Gas Metal Arc Welding (GMAW), Design of Experiments (DOE), mathematical models

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Authors: Hanifeh Imanian, Morteza Kolahdoozan

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The purpose of this study is to present a mathematical phrase for calculating the dispersion rate of spilled oil in water column under non-breaking waves. In this regard, a multiphase numerical model is applied for which waves and oil phase were computed concurrently, and accuracy of its hydraulic calculations have been proven. More than 200 various scenarios of oil spilling in wave waters were simulated using the multiphase numerical model and its outcome were collected in a database. The recorded results were investigated to identify the major parameters affected vertical oil dispersion and finally 6 parameters were identified as main independent factors. Furthermore, some statistical tests were conducted to identify any relationship between the dependent variable (dispersed oil mass in the water column) and independent variables (water wave specifications containing height, length and wave period and spilled oil characteristics including density, viscosity and spilled oil mass). Finally, a mathematical-statistical relationship is proposed to predict dispersed oil in marine waters. To verify the proposed relationship, a laboratory example available in the literature was selected. Oil mass rate penetrated in water body computed by statistical regression was in accordance with experimental data was predicted. On this occasion, it was necessary to verify the proposed mathematical phrase. In a selected laboratory case available in the literature, mass oil rate penetrated in water body computed by suggested regression. Results showed good agreement with experimental data. The validated mathematical-statistical phrase is a useful tool for oil dispersion prediction in oil spill events in marine areas.

Keywords: dispersion, marine environment, mathematical-statistical relationship, oil spill

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Authors: Raj K. Gupta, X. Gary Tan, Andrzej Przekwas

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Bomb blasts from Improvised Explosive Devices (IEDs) account for vast majority of terrorist attacks worldwide. Injuries caused by IEDs result from a combination of the primary blast wave, penetrating fragments, and human body accelerations and impacts. This paper presents a multiscale computational model of coupled blast physics, whole human body biodynamics and injury biomechanics of sensitive organs. The disparity of the involved space- and time-scales is used to conduct sequential modeling of an IED explosion event, CFD simulation of blast loads on the human body and FEM modeling of body biodynamics and injury biomechanics. The paper presents simulation results for blast-induced brain injury coupling macro-scale brain biomechanics and micro-scale response of sensitive neuro-axonal structures. Validation results on animal models and physical surrogates are discussed. Results of our model can be used to 'replicate' filed blast loadings in laboratory controlled experiments using animal models and in vitro neuro-cultures.

Keywords: blast waves, improvised explosive devices, injury biomechanics, mathematical models, traumatic brain injury

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Authors: Qian Zhang, Dongkai Shen, Yan Shi

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A new mechanical ventilator with automatic secretion clearance function can improve the secretion clearance safely and efficiently. However, in recent modeling studies on various mechanical ventilators, it was considered that human had one lung, and the coupling effect of double lungs was never illustrated. In this paper, to expound the coupling effect of double lungs, a mathematical model of a ventilation system of a bi-level positive airway pressure (BiPAP) controlled ventilator with secretion clearance was set up. Moreover, an experimental study about the mechanical ventilation system of double lungs on BiPAP ventilator was conducted to verify the mathematical model. Finally, the coupling effect of double lungs of the mathematical ventilation was studied by simulation and orthogonal experimental design. This paper adds to previous studies and can be referred to optimization methods in medical researches.

Keywords: double lungs, coupling effect, secretion clearance, orthogonal experimental design

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Authors: Xavi Vilajosana Guillen, Emilio José Pérez Salgado

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This document presents experimental results obtained in a realistic environment using an underwater LoRa link. It aims to analyze the behavior of electromagnetic waves underwater and determine this communication capability. With this it has been tried to empirically evaluate the results obtained in the mathematical model using a commercial device with low cost and low consumption that works at frequency 433Mhz. The mathematical results obtained for wireless communication at 433Mhz underwater indicate that a communication of up to 7.5 m is possible, however experimentally 8 m has been achieved.

Keywords: 433Mhz link, internet of things, LoRa link, underwater communication

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Authors: Md. Shah Alam

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Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.

Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix

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Authors: Angel Pérez Sánchez

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Background: Consider magnetic lines of force as a vector magnetic current was introduced by convention around 1830. But this leads to a dead end in traditional physics, and quantum explanations must be referred to explain the magnetic phenomenon. However, a study of magnetic lines as percussive waves leads to other paths capable of interpreting magnetism through traditional physics. Methodology: Brick used in the experiment: two parallel electric current cables attract each other if current goes in the same direction and its application at a microscopic level inside magnets. Significance: Consideration of magnetic lines as magnets themselves would mean a paradigm shift in the study of magnetism and open the way to provide solutions to mysteries of magnetism until now only revealed by quantum mechanics. Major findings: discover how a magnetic field is created, as well as reason how magnetic attraction and repulsion work, understand how magnets behave when splitting them, and reveal the impossibility of a Magnetic Monopole. All of this is presented as if it were a symphony in which all the notes fit together perfectly to create a beautiful, smart, and simple work.

Keywords: magnetic lines of force, magnetic field, magnetic attraction and repulsion, magnet split, magnetic monopole, magnetic lines of force as magnets, magnetic lines of force as waves

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Authors: Michaela Chovancova, Jakub Elcner

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Real bronchial tree is very complicated piping system. Analysis of flow and pressure losses in this system is very difficult. Due to the complex geometry and the very small size in the lower generations is examination by CFD possible only in the central part of bronchial tree. For specify the pressure losses of lower generations is necessary to provide a mathematical equation. Determination of mathematical formulas for calculating the pressure losses in the real lungs is due to its complexity and diversity lengthy and inefficient process. For these calculations is necessary the lungs to slightly simplify (same cross-section over the length of individual generation) or use one of the models of lungs. The simplification could cause deviations from real values. The article compares the values of pressure losses obtained from CFD simulation of air flow in the central part of the real bronchial tree with the values calculated in a slightly simplified real lungs by using a mathematical relationship derived from the Bernoulli equation and continuity equation. Then, evaluate the desirability of using this formula to determine the pressure loss across the bronchial tree.

Keywords: pressure gradient, airways resistance, real geometry of bronchial tree, breathing

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Authors: Abdelkhalek Bakkari

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Image segmentation is a critical step in image processing and pattern recognition. In this paper, we proposed a new robust automatic image classification based on a dynamic fuzzy c-means algorithm and mathematical morphology. The proposed segmentation algorithm (DFCM_MM) has been applied to MR perfusion images. The obtained results show the validity and robustness of the proposed approach.

Keywords: segmentation, classification, dynamic, fuzzy c-means, MR image

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Authors: Sarwat Jahan, Asker Rajin Rahman

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Management of offtake of any fluvial river is very sensitive in terms of long-term sustainability where the variation of water flow and sediment transport range are wide enough throughout a hydrological year. The Gorai River is a major distributary of the Ganges River in Bangladesh and is termed as a primary source of fresh water for the South-West part of the country. Every year, significant siltation of the Gorai offtake disconnects it from the Ganges during the dry season. As a result, the socio-economic and environmental condition of the downstream areas has been deteriorating for a few decades. To improve the overall situation of the Gorai offtake and its dependent areas, a study has been conducted by the Institute of Water Modelling, Bangladesh, in 2022. Using the mathematical morphological modeling tool MIKE 21C of DHI Water & Environment, Denmark, simulated results revealed the need for dredging/river training structures for offtake management at the Gorai offtake to ensure significant dry season flow towards the downstream. The dry season flow is found to increase significantly with the proposed river interventions, which also improves the environmental conditions in terms of salinity of the South-West zone of the country. This paper summarizes the primary findings of the analyzed results of the developed mathematical model for improving the existing condition of the Gorai River.

Keywords: Gorai river, mathematical modelling, offtake, siltation, salinity

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Authors: Emhimed Saffor

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In this paper, the problem of edge detection in digital images is considered. Three methods of edge detection based on mathematical morphology algorithm were applied on two sets (Brain and Chest) CT images. 3x3 filter for first method, 5x5 filter for second method and 7x7 filter for third method under MATLAB programming environment. The results of the above-mentioned methods are subjectively evaluated. The results show these methods are more efficient and satiable for medical images, and they can be used for different other applications.

Keywords: CT images, Matlab, medical images, edge detection

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Authors: Nessa-Amie T. Peñaflor, Antonio Cinto

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This is a descriptive research on the level of math anxiety and mathematics misconceptions in algebra. This research is composed of four parts: (1) analysis of the level of anxiety of the respondents; (2) analysis of the common mathematical misconceptions in algebra; (3) relationship of socio-demographic profile in math anxiety and mathematical misconceptions and (4) analysis of the relationship of math anxiety and misconceptions in algebra. Through the demographic profile questionnaire it was found out that most of the respondents were female. Majority had ages that ranged from 13-15. Most of them had parents who finished secondary education. The biggest portion of Grade Seven students where from families with annual family income ranging from PhP 100, 000 to PhP 299, 999. Most of them came from public school. Mathematics Anxiety Scale for Secondary and Senior Secondary School Students (MAS) and set of 10 open-ended algebraic expressions and polynomials were also administered to determine the anxiety level and the common misconceptions in algebra. Data analysis revealed that respondents had high anxiety in mathematics. Likewise, the common mathematical misconceptions of the Grade Seven students were: combining unlike terms; multiplying the base and exponents; regarding the variable x as 0; squaring the first and second terms only in product of two binomials; wrong meaning attached to brackets; writing the terms next to each other but not simplifying in using the FOIL Method; writing the literal coefficient even if the numerical coefficient is 0; and dividing the denominator by the numerator when the numerical coefficient in the numerator is smaller than the numerical coefficient of the denominator. Results of the study show that the socio-demographic characteristics were not related to mathematics anxiety and misconceptions. Furthermore, students from higher section had high anxiety than those students on the lower section. Thus, belonging to higher or lower section may affect the mathematical misconceptions of the respondents.

Keywords: algebra, grade 7 math, math anxiety, math misconceptions

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Authors: Atara Shriki, Ilana Lavy

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Teaching for the first time an online course dealing with the history of mathematics, we were struggling with questions related to the design of a proper learning environment (LE). Thirteen high school mathematics teachers, M.Ed. students, attended the course. The teachers were engaged in independent reading of mathematical texts, a task that is recognized as complex due to the unique characteristics of such texts. In order to support the learning processes and develop skills that are essential for succeeding in learning online (e.g. self-regulated learning skills, meta-cognitive skills, reflective ability, and self-assessment skills), the LE comprised of three components aimed at “scaffolding” the learning: (1) An online "self-feedback" questionnaires that included drill-and-practice questions. Subsequent to responding the questions the online system provided a grade and the teachers were entitled to correct their answers; (2) Open-ended questions aimed at stimulating critical thinking about the mathematical contents; (3) Reflective questionnaires designed to assist the teachers in steering their learning. Using a mixed-method methodology, an inquiry study examined the learning processes, the learners' difficulties in reading the mathematical texts and on the unique contribution of each component of the LE to the ability of teachers to comprehend the mathematical contents, and support the development of their learning skills. The results indicate that the teachers found the online feedback as most helpful in developing self-regulated learning skills and ability to reflect on deficiencies in knowledge. Lacking previous experience in expressing opinion on mathematical ideas, the teachers had troubles in responding open-ended questions; however, they perceived this assignment as nurturing cognitive and meta-cognitive skills. The teachers also attested that the reflective questionnaires were useful for steering the learning. Although in general the teachers found the LE as supportive, most of them indicated the need to strengthen instructor-learners and learners-learners interactions. They suggested to generate an online forum to enable them receive direct feedback from the instructor, share ideas with other learners, and consult with them about solutions. Apparently, within online LE, supporting learning merely with respect to cognitive aspects is not sufficient. Leaners also need an emotional support and sense a social presence.

Keywords: cognitive and meta-cognitive skills, independent reading of mathematical texts, online learning environment, self-regulated learning skills

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Authors: A. A. Okafor, C. H. Achebe, J. L. Chukwuneke, C. G. Ozoegwu

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The performance of an engine whose basic design parameters are known can be predicted with the assistance of simulation programs into the less time, cost and near value of actual. This paper presents a comprehensive mathematical model of the performance parameters of four stroke spark ignition engine. The essence of this research work is to develop a mathematical model for the analysis of engine performance parameters of four stroke spark ignition engine before embarking on full scale construction, this will ensure that only optimal parameters are in the design and development of an engine and also allow to check and develop the design of the engine and it’s operation alternatives in an inexpensive way and less time, instead of using experimental method which requires costly research test beds. To achieve this, equations were derived which describe the performance parameters (sfc, thermal efficiency, mep and A/F). The equations were used to simulate and optimize the engine performance of the model for various engine speeds. The optimal values obtained for the developed bivariate mathematical models are: sfc is 0.2833kg/kwh, efficiency is 28.77% and a/f is 20.75.

Keywords: bivariate models, engine performance, injector engine, optimization, performance parameters, simulation, spark ignition

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Authors: Purevdolgor Luvsantseren, Ajnai Luvsan-Ish, Oyuntsetseg Sandag, Javzmaa Tsend, Akhit Tileubai, Baasandorj Chilhaasuren, Jargalbat Puntsagdash, Galbadrakh Chuluunbaatar

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One of the indicators of the quality of university services is student satisfaction. Aim: We aimed to study the level of satisfaction of students in the first year of premedical courses in the course of Medical Physics using the cluster method. Materials and Methods: In the framework of this goal, a questionnaire was collected from a total of 324 students who studied the medical physics course of the 1st course of the premedical course at the Mongolian National University of Medical Sciences. When determining the level of satisfaction, the answers were obtained on five levels of satisfaction: "excellent", "good", "medium", "bad" and "very bad". A total of 39 questionnaires were collected from students: 8 for course evaluation, 19 for teacher evaluation, and 12 for student evaluation. From the research, a database with 39 fields and 324 records was created. Results: In this database, cluster analysis was performed in MATLAB and R programs using the k-means method of data mining. Calculated the Hopkins statistic in the created database, the values are 0.88, 0.87, and 0.97. This shows that cluster analysis methods can be used. The course evaluation sub-fund is divided into three clusters. Among them, cluster I has 150 objects with a "good" rating of 46.2%, cluster II has 119 objects with a "medium" rating of 36.7%, and Cluster III has 54 objects with a "good" rating of 16.6%. The teacher evaluation sub-base into three clusters, there are 179 objects with a "good" rating of 55.2% in cluster II, 108 objects with an "average" rating of 33.3% in cluster III, and 36 objects with an "excellent" rating in cluster I of 11.1%. The sub-base of student evaluations is divided into two clusters: cluster II has 215 objects with an "excellent" rating of 66.3%, and cluster I has 108 objects with an "excellent" rating of 33.3%. Evaluating the resulting clusters with the Silhouette coefficient, 0.32 for the course evaluation cluster, 0.31 for the teacher evaluation cluster, and 0.30 for student evaluation show statistical significance. Conclusion: Finally, to conclude, cluster analysis in the model of the medical physics lesson “good” - 46.2%, “middle” - 36.7%, “bad” - 16.6%; 55.2% - “good”, 33.3% - “middle”, 11.1% - “bad” in the teacher evaluation model; 66.3% - “good” and 33.3% of “bad” in the student evaluation model.

Keywords: questionnaire, data mining, k-means method, silhouette coefficient

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Authors: Hau-Wei Lee, Yu-Chi Liu, Chien-Hung Liu

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A mathematical model is presented for a system that measures rotational errors in a shaft using a ball lens. The geometric optical characteristics of the ball lens mounted on the shaft allows the measurement of rotation axis errors in both the radial and axial directions. The equipment used includes two quadrant detectors (QD), two laser diodes and a ball lens that is mounted on the rotating shaft to be evaluated. Rotational errors in the shaft cause changes in the optical geometry of the ball lens. The resulting deflection of the laser beams is detected by the QDs and their output signals are used to determine rotational errors. The radial and the axial rotational errors can be calculated as explained by the mathematical model. Results from system calibration show that the measurement error is within ±1 m and resolution is about 20 nm. Using a direct drive motor (DD motor) as an example, experimental results show a rotational error of less than 20 m. The most important features of this system are that it does not require the use of expensive optical components, it is small, very easy to set up, and measurements are highly accurate.

Keywords: ball lens, quadrant detector, axial error, radial error

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Authors: Manoj Kumar

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Ionization cross sections of molecules due to electron impact play an important role in chemical processes in various branches of applied physics, such as radiation chemistry, gas discharges, plasmas etching in semiconductors, planetary upper atmospheric physics, mass spectrometry, etc. In the present work, we have calculated the total ionization cross sections for Adenine (C₅H₅N₅), a biologically important molecule, by electron impact in the incident electron energy range from ionization threshold to 2 keV employing a well-known Jain-Khare semiempirical formulation based on Bethe and Möllor cross sections. In the non-availability of the experimental results, the present results are in good agreement qualitatively as well as quantitatively with available theoretical results. The present results drive our confidence for further investigation of complex bio-molecule with better accuracy. Notwithstanding, the present method can deduce reliable cross-sectional data for complex targets with adequate accuracy and may facilitate the acclimatization of calculated cross-sections into atomic molecular cross-section data sets for modeling codes and other applications.

Keywords: electron impact ionization cross-sections, oscillator strength, jain-khare semiempirical approach

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Andreas Johansson

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Conceptual understanding needs to be grounded on observation of physical phenomena, experiences or metaphors. Observation of physical phenomena using demonstration experiments has a long tradition within physics education and students need to develop mental models to relate the observations to concepts from scientific theories. This study investigates how live and video experiments involving an acoustic trap to visualize particle-field interaction, field properties and particle properties can help develop students' mental models and how they can be used differently to realize their potential as teaching tools. Initially, they were treated as analogs and the lesson designs were kept identical. With a design-based approach, the experimental and video designs, as well as best practices for a respective teaching tool, were then developed in iterations. Variation theory was used as a theoretical framework to analyze the planned respective realized pattern of variation and invariance in order to explain learning outcomes as measured by a pre-posttest consisting of conceptual multiple-choice questions inspired by the Force Concept Inventory and the Force and Motion Conceptual Evaluation. Interviews with students and teachers were used to inform the design of experiments and videos in each iteration. The lesson designs and the live and video experiments has been developed to help teachers improve student learning and make school physics more interesting by involving experimental setups that usually are out of reach and to bridge the gap between what happens in classrooms and in science research. As students’ conceptual knowledge also rises their interest in physics the aim is to increase their chances of pursuing careers within science, technology, engineering or mathematics.

Keywords: acoustic trap, design-based research, experiments, variation theory

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Authors: Ozgul Kartal, Wade Tillett, Lyn D. English

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Despite its global significance in curricula, mathematical modeling encounters persistent disparities in recognition and emphasis within regular mathematics classrooms and teacher education across countries with diverse educational and cultural traditions, including variations in the perceived role of mathematical modeling. Over the past two decades, increased attention has been given to the integration of mathematical modeling into national curriculum standards in the U.S. and other countries. Therefore, the mathematics education research community has dedicated significant efforts to investigate various aspects associated with the teaching and learning of mathematical modeling, primarily focusing on exploring the applicability of modeling in schools and assessing students', teachers', and preservice teachers' (PTs) competencies and engagement in modeling cycles and processes. However, limited attention has been directed toward examining potential resistance hindering teachers and PTs from effectively implementing mathematical modeling. This study focuses on how PTs, without prior modeling experience, resist and/or embrace mathematical modeling and its pedagogy as they learn about models and modeling perspectives, navigate the modeling process, design and implement their modeling activities and lesson plans, and experience the pedagogy enabling modeling. Model eliciting activities (MEAs) were employed due to their high potential to support the development of mathematical modeling pedagogy. The mathematical modeling module was integrated into a mathematics methods course to explore how PTs embraced or resisted mathematical modeling and its pedagogy. The module design included reading, reflecting, engaging in modeling, assessing models, creating a modeling task (MEA), and designing a modeling lesson employing an MEA. Twelve senior undergraduate students participated, and data collection involved video recordings, written prompts, lesson plans, and reflections. An open coding analysis revealed acceptance and resistance toward teaching mathematical modeling. The study identified four overarching themes, including both acceptance and resistance: pedagogy, affordance of modeling (tasks), modeling actions, and adjusting modeling. In the category of pedagogy, PTs displayed acceptance based on potential pedagogical benefits and resistance due to various concerns. The affordance of modeling (tasks) category emerged from instances when PTs showed acceptance or resistance while discussing the nature and quality of modeling tasks, often debating whether modeling is considered mathematics. PTs demonstrated both acceptance and resistance in their modeling actions, engaging in modeling cycles as students and designing/implementing MEAs as teachers. The adjusting modeling category captured instances where PTs accepted or resisted maintaining the qualities and nature of the modeling experience or converted modeling into a typical structured mathematics experience for students. While PTs displayed a mix of acceptance and resistance in their modeling actions, limitations were observed in embracing complexity and adhering to model principles. The study provides valuable insights into the challenges and opportunities of integrating mathematical modeling into teacher education, emphasizing the importance of addressing pedagogical concerns and providing support for effective implementation. In conclusion, this research offers a comprehensive understanding of PTs' engagement with modeling, advocating for a more focused discussion on the distinct nature and significance of mathematical modeling in the broader curriculum to establish a foundation for effective teacher education programs.

Keywords: mathematical modeling, model eliciting activities, modeling pedagogy, secondary teacher education

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Authors: Jamal Hussain Al-Smail

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Hydrogen fuel cells (HFCs) are environmentally friendly, energy converter devices that convert the chemical energy of the reactants (oxygen and hydrogen) to electricity through electrochemical reactions. The level of the electricity production of HFCs mainly increases depending on the oxygen distribution in the HFC’s cathode gas diffusion layer (GDL). With a constant porosity of the GDL, the electrochemical reaction can have a great variation that reduces the cell’s productivity and stability. Our findings bring a methodology in finding porosity designs of the diffusion layer to improve the oxygen distribution such that it results in a stable oxygen-hydrogen reaction. We first introduce a mathematical model involving the mass and momentum transport equations, in which a porosity function of the GDL is incorporated as a control for the fluid flow. We then derive numerical methods for solving the mathematical model. In conclusion, we present our numerical results to show how to design the GDL porosity to result in a uniform oxygen distribution.

Keywords: fuel cells, material porosity design, mathematical modeling, porous media

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Authors: Goulet Marie-Pier, Voyer Dominic, Simoneau Victoria

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In a previous research project (2011-2019) funded by the Quebec Ministry of Education, an educational approach was developed based on the teaching and learning of place value through children's literature. Subsequently, the effect of this approach on the conceptual understanding of the concept among first graders (6-7 years old) was studied. The current project aims to create a series of children's literature to help older elementary school students (8-10 years old) in developing a conceptual understanding of complex mathematical concepts taught at their grade level rather than a more typical procedural understanding. Knowing that there are no educational material or children's books that exist to achieve our goals, four stories, accompanied by mathematical activities, will be created to support students, and their teachers, in the learning and teaching of mathematical concepts that can be challenging within their mathematic curriculum. The stories will also introduce a mathematical dialogue into the characters' discourse with the aim to address various mathematical foundations for which there are often erroneous statements among students and occasionally among teachers. In other words, the stories aim to empower students seeking a real understanding of difficult mathematical concepts, as well as teachers seeking a way to teach these difficult concepts in a way that goes beyond memorizing rules and procedures. In order to choose the concepts that will be part of the stories, it is essential to understand the current landscape regarding the main difficulties experienced by students in third and fourth grade (8-10 years old) and their teacher’s needs. From this perspective, the preliminary phase of the study, as discussed in the presentation, will provide critical insight into the mathematical concepts with which the target grade levels struggle the most. From this data, the research team will select the concepts and develop their stories in the second phase of the study. Two questions are preliminary to the implementation of our approach, namely (1) what mathematical concepts are considered the most “difficult to teach” by teachers in the third and fourth grades? and (2) according to teachers, what are the main difficulties encountered by their students in numeracy? Self-administered online questionnaires using the SimpleSondage software will be sent to all third and fourth-grade teachers in nine school service centers in the Quebec region, representing approximately 300 schools. The data that will be collected in the fall of 2022 will be used to compare the difficulties identified by the teachers with those prevalent in the scientific literature. Considering that this ensures consistency between the proposed approach and the true needs of the educational community, this preliminary phase is essential to the relevance of the rest of the project. It is also an essential first step in achieving the two ultimate goals of the research project, improving the learning of elementary school students in numeracy, and contributing to the professional development of elementary school teachers.

Keywords: children’s literature, conceptual understanding, elementary school, learning and teaching, mathematics

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Authors: Lee Bih Ni, Nurul Asyikin Binti Hassan

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This paper discusses the use of mnemonic and mathematical methods in enhancing the understanding of history. Mnemonics can help students from all levels including high school and in various disciplines including language, math and history. At the secondary level, students are exposed to various courses that require them to remember many facts that can be mastered through the application of mnemonic techniques. Researchers use narrative literature studies to illustrate the current state of art and science in the field of research focused. Researchers used narrative literature reviews to build a scientific base of knowledge. Researchers gather all the key points in the discussion, and put it here by referring to the specific field where the paper is essentially based. The findings suggest that the use of mnemonic techniques can improve the individual's memory by adding little effort. In implementing mnemonic techniques, it is important to integrate mathematics and history in the course as both are interconnected as mathematics has shaped our history and vice versa. This study shows that memory skills can actually be improved; the human mind can remember something more than expected.

Keywords: cognitive strategy, mnemonic technique, secondary school level study, mathematical mnemonic

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Authors: Geetika Barman, B. S. Daya Sagar

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In this article, we proposed a pixel-wise classification of hyperspectral images using a mathematical morphology operator-based distance metric called “dilation distance” and “erosion distance”. This method involves measuring the spatial distance between the spectral features of a hyperspectral image across the bands. The key concept of the proposed approach is that the “dilation distance” is the maximum distance a pixel can be moved without changing its classification, whereas the “erosion distance” is the maximum distance that a pixel can be moved before changing its classification. The spectral signature of the hyperspectral image carries unique class information and shape for each class. This article demonstrates how easily the dilation and erosion distance can measure spatial distance compared to other approaches. This property is used to calculate the spatial distance between hyperspectral image feature vectors across the bands. The dissimilarity matrix is then constructed using both measures extracted from the feature spaces. The measured distance metric is used to distinguish between the spectral features of various classes and precisely distinguish between each class. This is illustrated using both toy data and real datasets. Furthermore, we investigated the role of flat vs. non-flat structuring elements in capturing the spatial features of each class in the hyperspectral image. In order to validate, we compared the proposed approach to other existing methods and demonstrated empirically that mathematical operator-based distance metric classification provided competitive results and outperformed some of them.

Keywords: dilation distance, erosion distance, hyperspectral image classification, mathematical morphology

Procedia PDF Downloads 55

Authors: W. I. Mazyan, A. Ahmadi, M. Hoorfar

Abstract:

Objectives/Scope: This paper proposes a mathematical model for calculating the solid-gas separation efficiency in cyclones. This model provides better agreement with experimental results compared to existing mathematical models. Methods: The separation ratio efficiency, ϵsp, is evaluated by calculating the outlet to inlet count ratio. Similar to mathematical derivations in the literature, the inlet and outlet particle count were evaluated based on Eulerian approach. The model also includes the external forces acting on the particle (i.e., centrifugal and drag forces). In addition, the proposed model evaluates the exact length that the particle travels inside the cyclone for the evaluation of number of turns inside the cyclone. The separation efficiency model derivation using Stoke’s law considers the effect of the inlet tangential velocity on the separation performance. In cyclones, the inlet velocity is a very important factor in determining the performance of the cyclone separation. Therefore, the proposed model provides accurate estimation of actual cyclone separation efficiency. Results/Observations/Conclusion: The separation ratio efficiency, ϵsp, is studied to evaluate the performance of the cyclone for particles ranging from 1 microns to 10 microns. The proposed model is compared with the results in the literature. It is shown that the proposed mathematical model indicates an error of 7% between its efficiency and the efficiency obtained from the experimental results for 1 micron particles. At the same time, the proposed model gives the user the flexibility to analyze the separation efficiency at different inlet velocities. Additive Information: The proposed model determines the separation efficiency accurately and could also be used to optimize the separation efficiency of cyclones at low cost through trial and error testing, through dimensional changes to enhance separation and through increasing the particle centrifugal forces. Ultimately, the proposed model provides a powerful tool to optimize and enhance existing cyclones at low cost.

Keywords: cyclone efficiency, solid-gas separation, mathematical model, models error comparison

Procedia PDF Downloads 363

Authors: N. Philipova

Abstract:

The influence of the geometric parameters of trapezoidal labyrinth channel on the emitter discharge is investigated in this work. The impact of the dentate angle, the dentate spacing, and the dentate height are studied among the geometric parameters of the labyrinth channel. Numerical simulations of the water flow movement are performed according to central cubic composite design using Commercial codes GAMBIT and FLUENT. Inlet pressure of the dripper is set up to be 1 bar. The objective of this paper is to derive a mathematical model of the emitter discharge depending on the dentate angle, the dentate spacing, the dentate height of the labyrinth channel. As a result, the obtained mathematical model is a second-order polynomial reporting 2-way interactions among the geometric parameters. The dentate spacing has the most important and positive influence on the emitter discharge, followed by the simultaneous impact of the dentate spacing and the dentate height. The dentate angle in the observed interval has no significant effect on the emitter discharge. The obtained model can be used as a basis for a future emitter design.

Keywords: drip irrigation, labyrinth channel hydrodynamics, numerical simulations, Reynolds stress model.

Procedia PDF Downloads 166

Authors: Hui-Yun Cao, Hai-Qing Zhou

Abstract:

The high precision measurements and experiments play more and more important roles in particle physics and atomic physics. To analyse the precise experimental data sets, the corresponding precise and reliable theoretical calculations are necessary. Until now, the form factors of elemental constituents such as pion and proton are still attractive issues in current Quantum Chromodynamics (QCD). In this work, the two-photon-exchange (TPE) effects in ep→enπ⁺ at small -t are discussed within a hadronic model. Under the pion dominance approximation and the limit mₑ→0, the TPE contribution to the amplitude can be described by a scalar function. We calculate TPE contributions to the amplitude, and the unpolarized differential cross section with the only elastic intermediate state is considered. The results show that the TPE corrections to the unpolarized differential cross section are about from -4% to -20% at Q²=1-1.6 GeV². After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections σ(L,T,LT,TT). We find that the TPE corrections (at Q²=1-1.6 GeV²) to σL are about from -10% to -30%, to σT are about 20%, and to σ(LT,TT) are much larger. By these analyses, we conclude that the TPE contributions in ep→enπ⁺ at small -t are important to extract the separated cross sections σ(L,T,LT,TT) and the electromagnetic form factor of π⁺ in the experimental analysis.

Keywords: differential cross section, form factor, hadronic, two-photon

Procedia PDF Downloads 103

Authors: Mohammadali Abedini Sanigy, Jiangang Fei

Abstract:

In this paper, a mathematical optimization model was developed to maximize the profit in a vegetable production planning problem. It serves as a decision support system that assists farmers in land allocation to crops and harvest scheduling decisions. The developed model can handle different rotation rules in two consecutive cycles of production, which is a common practice in organic production system. Moreover, different production methods of the same crop were considered in the model formulation. The main strength of the model is that it is not restricted to predetermined production periods, which makes the planning more flexible. The model is classified as a mixed integer programming (MIP) model and formulated in PYOMO -a Python package to formulate optimization models- and solved via Gurobi and CPLEX optimizer packages. The model was tested with secondary data from 'Australian vegetable growing farms', and the results were obtained and discussed with the computational test runs. The results show that the model can successfully provide reliable solutions for real size problems.

Keywords: crop rotation, harvesting, mathematical model formulation, vegetable production

Procedia PDF Downloads 157

Authors: Takuya Sumi, Syoko Nukaya, Takashi Kaburagi, Hiroshi Tanaka, Kajiro Watanabe, Yosuke Kurihara

Abstract:

We propose an unconstrained measurement system for scratching motion based on mathematical model of unconstrained bed sensing method which could measure the bed vibrations due to the motion of the person on the bed. In this paper, we construct mathematical model of the unconstrained bed monitoring system, and we apply the unconstrained bed sensing method to the system for detecting scratching motion. The proposed sensors are placed under the three bed feet. When the person is lying on the bed, the output signals from the sensors are proportional to the magnitude of the vibration due to the scratching motion. Hence, we could detect the subject’s scratching motion from the output signals from ceramic sensors. We evaluated two scratching motions using the proposed system in the validity experiment as follows: First experiment is the subject’s scratching the right side cheek with his right hand, and; second experiment is the subject’s scratching the shin with another foot. As the results of the experiment, we recognized the scratching signals that enable the determination when the scratching occurred. Furthermore, the difference among the amplitudes of the output signals enabled us to estimate where the subject scratched.

Keywords: unconstrained bed sensing method, scratching, body movement, itchy, piezoceramics

Procedia PDF Downloads 385