Search results for: mathematical physics

Authors: Charlene N. T. Mfangnia, Henri Tonnang, Berge Tsanou, Jeremy Herren

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The Microsporidia MB found in the populations of anopheles is a recently discovered symbiont responsible for the Plasmodium transmission blocking. From early studies, it was established that the symbiont can be transmitted vertically and horizontally. The present study uses compartmental mathematical modelling approach to investigate the dynamics of Microsporidia transmission in the mosquito population with the mindset of establishing a mechanism for use to control malaria. Data and information obtained from laboratory experiments are used to estimate the model parameters with and without temperature dependency of mosquito traits. We carry out the mathematical analysis focusing on the equilibria states and their stability for the autonomous model. Through the modelling experiments, we are able to assess and confirm the contribution of vertical and horizontal transmission in the proliferation of Microsporidia MB in the mosquito population. In addition, the basic and target reproductions are computed, and some long-term behaviours of the model, such as the local (and global) stability of equilibrium points, are rigorously analysed and illustrated numerically. We establish the conditions responsible for the low prevalence of the symbiont-infected mosquitoes observed in nature. Moreover, we identify the male death rate, the mating rate and the attractiveness of MB-positive mosquitoes as mosquito traits that significantly influence the spread of Microsporidia MB. Furthermore, we highlight the influence of temperature in the establishment and persistence of MB-infected mosquitoes in a given area.

Keywords: microsporidia MB, vertical transmission, horizontal transmission, compartmental modelling approach, temperature-dependent mosquito traits, malaria, plasmodium-transmission blocking

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Authors: Ella Tyuryumina, Alexey Neznanov

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This study is an attempt to obtain reliable data on the natural history of breast cancer growth. We analyze the opportunities for using classical mathematical models (exponential and logistic tumor growth models, Gompertz and von Bertalanffy tumor growth models) to try to describe growth of the primary tumor and the secondary distant metastases of human breast cancer. The research aim is to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoMPaS and corresponding software. We are interested in: 1) modelling the whole natural history of the primary tumor and the secondary distant metastases; 2) developing adequate and precise CoMPaS which reflects relations between the primary tumor and the secondary distant metastases; 3) analyzing the CoMPaS scope of application; 4) implementing the model as a software tool. The foundation of the CoMPaS is the exponential tumor growth model, which is described by determinate nonlinear and linear equations. The CoMPaS corresponds to TNM classification. It allows to calculate different growth periods of the primary tumor and the secondary distant metastases: 1) ‘non-visible period’ for the primary tumor; 2) ‘non-visible period’ for the secondary distant metastases; 3) ‘visible period’ for the secondary distant metastases. The CoMPaS is validated on clinical data of 10-years and 15-years survival depending on the tumor stage and diameter of the primary tumor. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer growth models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. The CoMPaS model and predictive software: a) fit to clinical trials data; b) detect different growth periods of the primary tumor and the secondary distant metastases; c) make forecast of the period of the secondary distant metastases appearance; d) have higher average prediction accuracy than the other tools; e) can improve forecasts on survival of breast cancer and facilitate optimization of diagnostic tests. The following are calculated by CoMPaS: the number of doublings for ‘non-visible’ and ‘visible’ growth period of the secondary distant metastases; tumor volume doubling time (days) for ‘non-visible’ and ‘visible’ growth period of the secondary distant metastases. The CoMPaS enables, for the first time, to predict ‘whole natural history’ of the primary tumor and the secondary distant metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on the primary tumor sizes. Summarizing: a) CoMPaS describes correctly the primary tumor growth of IA, IIA, IIB, IIIB (T1-4N0M0) stages without metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and inception of the secondary distant metastases.

Keywords: breast cancer, exponential growth model, mathematical model, metastases in lymph nodes, primary tumor, survival

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Authors: Jun-Ki Choi

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The usage of valuable resources and the potential for waste generation at the end of the life cycle of photovoltaic (PV) technologies necessitate a proactive planning for a PV recycling infrastructure. To ensure the sustainability of PV in large scales of deployment, it is vital to develop and institute low-cost recycling technologies and infrastructure for the emerging PV industry in parallel with the rapid commercialization of these new technologies. There are various issues involved in the economics of PV recycling and this research examine those at macro and micro levels, developing a holistic interpretation of the economic viability of the PV recycling systems. This study developed mathematical models to analyze the profitability of recycling technologies and to guide tactical decisions for allocating optimal location of PV take-back centers (PVTBC), necessary for the collection of end of life products. The economic decision is usually based on the level of the marginal capital cost of each PVTBC, cost of reverse logistics, distance traveled, and the amount of PV waste collected from various locations. Results illustrated that the reverse logistics costs comprise a major portion of the cost of PVTBC; PV recycling centers can be constructed in the optimally selected locations to minimize the total reverse logistics cost for transporting the PV wastes from various collection facilities to the recycling center. In the micro- process level, automated recycling processes should be developed to handle the large amount of growing PV wastes economically. The market price of the reclaimed materials are important factors for deciding the profitability of the recycling process and this illustrates the importance of the recovering the glass and expensive metals from PV modules.

Keywords: photovoltaic, recycling, mathematical models, sustainability

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Authors: Eunice Christabel Chukwu

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Introduction: Diabetes is a chronic medical condition which is characterized by high levels of glucose in the blood and urine; it is usually diagnosed by means of a glucose tolerance test (GTT). Diabetes can cause a range of health problems if left unmanaged, as it can lead to serious complications. It is essential to manage the condition effectively, particularly in the workplace where the impact on work productivity can be significant. This paper discusses the modelling of optimal control of diabetes in the workplace using a control theory approach. Background: Diabetes mellitus is a condition caused by too much glucose in the blood. Insulin, a hormone produced by the pancreas, controls the blood sugar level by regulating the production and storage of glucose. In diabetes, there may be a decrease in the body’s ability to respond to insulin or a decrease in insulin produced by the pancreas which will lead to abnormalities in the metabolism of carbohydrates, proteins, and fats. In addition to the health implications, the condition can also have a significant impact on work productivity, as employees with uncontrolled diabetes are at risk of absenteeism, reduced performance, and increased healthcare costs. While several interventions are available to manage diabetes, the most effective approach is to control blood glucose levels through a combination of lifestyle modifications and medication. Methodology: The control theory approach involves modelling the dynamics of the system and designing a controller that can regulate the system to achieve optimal performance. In the case of diabetes, the system dynamics can be modelled using a mathematical model that describes the relationship between insulin, glucose, and other variables. The controller can then be designed to regulate the glucose levels to maintain them within a healthy range. Results: The modelling of optimal control of diabetes in the workplace using a control theory approach has shown promising results. The model has been able to predict the optimal dose of insulin required to maintain glucose levels within a healthy range, taking into account the individual’s lifestyle, medication regimen, and other relevant factors. The approach has also been used to design interventions that can improve diabetes management in the workplace, such as regular glucose monitoring and education programs. Conclusion: The modelling of optimal control of diabetes in the workplace using a control theory approach has significant potential to improve diabetes management and work productivity. By using a mathematical model and a controller to regulate glucose levels, the approach can help individuals with diabetes to achieve optimal health outcomes while minimizing the impact of the condition on their work performance. Further research is needed to validate the model and develop interventions that can be implemented in the workplace.

Keywords: mathematical model, blood, insulin, pancreas, model, glucose

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Authors: B. El Fadil, R. Najar

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STEM education is promoted by many scholars and curricula around the world, but it is not yet well established in the province of Quebec in Canada. In addition, effective instructional STEM activities and design methods are required to ensure that students and teachers' needs are being met. One potential method is the Engineering Design Process (EDP), a methodology that emphasizes the importance of creativity and collaboration in problem-solving strategies. This article reports on a case study that focused on using the EDP to develop instructional materials by means of making a technological artifact to teach mathematical variables and functions at the secondary level. The five iterative stages of the EDP (design, make, test, infer, and iterate) were integrated into the development of the course materials. Data was collected from different sources: pre- and post-questionnaires, as well as a working document dealing with pupils' understanding based on designing, making, testing, and simulating. Twenty-four grade seven (13 years old) students in Northern Quebec participated in the study. The findings of this study indicate that STEM activities have a positive impact not only on students' engagement in classroom activities but also on learning new mathematical concepts. Furthermore, STEM-focused activities have a significant effect on problem-solving skills development in an interdisciplinary approach. Based on the study's results, we can conclude, inter alia, that teachers should integrate STEM activities into their teaching practices to increase learning outcomes and attach more importance to STEM-focused activities to develop students' reflective thinking and hands-on skills.

Keywords: engineering design process, motivation, stem, integration, variables, functions

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Authors: Sanaz Ahmadzadeh Siyahrood, Arghavan Ebrahimi, Mohammadjavad Mahdavinejad

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Islamic culture was accountable for a plethora of development in astronomy and science in the medieval term, and in geometry likewise. Geometric patterns are reputable in a considerable number of cultures, but in the Islamic culture the patterns have specific features that connect the Islamic faith to mathematics. In Islamic art, three fundamental shapes are generated from the circle shape: triangle, square and hexagon. Originating from their quiddity, each of these geometric shapes has its own specific structure. Even though the geometric patterns were generated from such simple forms as the circle and the square, they can be combined, duplicated, interlaced, and arranged in intricate combinations. So in order to explain geometrical interaction principles between square and equal triangle, in the first definition step, all types of their linear forces individually and in the second step, between them, would be illustrated. In this analysis, some angles will be created from intersection of their directions. All angles are categorized to some groups and the mathematical expressions among them are analyzed. Since the most geometric patterns in Islamic art and architecture are based on the repetition of a single motif, the evaluation results which are obtained from a small portion, is attributable to a large-scale domain while the development of infinitely repeating patterns can represent the unchanging laws. Geometric ornamentation in Islamic art offers the possibility of infinite growth and can accommodate the incorporation of other types of architectural layout as well, so the logic and mathematical relationships which have been obtained from this analysis are applicable in designing some architecture layers and developing the plan design.

Keywords: angle, equal triangle, square, structural hierarchy

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Authors: Akaki Qatamidze

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Implementation of the project will be a step forward in terms of reliability in Georgia and the improvement of the construction and the development of construction. Completion of the project is expected to result in a complete knowledge, which is expressed in concrete and stone structures of assessing the technical condition of the processing. This method is based on a detailed examination of the structure, in order to establish the injuries and the elimination of the possibility of changing the structural scheme of the new requirements and architectural preservationists. Reinforced concrete and stone structures research project carried out in a systematic analysis of the important approach is to optimize the process of research and development of new knowledge in the neighboring areas. In addition, the problem of physical and mathematical models of rational consent, the main pillar of the physical (in-situ) data and mathematical calculation models and physical experiments are used only for the calculation model specification and verification. Reinforced concrete and stone construction defects and failures the causes of the proposed research to enhance the effectiveness of their maximum automation capabilities and expenditure of resources to reduce the recommended system analysis of the methodological concept-based approach, as modern science and technology major particularity of one, it will allow all family structures to be identified for the same work stages and procedures, which makes it possible to exclude subjectivity and addresses the problem of the optimal direction. It discussed the methodology of the project and to establish a major step forward in the construction trades and practical assistance to engineers, supervisors, and technical experts in the construction of the settlement of the problem.

Keywords: building, reinforced concrete, expertise, stone structures

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Authors: Gary Miller, Andriy Didenko, David Allison

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The boundary of a region in the plane shrinks according to its curvature. A simple algorithm based upon this motion by curvature performed by a spreadsheet simulates the evaporation/dissipation behavior of oil spill boundaries.

Keywords: mathematical modeling, oil, evaporation, dissipation, boundary

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Authors: Krishna Chandra Paudel

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This paper explores the association between the perceived classroom environment and mathematics learning and test anxiety among secondary level students in Nepal. Categorizing the students in three dominant variables- gender, ethnicity and previous schooling, and selecting sample students with respect to higher mathematics anxiety from five heterogeneous classes, the research explores disparities in student's mathematics cognition and reveals nexus between classroom environment and mathematics learning and test anxiety. This research incorporates social learning theory and social development theory as interpretive tool for analyzing themes through qualitative data. Focussing on the interviews with highly mathematics learning anxious students, the study sheds light on how mathematics anxiety among the targeted students is interlinked with multiple factors. The research basically exposes the students’ lack of mathematical passion, their association with other students and participation in classroom learning, asymmetrical content and their lack of preparedness for the tests as caustic factors behind such anxieties. The study further reveals that students’ lack of foundational knowledge and complexity of mathematical content have jointly contributed to mathematics anxiety. Admitting learning as a reciprocal experience, the study points out that the students’ gender, ethnicity and disparities in previous schooling in the context of Nepal has very insignificant impact on students’ mathematics anxiety. It finally recommends that the students who get trapped into the vicious cycle of mathematics anxiety require positive and supportive classroom environment along with inspiring comments/compliments and symmetrical course contents.

Keywords: anxiety, asymmetry, cognition, habitus, pedagogy, preparedness

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Authors: Tahsen Abdalwahab Ibraheem Albehege

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Exhaust fuel purification is of great importance to prevent the emission of major pollutants into the atmosphere such as diesel particulates and nitrogen oxides and meet environmental regulations, so environmental impacts are a primary concern of Diesel Exhaust Gas (DEG) which contains hazardous substances harmful to the environment as well as human health.We can not plasma formed through directing electrical energy to create free electrons, which in turn can react with gaseous species, but we can by used to treat engine exhaust gases. . By NO that has been reportedly oxidized to HNO3 and then into ammonium nitrate, and then condensed and removed. In general, thermal plasmas are formed by heating a system to high temperatures 2,000 degrees C, however this can be inefficient and can require extensive thermal management.

Keywords: plasma system application, project physics, oxidizing environment, electromagnetically

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Authors: Javier Navarro Garcia, Narciso Vazquez Carretero

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Eurocode 1, part 1-4, wind actions, includes in its article 1.5 the possibility of using numerical calculation methods to obtain information on the loads acting on a building. On the other hand, the analysis using computational fluids dynamics (CFD) in aerospace, aeronautical, and industrial applications is already in widespread use. The application of techniques based on CFD analysis on the building to study its aerodynamic behavior now opens a whole alternative field of possibilities for civil engineering and architecture; optimization of the results with respect to those obtained by applying the regulations, the possibility of obtaining information on pressures, speeds at any point of the model for each moment, the analysis of turbulence and the possibility of modeling any geometry or configuration. The present work compares the results obtained on a building, with respect to its aerodynamic behavior, from a mathematical model based on the analysis by CFD with the results obtained by applying Eurocode1, part1-4, wind actions. It is verified that the results obtained by CFD techniques suppose an optimization of the wind action that acts on the building with respect to the wind action obtained by applying the Eurocode1, part 1-4, wind actions. In order to carry out this verification, a 45m high square base truncated pyramid building has been taken. The mathematical model on CFD, based on finite volumes, has been calculated using the FLUENT commercial computer application using a scale-resolving simulation (SRS) type large eddy simulation (LES) turbulence model for an atmospheric boundary layer wind with turbulent component in the direction of the flow.

Keywords: aerodynamic, CFD, computacional fluids dynamics, computational mechanics

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Authors: Matthew Stephenson

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We study the electrical conductivity of strongly disordered, strongly coupled quantum field theories, holographically dual to non-perturbatively disordered uncharged black holes. The computation reduces to solving a diffusive hydrostatic equation for an emergent horizon fluid. We demonstrate that a large class of theories in two spatial dimensions have a universal conductivity independent of disorder strength, and rigorously rule out disorder-driven conductor-insulator transitions in many theories. We present a (fine-tuned) axion-dilaton bulk theory which realizes the conductor-insulator transition, interpreted as a classical percolation transition in the horizon fluid. We address aspects of strongly disordered holography that can and cannot be addressed via mean-field modeling, such as massive gravity.

Keywords: theoretical physics, black holes, holography, high energy

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Authors: G. Martino, F. Silva, E. Marchal

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The control over delivered iron ore blend characteristics is one of the most important aspects of the mining business. The iron ore price is a function of its composition, which is the outcome of the beneficiation process. So, end-to-end integrated planning of mine operations can reduce risks of penalties on the iron ore price. In a standard iron mining company, the production chain is composed of mining, ore beneficiation, and client supply. When mine planning and client supply decisions are made uncoordinated, the beneficiation plant struggles to deliver the best blend possible. Technological improvements in several fields allowed bridging the gap between departments and boosting integrated decision-making processes. Clusterization and classification algorithms over historical production data generate reasonable previsions for quality and volume of iron ore produced for each pile of run-of-mine (ROM) processed. Mathematical modeling can use those deterministic relations to propose iron ore blends that better-fit specifications within a delivery schedule. Additionally, a model capable of representing the whole production chain can clearly compare the overall impact of different decisions in the process. This study shows how flexibilization combined with a planning optimization model between the mine and the ore beneficiation processes can reduce risks of out of specification deliveries. The model capabilities are illustrated on a hypothetical iron ore mine with magnetic separation process. Finally, this study shows ways of cost reduction or profit increase by optimizing process indicators across the production chain and integrating the different plannings with the sales decisions.

Keywords: clusterization and classification algorithms, integrated planning, mathematical modeling, optimization, penalty minimization

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Authors: Anne Bubriski

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Despite improvements in gender inequalities, women and girls continue to face glass ceilings, underrepresentation, and harmful stereotypes that can limit their aspirations and opportunities in STEM. While girls are taking similar high school math and science classes, boys are more likely to take physics and six times more likely to take an engineering course. The gap becomes even larger for minority or low-income girls. This gender gap is not due to biology; rather, it is due to cultural, social, and institutional forces. As girls get older, these forces often ‘teach’ them ‘STEM is more for boys’. The STEM gender gap widens in college, with only 20% of engineering degrees being awarded to women, and by the time women enter the workforce, they only occupy about 13% of engineering jobs. At the University of Central Florida, the Women’s and Gender Studies Program has developed a unique mentoring program to address these issues, Science Leadership and Mentoring (SLAM). What is unique about the approach of SLAM is that we look to address this problem through leadership and STEM. We look to help girls make connections between leadership and STEM—that young women can be leaders as scientists and that scientists are leaders making a change. This is particularly needed and relevant to our community because while there are mentoring programs to our knowledge, SLAM is one of the only, if not only, mentoring programs pairing college women and 7th-grade girls that includes a focus both on STEM and leadership in the United States. SLAM is a curriculum-based mentoring program pairing one 7th-grade girl with one UCF undergraduate STEM major. SLAM empowers young women to be assertive, brave, confident, independent, inquisitive and proud leaders in STEM. SLAM seeks to promote young women’s inspiration and excitement into STEM fields and careers while also building leadership abilities such as problem-solving, teamwork and cooperation, cultural identity and ethnic pride, advocacy for positive change, and goals for the future. SLAM serves about fifteen 7th-grade girls for the academic year and about 20 UCF students. SLAM holds weekly mentoring meetings lasting about 90 minutes, covering topics on leadership, STEM majors and careers, and STEM leadership. This past year, SLAM received a Community Action Grant from the American Association of University Women (AAUW) to run a sub-program, SLAM-Space. SLAM-Space focused on exposing SLAM participants to aerospace engineering and other space-related STEM fields, such as physics and astronomy, through guest speakers, workshops and field trips, including the Kenndy Space Center. The proposed paper presentation will present an overview of SLAM-Space and the data findings from pre and post-surveys, in-depth interviews and focus groups from the SLAM participants' experiences in the program.

Keywords: gender, leadership, STEM, empowerment

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Authors: Pooria Norouzi, Nicholas Tsang, Adam van der Goes, Joseph Yu, Douglas Zheng, Sirine Maleej

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In this study, virtual meters will be designed and used for energy balance measurements of an air handling unit (AHU). The method aims to replace traditional physical sensors in heating, ventilation, and air conditioning (HVAC) systems with simulated virtual meters. Due to the inability to manage and monitor these systems, many HVAC systems have a high level of inefficiency and energy wastage. Virtual meters are implemented and applied in an actual HVAC system, and the result confirms the practicality of mathematical sensors for alternative energy measurement. While most residential buildings and offices are commonly not equipped with advanced sensors, adding, exploiting, and monitoring sensors and measurement devices in the existing systems can cost thousands of dollars. The first purpose of this study is to provide an energy consumption rate based on available sensors and without any physical energy meters. It proves the performance of virtual meters in HVAC systems as reliable measurement devices. To demonstrate this concept, mathematical models are created for AHU-07, located in building NE01 of the British Columbia Institute of Technology (BCIT) Burnaby campus. The models will be created and integrated with the system’s historical data and physical spot measurements. The actual measurements will be investigated to prove the models' accuracy. Based on preliminary analysis, the resulting mathematical models are successful in plotting energy consumption patterns, and it is concluded confidently that the results of the virtual meter will be close to the results that physical meters could achieve. In the second part of this study, the use of virtual meters is further assisted by artificial intelligence (AI) in the HVAC systems of building to improve energy management and efficiency. By the data mining approach, virtual meters’ data is recorded as historical data, and HVAC system energy consumption prediction is also implemented in order to harness great energy savings and manage the demand and supply chain effectively. Energy prediction can lead to energy-saving strategies and considerations that can open a window in predictive control in order to reach lower energy consumption. To solve these challenges, the energy prediction could optimize the HVAC system and automates energy consumption to capture savings. This study also investigates AI solutions possibility for autonomous HVAC efficiency that will allow quick and efficient response to energy consumption and cost spikes in the energy market.

Keywords: virtual meters, HVAC, artificial intelligence, energy consumption prediction

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Authors: L. J. Díaz, M. A. Hernández, A. K. Molina, A. Bermúdez, C. Crane, V. M. Pabón

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One of the most important biological indicators that show the exposure to the radiation is the micronuclei (MN). This technique is using to determinate the radiation effects in blood cultures as a biological control and a complement to the physics dosimetry. In Colombia the necessity to apply this analysis has emerged due to the current biological indicator most used is the chromosomal aberrations (CA), that is why it is essential the MN technique’s standardization and validation to have enough tools to improve the radioprotection topic in the country. Besides, this technique will be applied on the construction of a dose-response curve, that allow measure an approximately dose to irradiated people according to MN frequency found. Inside the steps that carried out to accomplish the standardization and validation is the statistic analysis from the lectures of “in vitro” peripheral blood cultures with different analysts, also it was determinate the best culture medium and conditions for the MN can be detected easily.

Keywords: micronuclei, radioprotection, standardization, validation

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Authors: Yasin Tadayonrad

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Most of the supply chain networks have many nodes starting from the suppliers’ side up to the customers’ side that each node sends/receives the raw materials/products from/to the other nodes. One of the major concerns in this kind of supply chain network is finding the best schedule for loading /unloading the shipments through the whole network by which all the constraints in the source and destination nodes are met and all the shipments are delivered on time. One of the main constraints in this problem is loading/unloading capacity in each source/ destination node at each time slot (e.g., per week/day/hour). Because of the different characteristics of different products/groups of products, the capacity of each node might differ based on each group of products. In most supply chain networks (especially in the Fast-moving consumer goods industry), there are different planners/planning teams working separately in different nodes to determine the loading/unloading timeslots in source/destination nodes to send/receive the shipments. In this paper, a mathematical problem has been proposed to find the best timeslots for loading/unloading the shipments minimizing the overall delays subject to respecting the capacity of loading/unloading of each node, the required delivery date of each shipment (considering the lead-times), and working-days of each node. This model was implemented on python and solved using Python-MIP on a sample data set. Finally, the idea of a heuristic algorithm has been proposed as a way of improving the solution method that helps to implement the model on larger data sets in real business cases, including more nodes and shipments.

Keywords: supply chain management, transportation, multiple-multiple network, timeslots management, mathematical modeling, mixed integer programming

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Authors: Samira Laidaoui, Mohammed Djermane, Nazihe Terfaya

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The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.

Keywords: ALE, coupling, FEM, fluid-structure, interaction, one-way method, two-way method

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Authors: Ricardo Merlo

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In this paper, we analyzed the different didactic proposals for teaching about the free fall motion of bodies available online. An important aspect was the interpretation of the direction and sense of the acceleration of gravity and of the falling velocity of a body, which is why we found different applications of the Cartesian reference system used and also different graphical presentations of the velocity as a function of time and of the distance traveled vertically by the body in the period of time that it was dropped from a height h0. In this framework, a survey of previous concepts was applied to a voluntary group of first-year university students of an Engineering degree before and after the development of the class of the subject in question. Then, Hake's index (0.52) was determined, which resulted in an average learning gain from the meaningful use of the reference system and the respective graphs of v=ƒ (t) and h=ƒ (t).

Keywords: didactic gain, free–fall, physics teaching, previous knowledge

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Authors: Kevin Giraldo, Juan A. Gallego, Uriel Zapata, Fanny L. Casado

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Compliant mechanisms are designed to deform in a controlled manner in response to external forces, utilizing the flexibility of their components to store potential elastic energy during deformation, gradually releasing it upon returning to its original form. This article explores the design of a knee orthosis intended to assist users during stand-up motion. The orthosis makes use of a compliant mechanism to balance the user’s weight, thereby minimizing the strain on leg muscles during standup motion. The primary function of the compliant mechanism is to store and exchange potential energy, so when coupled with the gravitational potential of the user, the total potential energy variation is minimized. The design process for the semi-rigid knee orthosis involved material selection and the development of a numerical model for the compliant mechanism seen as a spring. Geometric properties are obtained through the numerical modeling of the spring once the desired stiffness and safety factor values have been attained. Subsequently, a 3D finite element analysis was conducted. The study demonstrates a strong correlation between the maximum stress in the mathematical model (250.22 MPa) and the simulation (239.8 MPa), with a 4.16% error. Both analyses safety factors: 1.02 for the mathematical approach and 1.1 for the simulation, with a consistent 7.84% margin of error. The spring’s stiffness, calculated at 90.82 Nm/rad analytically and 85.71 Nm/rad in the simulation, exhibits a 5.62% difference. These results suggest significant potential for the proposed device in assisting patients with knee orthopedic restrictions, contributing to ongoing efforts in advancing the understanding and treatment of knee osteoarthritis.

Keywords: biomechanics, complaint mechanisms, gonarthrosis, orthoses

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Authors: B. L. Ho, L. Shi, D. F. Wang, V. C. T. Mok

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The brain’s functional connectivity while temporally non-stationary does express consistency at a macro spatial level. The study of stable resting state connectivity patterns hence provides opportunities for identification of diseases if such stability is severely perturbed. A mathematical model replicating the brain’s spatial connections will be useful for understanding brain’s representative geometry and complements the empirical model where it falls short. Empirical computations tend to involve large matrices and become infeasible with fine parcellation. However, the proposed analytical model has no such computational problems. To improve replicability, 92 subject data are obtained from two open sources. The proposed methodology, inspired by financial theory, uses multivariate regression to find relationships of every cortical region of interest (ROI) with some pre-identified hubs. These hubs acted as representatives for the entire cortical surface. A variance-covariance framework of all ROIs is then built based on these relationships to link up all the ROIs. The result is a high level of match between model and empirical correlations in the range of 0.59 to 0.66 after adjusting for sample size; an increase of almost forty percent. More significantly, the model framework provides an intuitive way to delineate between systemic drivers and idiosyncratic noise while reducing dimensions by more than 30 folds, hence, providing a way to conduct attribution analysis. Due to its analytical nature and simple structure, the model is useful as a standalone toolkit for network dependency analysis or as a module for other mathematical models.

Keywords: functional magnetic resonance imaging, multivariate regression, network hubs, resting state functional connectivity

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Authors: Ladislav Écsi, Roland Jančo

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Contemporary multiplicative plasticity models assume that the body's intermediate configuration consists of an assembly of locally unloaded neighbourhoods of material particles that cannot be reassembled together to give the overall stress-free intermediate configuration since the neighbourhoods are not necessarily compatible with each other. As a result, the plastic deformation gradient, an inelastic component in the multiplicative split of the deformation gradient, cannot be integrated, and the material particle moves from the initial configuration to the intermediate configuration without a position vector and a plastic displacement field when plastic flow occurs. Such behaviour is incompatible with the continuum theory and the continuum physics of elastoplastic deformations, and the related material models can hardly be denoted as truly continuum-based. The paper presents a proper continuum-based reformulation of current problems in finite strain plasticity. It will be shown that the incompatible neighbourhoods in real material are modelled by the product of the plastic multiplier and the yield surface normal when the plastic flow is defined in the current configuration. The incompatible plastic factor can also model the neighbourhoods as the solution of the system of differential equations whose coefficient matrix is the above product when the plastic flow is defined in the intermediate configuration. The incompatible tensors replace the compatible spatial plastic velocity gradient in the former case or the compatible plastic deformation gradient in the latter case in the definition of the plastic flow rule. They act as local imperfections but have the same position vector as the compatible plastic velocity gradient or the compatible plastic deformation gradient in the definitions of the related plastic flow rules. The unstressed intermediate configuration, the unloaded configuration after the plastic flow, where the residual stresses have been removed, can always be calculated by integrating either the compatible plastic velocity gradient or the compatible plastic deformation gradient. However, the corresponding plastic displacement field becomes permanent with both elastic and plastic components. The residual strains and stresses originate from the difference between the compatible plastic/permanent displacement field gradient and the prescribed incompatible second-order tensor characterizing the plastic flow in the definition of the plastic flow rule, which becomes an assignment statement rather than an equilibrium equation. The above also means that the elastic and plastic factors in the multiplicative split of the deformation gradient are, in reality, gradients and that there is no problem with the continuum physics of elastoplastic deformations. The formulation is demonstrated in a numerical example using the regularized Mooney-Rivlin material model and modified equilibrium statements where the intermediate configuration is calculated, whose analysis results are compared with the identical material model using the current equilibrium statements. The advantages and disadvantages of each formulation, including their relationship with multiplicative plasticity, are also discussed.

Keywords: finite strain plasticity, continuum formulation, regularized Mooney-Rivlin material model, compatibility

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Authors: Xiaoyuan Suo

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3D object reconstruction is a broad research area within the computer vision field involving many stages and still open problems. One of the existing challenges in this field lies with micromotion, such as the facial expressions on the appearance of the human or animal face. Similar literatures in this field focuses on 3D reconstruction in stable conditions such as an existing image or photos taken in a rather static environment, while the purpose of this work is to discuss a flexible scan system using multiple cameras that can correctly reconstruct 3D stable and moving objects -- human face with expression in particular. Further, a mathematical model is proposed at the end of this literature to automate the 3D object reconstruction process. The reconstruction process takes several stages. Firstly, a set of simple 2D lines would be projected onto the object and hence a set of uneven curvy lines can be obtained, which represents the 3D numerical data of the surface. The lines and their shapes will help to identify object’s 3D construction in pixels. With the two-recorded angles and their distance from the camera, a simple mathematical calculation would give the resulting coordinate of each projected line in an absolute 3D space. This proposed research will benefit many practical areas, including but not limited to biometric identification, authentications, cybersecurity, preservation of cultural heritage, drama acting especially those with rapid and complex facial gestures, and many others. Specifically, this will (I) provide a brief survey of comparable techniques existing in this field. (II) discuss a set of specialized methodologies or algorithms for effective reconstruction of 3D objects. (III)implement, and testing the developed methodologies. (IV) verify findings with data collected from experiments. (V) conclude with lessons learned and final thoughts.

Keywords: 3D photogrammetry, 3D object reconstruction, facial expression recognition, facial recognition

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Authors: Sreeparna Majee, G. C. Shit

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A study on targeted drug delivery is carried out in an unsteady flow of blood infused with magnetic NPs (nanoparticles) with an aim to understand the flow pattern and nanoparticle aggregation in a diseased arterial segment having stenosis. The magnetic NPs are supervised by the magnetic field which is significant for therapeutic treatment of arterial diseases, tumor and cancer cells and removing blood clots. Coupled thermal energy have also been analyzed by considering dissipation of energy because of the application of the magnetic field and the viscosity of blood. Simulation technique used to solve the mathematical model is vorticity-stream function formulations in the diseased artery. An elevation in SLP (Specific loss power) is noted in the aortic bloodstream when the agglomeration of nanoparticles is higher. This phenomenon has potential application in the treatment of hyperthermia. The study focuses on the lowering of WSS (Wall Shear Stress) with increasing particle concentration at the downstream of the stenosis which depicts the vigorous flow circulation zone. These low shear stress regions prolong the residing time of the nanoparticles carrying drugs which soaks up the LDL (Low Density Lipoprotein) deposition. Moreover, an increase in NP concentration enhances the Nusselt number which marks the increase of heat transfer from the arterial wall to the surrounding tissues to destroy tumor and cancer cells without affecting the healthy cells. The results have a significant influence in the study of medicine, to treat arterial diseases such as atherosclerosis without the need for surgery which can minimize the expenditures on cardiovascular treatments.

Keywords: magnetic nanoparticles, blood flow, atherosclerosis, hyperthermia

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Authors: Verónica Díaz

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A Cartesian graph, as a mathematical object, becomes a tool for configuration of change. Its best comprehension is done through everyday life problem-solving associated with its representation. Despite this, the current educational framework favors general graphs, without consideration of their argumentation. Students are required to find the mathematical function without associating it to the development of graphical language. This research describes the use made by students of configurations made prior to Cartesian graphs with regards to an everyday life problem related to a time and distance variation phenomenon. The theoretical framework describes the function conditions of study and their modeling. This is a qualitative, descriptive study involving six undergraduate case studies that were carried out during the first term in 2016 at University of Los Lagos. The research problem concerned the graphic modeling of a real person’s movement phenomenon, and two levels of analysis were identified. The first level aims to identify local and global graph interpretations; a second level describes the iconicity and referentiality degree of an image. According to the results, students were able to draw no figures before the Cartesian graph, highlighting the need for students to represent the context and the movement of which causes the phenomenon change. From this, they managed Cartesian graphs representing changes in position, therefore, achieved an overall view of the graph. However, the local view only indicates specific events in the problem situation, using graphic and verbal expressions to represent movement. This view does not enable us to identify what happens on the graph when the movement characteristics change based on possible paths in the person’s walking speed.

Keywords: cartesian graphs, higher education, movement modeling, problem solving

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Authors: Stefano M. Spagocci

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The efficiency of photovoltaic panels can be calculated with such software packages as RETScreen that allow design engineers to take financial as well as technical considerations into account. RETScreen is interfaced with meteorological databases, so that efficiency calculations can be realistically carried out. The author has recently contributed to the development of solar modules with accumulation capability and an embedded water purifier, aimed at off-grid users such as users in developing countries. The software packages examined do not allow to take ancillary equipment into account, hence the decision to implement a technical and financial model of the system. The author realized that, rather than re-implementing the quite sophisticated model of RETScreen - a mathematical description of which is anyway not publicly available - it was possible to drastically simplify it, including the meteorological factors which, in RETScreen, are presented in a numerical form. The day-by-day efficiency of a photovoltaic solar panel was parametrized by the product of factors expressing, respectively, daytime duration, solar right ascension motion, solar declination motion, cloudiness, temperature. For the sun-motion-dependent factors, positional astronomy formulae, simplified by the author, were employed. Meteorology-dependent factors were fitted by simple trigonometric functions, employing numerical data supplied by RETScreen. The accuracy of our model was tested by comparing it to the predictions of RETScreen; the accuracy obtained was 11%. In conclusion, our study resulted in a model that can be easily implemented in a spreadsheet - thus being easily manageable by non-specialist personnel - or in more sophisticated software packages. The model was used in a number of design exercises, concerning photovoltaic solar panels and ancillary equipment like the above-mentioned water purifier.

Keywords: clean energy, energy engineering, mathematical modelling, photovoltaic panels, solar energy

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Authors: Frederick Ferguson, Dehua Feng, Yang Gao

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No doubt, current CFD tools have a great many technical limitations, and active research is being done to overcome these limitations. Current areas of limitations include vortex-dominated flows, separated flows, and turbulent flows. In general, turbulent flows are unsteady solutions to the fluid dynamic equations, and instances of these solutions can be computed directly from the equations. One of the approaches commonly implemented is known as the ‘direct numerical simulation’, DNS. This approach requires a spatial grid that is fine enough to capture the smallest length scale of the turbulent fluid motion. This approach is called the ‘Kolmogorov scale’ model. It is of interest to note that the Kolmogorov scale model must be captured throughout the domain of interest and at a correspondingly small-time step. In typical problems of industrial interest, the ratio of the length scale of the domain to the Kolmogorov length scale is so great that the required grid set becomes prohibitively large. As a result, the available computational resources are usually inadequate for DNS related tasks. At this time in its development, DNS is not applicable to industrial problems. In this research, an attempt is made to develop a numerical technique that is capable of delivering DNS quality solutions at the scale required by the industry. To date, this technique has delivered preliminary results for both steady and unsteady, viscous and inviscid, compressible and incompressible, and for both high and low Reynolds number flow fields that are very accurate. Herein, it is proposed that the Integro-Differential Scheme (IDS) be applied to a set of vortex-shockwave interaction problems with the goal of investigating the nonstationary physics within the resulting interaction regions. In the proposed paper, the IDS formulation and its numerical error capability will be described. Further, the IDS will be used to solve the inviscid and viscous Burgers equation, with the goal of analyzing their solutions over a considerable length of time, thus demonstrating the unsteady capabilities of the IDS. Finally, the IDS will be used to solve a set of fluid dynamic problems related to flow that involves highly vortex interactions. Plans are to solve the following problems: the travelling wave and vortex problems over considerable lengths of time, the normal shockwave–vortex interaction problem for low supersonic conditions and the reflected oblique shock–vortex interaction problem. The IDS solutions obtained in each of these solutions will be explored further in efforts to determine the distributed density gradients and vorticity, as well as the Q-criterion. Parametric studies will be conducted to determine the effects of the Mach number on the intensity of vortex-shockwave interactions.

Keywords: vortex dominated flows, shockwave interactions, high Reynolds number, integro-differential scheme

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Authors: Marcel Heimar Ribeiro Utiyama, Fernanda Caveiro Correia, Dario Henrique Alliprandini

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The importance of the correct allocation of improvement programs is of growing interest in recent years. Due to their limited resources, companies must ensure that their financial resources are directed to the correct workstations in order to be the most effective and survive facing the strong competition. However, to our best knowledge, the literature about allocation of improvement programs does not analyze in depth this problem when the flow shop process has two capacity constrained resources. This is a research gap which is deeply studied in this work. The purpose of this work is to identify the best strategy to allocate improvement programs in a flow shop with two capacity constrained resources. Data were collected from a flow shop process with seven workstations in an industrial control and automation company, which process 13.690 units on average per month. The data were used to conduct a simulation with the System Dynamics-Factory Physics model. The main variables considered, due to their importance on lead time reduction, were the mean time between failures and the mean time to repair. The lead time reduction was the output measure of the simulations. Ten different strategies were created: (i) focused time to repair improvement, (ii) focused time between failures improvement, (iii) distributed time to repair improvement, (iv) distributed time between failures improvement, (v) focused time to repair and time between failures improvement, (vi) distributed time to repair and between failures improvement, (vii) hybrid time to repair improvement, (viii) hybrid time between failures improvements, (ix) time to repair improvement strategy towards the two capacity constrained resources, (x) time between failures improvement strategy towards the two capacity constrained resources. The ten strategies tested are variations of the three main strategies for improvement programs named focused, distributed and hybrid. Several comparisons among the effect of the ten strategies in lead time reduction were performed. The results indicated that for the flow shop analyzed, the focused strategies delivered the best results. When it is not possible to perform a large investment on the capacity constrained resources, companies should use hybrid approaches. An important contribution to the academy is the hybrid approach, which proposes a new way to direct the efforts of improvements. In addition, the study in a flow shop with two strong capacity constrained resources (more than 95% of utilization) is an important contribution to the literature. Another important contribution is the problem of allocation with two CCRs and the possibility of having floating capacity constrained resources. The results provided the best improvement strategies considering the different strategies of allocation of improvement programs and different positions of the capacity constrained resources. Finally, it is possible to state that both strategies, hybrid time to repair improvement and hybrid time between failures improvement, delivered best results compared to the respective distributed strategies. The main limitations of this study are mainly regarding the flow shop analyzed. Future work can further investigate different flow shop configurations like a varying number of workstations, different number of products or even different positions of the two capacity constrained resources.

Keywords: allocation of improvement programs, capacity constrained resource, hybrid strategy, lead time, mean time to repair, mean time between failures

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Authors: Zhang Tianping, Jia Yanhui, Li Juan, Yang Le, Yang Hao, Yang Wei, Sun Xiaojing, Shi Kai, Li Xingda, Sun Yunkui

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Lanzhou Institute of Physics (LIP) is the major supplier of electric propulsion subsystems for Chinese satellite platforms. The development statuses of these electric propulsion subsystems were summarized including the LIPS-200 ion electric propulsion subsystem (IEPS) for DFH-3B platform, the LIPS-300 IEPS for DFH-5 and DFH-4SP platform, the LIPS-200+ IEPS for DFH-4E platform and near-earth asteroid exploration spacecraft, the LIPS-100 IEPS for small satellite platform, the LHT-100 hall electric propulsion subsystem (HEPS) for flight test on XY-2 satellite, the LHT-140 HEPS for large LEO spacecraft, the LIPS-400 IEPS for deep space exploration mission and other EPS for other Chinese spacecraft.

Keywords: ion electric propulsion, hall electric propulsion, satellite platform, LIP

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Authors: Wedad Albalawi

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The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

Procedia PDF Downloads 87