Search results for: Mathematical model

Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

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Concurrent planning of project scheduling and material ordering can provide more flexibility to the project scheduling problem, as the project execution costs can be enhanced. Hence, the issue has been taken into account in this paper. To do so, a mixed-integer mathematical model is developed which considers the aforementioned flexibility, in addition to the materials quantity discount and space availability restrictions. Moreover, the activities duration has been treated as decision variables. Finally, the efficiency of the proposed model is tested by different instances. Additionally, the influence of the aforementioned parameters is investigated on the model performance.

Keywords: material ordering, project scheduling, quantity discount, space availability

Procedia PDF Downloads 367

Authors: Bin Wang, Hengyu Ji, Zhifeng Ye

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Fuel Metering Unit (FMU) in fuel system of an aeroengine sometimes has direct influence on the engine performance, which is neglected for the sake of easy access to mathematical model of the engine in most cases. In order to verify the influence of FMU on an engine model, this paper presents a co-simulation of a stepping motor driven FMU (digital FMU) in a turboshaft aeroengine, using AMESim and MATLAB to obtain the steady and dynamic characteristics of the FMU. For this method, mechanical and hydraulic section of the unit is modeled through AMESim, while the stepping motor is mathematically modeled through MATLAB/Simulink. Combining these two sub-models yields an AMESim/MATLAB co-model of the FMU. A simplified component level model for the turboshaft engine is established and connected with the FMU model. Simulation results on the full model show that the engine model considering FMU characteristics describes the engine more precisely especially in its transition state. An FMU dynamics will cut down the rotation speed of the high pressure shaft and the inlet pressure of the combustor during the step response. The work in this paper reveals the impact of FMU on engine operation characteristics and provides a reference to an engine model for ground tests.

Keywords: fuel metering unit, stepping motor, AMESim/Matlab, full digital simulation

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Authors: F. R. M. Nascimento, E. E. S. Lora, J. C. E. Palácio

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A mathematical model to investigate the performance of a two stage fixed bed downdraft gasifier operating with air, steam and oxygen mixtures as the gasifying fluid has been developed. The various conditions of mixtures for a double stage fluid entry, have been performed. The model has been validated through a series of experimental tests performed by NEST – The Excellence Group in Thermal and Distributed Generation of the Federal University of Itajubá. Influence of mixtures are analyzed through the Steam to Biomass (SB), Equivalence Ratio (ER) and the Oxygen Concentration (OP) parameters in order to predict the best operating conditions to obtain adequate output gas quality, once is a key parameter for subsequent gas processing in the synthesis of biofuels, heat and electricity generation. Results show that there is an optimal combination in the steam and oxygen content of the gasifying fluid which allows the user find the best conditions to design and operate the equipment according to the desired application.

Keywords: air, equilibrium, downdraft, fixed bed gasification, mathematical modeling, mixtures, oxygen steam

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Authors: Shahul Hamid Khan, S. Santhosh, Abhinav Kumar Sharma

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Environmental performance along with social performance is becoming vital factors for industries to achieve global standards. With a good environmental policy global industries are differentiating them from their competitors. This paper concentrates on multi stage, multi product and multi period manufacturing network. Bi-objective mathematical models for total cost and total emission for the entire forward supply chain are considered. Here five different problems are considered by varying the number of suppliers, manufacturers, and environmental levels, for illustrating the taken mathematical model. GA, and Random search are used for finding the optimal solution. The input parameters of the optimal solution are used to find the tradeoff between the initial investment by the industry and the long term benefit of the environment.

Keywords: closed loop supply chain, genetic algorithm, random search, green supply chain

Procedia PDF Downloads 549

Authors: Nitish Kumar Vaja, Oumar Barry, Brian DeJong

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Aeolian vibrations are the major cause for the failure of conductor cables. Using a Stockbridge damper reduces these vibrations and increases the life span of the conductor cable. Designing an efficient Stockbridge damper that suits the conductor cable requires a robust mathematical model with minimum assumptions. However it is not easy to analytically model the complex geometry of the messenger. Therefore an equivalent stiffness must be determined so that it can be used in the analytical model. This paper examines the bending stiffness of the cable and discusses the effect of this stiffness on the natural frequencies. The obtained equivalent stiffness compensates for the assumption of modeling the messenger as a rod. The results from the free vibration analysis of the analytical model with the equivalent stiffness is validated using the full scale finite element model of the Stockbridge damper.

Keywords: equivalent stiffness, finite element model, free vibration response, Stockbridge damper

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Authors: Aleš Kratochvíl, Svatomír Slavík

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The paper presents an aircraft flutter suppression by active damping of supplementary control surface at trailing edge. The mathematical model of thin oscillation airfoil with control surface driven by pilot is developed. The supplementary control surface driven by control law is added. Active damping of flutter by several control law is present. The structural model of tailplane with an aerodynamic strip theory based on the airfoil model is developed by a finite element method. The optimization process of stiffens parameters is carried out to match the structural model with results from a ground vibration test of a small sport airplane. The implementation of supplementary control surface driven by control law is present. The active damping of tailplane model is shown.

Keywords: active damping, finite element method, flutter, tailplane model

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Authors: Tariq Aljuneidi, Akif Asil Bulgak

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Remanufacturing may be defined as the process of bringing used products to “like-new” functional state with warranty to match, and it is one of the most popular product end-of-life scenarios. An efficient remanufacturing network lead to an efficient design of sustainable manufacturing enterprise. In remanufacturing network, products are collected from the customer zone, disassembled and remanufactured at a suitable remanufacturing facility. In this respect, another issue to consider is how the returned product to be remanufactured, in other words, what is the best layout for such facility. In order to achieve a sustainable manufacturing system, Cellular Manufacturing System (CMS) designs are highly recommended, CMSs combine high throughput rates of line layouts with the flexibility offered by functional layouts (job shop). Introducing the CMS while designing a remanufacturing network will benefit the utilization of such a network. This paper presents and analyzes a comprehensive mathematical model for the design of Dynamic Cellular Remanufacturing Systems (DCRSs). In this paper, the proposed model is the first one to date that consider CMS and remanufacturing system simultaneously. The proposed DCRS model considers several manufacturing attributes such as multi-period production planning, dynamic system reconfiguration, duplicate machines, machine capacity, available time for workers, worker assignments, and machine procurement, where the demand is totally satisfied from a returned product. A numerical example is presented to illustrate the proposed model.

Keywords: cellular manufacturing system, remanufacturing, mathematical programming, sustainability

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Authors: Anuruddha Jayasuriya, Thanakorn Pheeraphan

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In this paper, a review of different mathematical models which can be used as prediction tools to assess the time to crack reinforced concrete (RC) due to corrosion is investigated. This investigation leads to an experimental study to validate a selected prediction model. Most of these mathematical models depend upon the mechanical behaviors, chemical behaviors, electrochemical behaviors or geometric aspects of the RC members during a corrosion process. The experimental program is designed to verify the accuracy of a well-selected mathematical model from a rigorous literature study. Fundamentally, the experimental program exemplifies both one-dimensional chloride diffusion using RC squared slab elements of 500 mm by 500 mm and two-dimensional chloride diffusion using RC squared column elements of 225 mm by 225 mm by 500 mm. Each set consists of three water-to-cement ratios (w/c); 0.4, 0.5, 0.6 and two cover depths; 25 mm and 50 mm. 12 mm bars are used for column elements and 16 mm bars are used for slab elements. All the samples are subjected to accelerated chloride corrosion in a chloride bath of 5% (w/w) sodium chloride (NaCl) solution. Based on a pre-screening of different models, it is clear that the well-selected mathematical model had included mechanical properties, chemical and electrochemical properties, nature of corrosion whether it is accelerated or natural, and the amount of porous area that rust products can accommodate before exerting expansive pressure on the surrounding concrete. The experimental results have shown that the selected model for both one-dimensional and two-dimensional chloride diffusion had ±20% and ±10% respective accuracies compared to the experimental output. The half-cell potential readings are also used to see the corrosion probability, and experimental results have shown that the mass loss is proportional to the negative half-cell potential readings that are obtained. Additionally, a statistical analysis is carried out in order to determine the most influential factor that affects the time to corrode the reinforcement in the concrete due to chloride diffusion. The factors considered for this analysis are w/c, bar diameter, and cover depth. The analysis is accomplished by using Minitab statistical software, and it showed that cover depth is the significant effect on the time to crack the concrete from chloride induced corrosion than other factors considered. Thus, the time predictions can be illustrated through the selected mathematical model as it covers a wide range of factors affecting the corrosion process, and it can be used to predetermine the durability concern of RC structures that are vulnerable to chloride exposure. And eventually, it is further concluded that cover thickness plays a vital role in durability in terms of chloride diffusion.

Keywords: accelerated corrosion, chloride diffusion, corrosion cracks, passivation layer, reinforcement corrosion

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Authors: Manoja Rajalakshmi Aravindakshana, Devleena Ghosha, Chittaranjan Mandala, K. V. Venkateshb, Jit Sarkarc, Partha Chakrabartic, Sujay K. Maity

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Oral Glucose Tolerance Test (OGTT) is the primary test used to diagnose type 2 diabetes mellitus (T2DM) in a clinical setting. Analysis of OGTT data using the Oral Minimal Model (OMM) along with the rate of appearance of ingested glucose (Ra) is performed to study differences in model parameters for control and T2DM groups. The differentiation of parameters of the model gives insight into the behaviour and physiology of T2DM. The model is also studied to find parameter differences among obese and non-obese T2DM subjects and the sensitive parameters were co-related to the known physiological findings. Sensitivity analysis is performed to understand changes in parameter values with model output and to support the findings, appropriate statistical tests are done. This seems to be the first preliminary application of the OMM with obesity as a distinguishing factor in understanding T2DM from estimated parameters of insulin-glucose model and relating the statistical differences in parameters to diabetes pathophysiology.

Keywords: oral minimal model, OGTT, obese and non-obese T2DM, mathematical modeling, parameter estimation

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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: Anurag Savarnya

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The reliability of the various parts of electric mining shovel has been assessed through the application of Weibull Model. The study was initiated to find reliability of components of electric mining shovel. The paper aims to optimize the reliability of components and increase the life cycle of component. A multilevel decomposition of the electric mining shovel was done and maintenance records were used to evaluate the failure data and appropriate system characterization was done to model the system in terms of reasonable number of components. The approach used develops a mathematical model to assess the reliability of the electric mining shovel components. The model can be used to predict reliability of components of the hydraulic mining shovel and system performance. Reliability is an inherent attribute to a system. When the life-cycle costs of a system are being analyzed, reliability plays an important role as a major driver of these costs and has considerable influence on system performance. It is an iterative process that begins with specification of reliability goals consistent with cost and performance objectives. The data were collected from an Indian open cast coal mine and the reliability of various components of the electric mining shovel has been assessed by following a Weibull Model.

Keywords: reliability, Weibull model, electric mining shovel

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Authors: Mitat Uysal, Aynur Uysal

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Artificial Intelligence (AI) is fundamentally driven by mathematics, with many of its core algorithms rooted in mathematical principles such as linear algebra, probability theory, calculus, and optimization techniques. This paper explores the deep connection between AI and mathematics, highlighting the role of mathematical concepts in key AI techniques like machine learning, neural networks, and optimization. To demonstrate this connection, a case study involving the implementation of a neural network using Python is presented. This practical example illustrates the essential role that mathematics plays in training a model and solving real-world problems.

Keywords: AI, mathematics, machine learning, optimization techniques, image processing

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Authors: Temur Chilachava

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In work the new nonlinear mathematical model describing assimilation of the people (population) with some less widespread language by two states with two various widespread languages, taking into account demographic factor is offered. In model three subjects are considered: the population and government institutions with the widespread first language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the population and government institutions with the widespread second language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the third population (probably small state formation, an autonomy), exposed to bilateral assimilation from two rather powerful states. Earlier by us it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimilated population) is connected with initial quantities, technological and economic capabilities of the assimilating states. In considered model taking into account demographic factor natural decrease in the population of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coefficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model "predator - the victim", thus, naturally a role of the victim plays the population which has undergone assimilation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation of the population of assimilators in an initial time point) to the population of the first assimilator. In the second case the problem is actually reduced to nonlinear system of two differential equations describing type model "a predator – the victim", with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical models which in some approach can model real situations, with the real assimilating countries and the state formations (an autonomy or formation with the unrecognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in population and hope for natural decrease in the population of the assimilating states.

Keywords: nonlinear mathematical model, bilateral assimilation, demographic factor, first integrals, result of assimilation, intervals of change of number of the population

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Authors: Jagdish Prasad Maurya, Sanjay Kumar Pandey

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Inadequate understanding of the complex nature of flow features in tornado vortex is a major problem in modelling tornadoes. Tornadoes are violent atmospheric phenomenon that appear all over the world. Modelling tornadoes aim to reduce the loss of the human lives and material damage caused by the tornadoes. Dynamics of tornado is investigated by a numerical technique, the improved version of the projection method. In this paper, authors solve the problem for axisymmetric tornado vortex by the said method that uses a finite difference approach for getting an accurate and stable solution. The conclusions drawn are that large radial inflow velocity occurs near the ground that leads to increase the tangential velocity. The increased velocity phenomenon occurs close to the boundary and absolute maximum wind is obtained near the vortex core. The results validate previous numerical and theoretical models.

Keywords: computational fluid dynamics, mathematical model, Navier-Stokes equations, tornado

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Authors: Farhad Salek, Shahaboddin Resalati

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The production of electric vehicles (EVs) featuring lithium-ion battery technology has substantially escalated over the past decade, demonstrating a steady and persistent upward trajectory. The imminent retirement of electric vehicle (EV) batteries after approximately eight years underscores the critical need for their redirection towards recycling, a task complicated by the current inadequacy of recycling infrastructures globally. A potential solution for such concerns involves extending the operational lifespan of electric vehicle (EV) batteries through their utilization in stationary energy storage systems during secondary applications. Such adoptions, however, require addressing the safety concerns associated with batteries’ knee points and thermal runaways. This paper develops an accurate mathematical model representative of the second-life battery packs from a cell-to-pack scale using an equivalent circuit model (ECM) methodology. Neural network algorithms are employed to forecast the degradation parameters based on the EV batteries' aging history to develop a degradation model. The degradation model is integrated with the ECM to reflect the impacts of the cycle aging mechanism on battery parameters during operation. The developed model is tested under real-life load profiles to evaluate the life span of the batteries in various operating conditions. The methodology and the algorithms introduced in this paper can be considered the basis for Battery Management System (BMS) design and techno-economic analysis of such technologies.

Keywords: second life battery, electric vehicles, degradation, neural network

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Authors: Asma Hanif, A. I. K. Butt, Shabir Ahmad, Rahim Ud Din, Mustafa Inc

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This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo’s sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.

Keywords: Caputo fractional derivative, existence and uniqueness, gronwall inequality, Lyapunov theory

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Authors: Amal G. Kurian

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The use of mathematical modeling has seen a considerable boost in recent times with the development of many advanced algorithms and mathematical modeling capabilities. The advantages this method has over other methods are that they are much closer to standard physics theories and thus represent a better theoretical model. They take lesser solving time and have the ability to change various parameters for optimization, which is a big advantage, especially in automotive industry. This thesis work focuses on a thorough investigation of the effects of vehicle speed and road roughness on a heavy commercial vehicle ride and structural dynamic responses. Since commercial vehicles are kept in operation continuously for longer periods of time, it is important to study effects of various physical conditions on the vehicle and its user. For this purpose, various experimental as well as simulation methodologies, are adopted ranging from experimental transfer path analysis to various road scenario simulations. To effectively investigate and eliminate several causes of unwanted responses, an efficient and robust technique is needed. Carrying forward this motivation, the present work focuses on the development of a mathematical model of a 4-axle configuration heavy commercial vehicle (HCV) capable of calculating responses of the vehicle on different road PSD inputs and vehicle speeds. Outputs from the model will include response transfer functions and PSDs and wheel forces experienced. A MATLAB code will be developed to implement the objectives in a robust and flexible manner which can be exploited further in a study of responses due to various suspension parameters, loading conditions as well as vehicle dimensions. The thesis work resulted in quantifying the effect of various physical conditions on ride comfort of the vehicle. An increase in discomfort is seen with velocity increase; also the effect of road profiles has a considerable effect on comfort of the driver. Details of dominant modes at each frequency are analysed and mentioned in work. The reduction in ride height or deflection of tire and suspension with loading along with load on each axle is analysed and it is seen that the front axle supports a greater portion of vehicle weight while more of payload weight comes on fourth and third axles. The deflection of the vehicle is seen to be well inside acceptable limits.

Keywords: mathematical modeling, HCV, suspension, ride analysis

Procedia PDF Downloads 258

Authors: Pakhapoom Sarapat, James M. Hill, Duangkamon Baowan

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Carbon nanotori provide several properties such as high tensile strength and heat resistance. They are promised to be ideal structures for encapsulation, and their encapsulation ability can be determined by the interaction energy between the carbon nanotori and the encapsulated nanostructures. Such interaction energy is evaluated using Lennard-Jones potential and continuum approximation. Here, four problems relating to toroidal molecules are determined in order to find the most stable configuration. Firstly, the interaction energy between a carbon nanotorus and an atom is examined. The second problem relates to the energy of a fullerene encapsulated inside a carbon nanotorus. Next, the interaction energy between two symmetrically situated and parallel nanotori is considered. Finally, the classical mechanics is applied to model the interaction energy between the toroidal structure of cyclodextrin and the spherical DNA molecules. These mathematical models might be exploited to study a number of promising devices for future developments in bio and nanotechnology.

Keywords: carbon nanotori, continuum approximation, interaction energy, Lennard-Jones potential, nanotechnology

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Authors: Lely A. Luengas, Pedro R. Vizcaya, Giovanni Sánchez

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In this paper, a methodology is presented to obtain the Static Alignment Model for any transtibial amputee person. The proposed methodology starts from experimental data collected on the Hospital Militar Central, Bogotá, Colombia. The effects of transtibial prosthesis malalignment on amputees were measured in terms of joint angles, center of pressure (COP) and weight distribution. Some statistical tools are used to obtain the model parameters. Mathematical predictive models of prosthetic alignment were created. The proposed models are validated in amputees and finding promising results for the prosthesis Static Alignment. Static alignment process is unique to each subject; nevertheless the proposed methodology can be used in each transtibial amputee.

Keywords: information theory, prediction model, prosthetic alignment, transtibial prosthesis

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Authors: Paula Verdugo-Hernandez, Patricio Cumsille

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We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of mathematical working spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: convergence, graphical representations, mathematical working spaces, paradigms of real analysis, real number sequences

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Authors: Khin Fai Chen, Jee-Hou Ho, Eng Hwa Yap

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An acoustic micro-energy harvester (AMEH) is developed to convert wasted acoustical energy into useful electrical energy. AMEH is mathematically modeled using lumped element modelling (LEM) and Euler-Bernoulli beam (EBB) modelling. An experiment is designed to validate the mathematical model and assess the feasibility of AMEH. Comparison of theoretical and experimental data on critical parameter value such as Mm, Cms, dm and Ceb showed the variances are within 1% to 6%, which is reasonably acceptable. Hence, AMEH mathematical model is validated. Then, AMEH undergoes bandwidth tuning for performance optimization for further experimental work. The AMEH successfully produces 0.9 V⁄(m⁄s^2) and 1.79 μW⁄(m^2⁄s^4) at 60Hz and 400kΩ resistive load which only show variances about 7% compared to theoretical data. By integrating a capacitive load of 200µF, the discharge cycle time of AMEH is 1.8s and the usable energy bandwidth is available as low as 0.25g. At 1g and 60Hz resonance frequency, the averaged power output is about 2.2mW which fulfilled a range of wireless sensors and communication peripherals power requirements. Finally, the design for AMEH is assessed, validated and deemed as a feasible design.

Keywords: piezoelectric, acoustic, energy harvester

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Authors: Benjamin Aina Peter, Amos Wale Ogunsola

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In this paper, a mathematical model of malaria transmission was presented with the effect of seasonal shift, due to global fluctuation in temperature, on the increase of conveyor of the infectious disease, which probably alters the region transmission potential of malaria. A deterministic compartmental model was proposed and analyzed qualitatively. Both qualitative and quantitative approaches of the model were considered. The next-generation matrix is employed to determine the basic reproduction number of the model. Equilibrium points of the model were determined and analyzed. The numerical simulation is carried out using Excel Micro Software to validate and support the qualitative results. From the analysis of the result, the optimal temperature for the transmission of malaria is between and . The result also shows that an increase in temperature due to seasonal shift gives rise to the development of parasites which consequently leads to an increase in the widespread of malaria transmission in Kampala. It is also seen from the results that an increase in temperature leads to an increase in the number of infectious human hosts and mosquitoes.

Keywords: seasonal variation, indoor residual spray, efficacy of spray, temperature-dependent model

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Authors: Asadullah I. Qazi, Mansoor Ahsan, Zahir Ashraf, Uzair Ahmad

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System identification of an Unmanned Aerial Vehicle (UAV), to acquire its mathematical model, is a significant step in the process of aircraft flight automation. The need for reliable mathematical model is an established requirement for autopilot design, flight simulator development, aircraft performance appraisal, analysis of aircraft modifications, preflight testing of prototype aircraft and investigation of fatigue life and stress distribution etc.  This research is aimed at system identification of a fixed wing UAV by means of specifically designed flight experiment. The purposely designed flight maneuvers were performed on the UAV and aircraft states were recorded during these flights. Acquired data were preprocessed for noise filtering and bias removal followed by parameter estimation of longitudinal dynamics transfer functions using MATLAB system identification toolbox. Black box identification based transfer function models, in response to elevator and throttle inputs, were estimated using least square error   technique. The identification results show a high confidence level and goodness of fit between the estimated model and actual aircraft response.

Keywords: fixed wing UAV, system identification, black box modeling, longitudinal dynamics, least square error

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Authors: Trudon Kabangu Mpinga, Ruth Mutala, Shaloom Mbambu, Yvette Kalubi Kashama, Kabeya Mukeba Yakasham

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A mathematical model is developed to describe the contact dynamics between the landing gear wheels of an aircraft and a wet pavement during landing. The model is based on nonlinear partial differential equations, using the Yakam Matrix to account for the interaction between solid, liquid, and solid phases. This framework incorporates the influence of environmental factors, particularly water or rain on the runway, on braking performance and aircraft stability. Given the absence of exact analytical solutions, our approach enhances the understanding of key physical phenomena, including Coulomb friction forces, hydrodynamic effects, and the deformation of the pavement under the aircraft's load. Additionally, the dynamics of aquaplaning are simulated numerically to estimate the braking performance limits on wet surfaces, thereby contributing to strategies aimed at minimizing risk during landing on wet runways.

Keywords: aircraft, modeling, simulation, yakam matrix, contact, wet runway

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Authors: N. Bazyar Shourabi, K. Nyarko, C. Scott, M. Jeihnai

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Ground drones have the potential to reduce the cost and time of making last-mile deliveries. They also have the potential to make a huge impact on human life. Despite this potential, little work has gone into developing a suitable feasibility model for ground drone delivery in dense urban areas. Today, most of the experimental ground delivery drones utilize sidewalks only, with just a few of them starting to use bike lanes, which a significant portion of some urban areas have. This study works on the feasibility of using bike lanes in conjunction with sidewalks for ground drone applications in last-mile delivery for dense urban areas. This work begins with surveying bike lanes and sidewalks within the city of Boston using Geographic Information System (GIS) software to determine the percentage of coverage currently available within the city. Then six scenarios are examined. Based on this research, a mathematical model is developed. The daily cost of delivering packages using each scenario is calculated by the mathematical model. Comparing the drone delivery scenarios with the traditional method of package delivery using trucks will provide essential information concerning the feasibility of implementing routing protocols that combine the use of sidewalks and bike lanes. The preliminary results of the model show that ground drones that can travel via sidewalks or bike lanes have the potential to significantly reduce delivery cost.

Keywords: ground drone, intelligent transportation system, last-mile delivery, sidewalk robot

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Authors: Alexander I. Dovgyallo, Evgeniy A. Zinoviev, Svetlana O. Nekrasova

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The most of works applied for the pulse tube converters contain the workflow description implemented through the use of mathematical models on stationary modes. However, the study of the thermoacoustic systems unsteady behavior in the start, stop, and acoustic load changes modes is in the particular interest. The aim of the present study was to develop a mathematical thermal excitation model of acoustic oscillations in pulse tube engine (PTE) as a small-scale scheme of pulse tube engine operating at atmospheric air. Unlike some previous works this standing wave configuration is a fully closed system. The improvements over previous mathematical models are the following: the model allows specifying any values of porosity for regenerator, takes into account the piston weight and the friction in the cylinder and piston unit, and determines the operating frequency. The numerical method is based on the relation equations between the pressure and volume velocity variables at the ends of each element of PTE which is recorded through the appropriate transformation matrix. A solution demonstrates that the PTE operation frequency is the complex value, and it depends on the piston mass and the dynamic friction due to its movement in the cylinder. On the basis of the determined frequency thermoacoustically induced heat transport and generation of acoustic power equations were solved for channel with temperature gradient on its ends. The results of numerical simulation demonstrate the features of the initialization process of oscillation and show that that generated acoustic power more than power on the steady mode in a factor of 3…4. But doesn`t mean the possibility of its further continuous utilizing due to its existence only in transient mode which lasts only for a 30-40 sec. The experiments were carried out on small-scale PTE. The results shows that the value of acoustic power is in the range of 0.7..1.05 W for the defined frequency range f = 13..18 Hz and pressure amplitudes 11..12 kPa. These experimental data are satisfactorily correlated with the numerical modeling results. The mathematical model can be straightforwardly applied for the thermoacoustic devices with variable temperatures of thermal reservoirs and variable transduction loads which are expected to occur in practical implementations of portable thermoacoustic engines.

Keywords: nonlinear processes, pulse tube engine, thermal excitation, standing wave

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Authors: Zahid Ullah, Atlas Khan

Abstract:

The rapid advancements in data collection, storage, and processing capabilities have led to an explosion of data in various domains. In this era of big data, mathematical sciences play a crucial role in uncovering valuable insights and driving informed decision-making through data analytics. The purpose of this abstract is to present the latest advances in mathematical sciences and their application in harnessing the power of data analytics. This abstract highlights the interdisciplinary nature of data analytics, showcasing how mathematics intersects with statistics, computer science, and other related fields to develop cutting-edge methodologies. It explores key mathematical techniques such as optimization, mathematical modeling, network analysis, and computational algorithms that underpin effective data analysis and interpretation. The abstract emphasizes the role of mathematical sciences in addressing real-world challenges across different sectors, including finance, healthcare, engineering, social sciences, and beyond. It showcases how mathematical models and statistical methods extract meaningful insights from complex datasets, facilitating evidence-based decision-making and driving innovation. Furthermore, the abstract emphasizes the importance of collaboration and knowledge exchange among researchers, practitioners, and industry professionals. It recognizes the value of interdisciplinary collaborations and the need to bridge the gap between academia and industry to ensure the practical application of mathematical advancements in data analytics. The abstract highlights the significance of ongoing research in mathematical sciences and its impact on data analytics. It emphasizes the need for continued exploration and innovation in mathematical methodologies to tackle emerging challenges in the era of big data and digital transformation. In summary, this abstract sheds light on the advances in mathematical sciences and their pivotal role in unveiling the power of data analytics. It calls for interdisciplinary collaboration, knowledge exchange, and ongoing research to further unlock the potential of mathematical methodologies in addressing complex problems and driving data-driven decision-making in various domains.

Keywords: mathematical sciences, data analytics, advances, unveiling

Procedia PDF Downloads 93

Authors: Mohammed Abubakar Ndanusa, A. A. Hassan, R. W. Gimba, A. M. Alfa, M. T. Abari

Abstract:

This study investigated the Impact of Mathematical Modeling on Mathematics Achievement, Attitude and Interest of Pre-Service Teachers in Niger States, Nigeria. It was an attempt to ease students’ difficulties in comprehending mathematics. The study used randomized pretest, posttest control group design. Two Colleges of Education were purposively selected from Niger State with a sample size of eighty-four 84 students. Three research instruments used are Mathematical Modeling Achievement Test (MMAT), Attitudes Towards Mathematical Modeling Questionnaire (ATMMQ) and Mathematical Modeling Students Interest Questionnaire (MMSIQ). Pearson Product Moment Correlation (PPMC) formula was used for MMAT and Alpha Cronbach was used for ATMMQ and MMSIQ to determine their reliability coefficient and the values the following values were obtained respectively 0.76, 0.75 and 0.73. Independent t-test statistics was used to test hypothesis One while Mann Whitney U-test was used to test hypothesis Two and Three. Findings revealed that students taught Mathematics using Mathematical Modeling performed better than their counterparts taught using lecture method. However, there was a significant difference in the attitude and interest of pre-service mathematics teachers after being exposed to mathematical modeling. The strategy, therefore, was recommended to be used by Mathematics teachers with a view to improving students’ attitude and interest towards Mathematics. Also, modeling should be taught at NCE level in order to prepare pre-service teachers towards real task in the field of Mathematics.

Keywords: achievement, attitude, interest, mathematical modeling, pre-service teachers

Procedia PDF Downloads 304

Authors: Seyedmirsajad Mokhtarimousavi, Danial Talebi, Hamidreza Asgari

Abstract:

Assigning aircrafts’ activities to appropriate gates is one the most challenging issues in airport authorities’ multiple criteria decision making. The potential financial loss due to imbalances of demand and supply in congested airports, higher occupation rates of gates, and the existing restrictions to expand facilities provide further evidence for the need for an optimal supply allocation. Passengers walking distance, towing movements, extra fuel consumption (as a result of awaiting longer to taxi when taxi conflicts happen at the apron area), etc. are the major traditional components involved in GAP models. In particular, the total cost associated with gate assignment problem highly depends on the airport terminal layout. The study herein presents a well-elaborated literature review on the topic focusing on major concerns, applicable variables and objectives, as well as proposing a three-objective mathematical model for the gate assignment problem. The model has been tested under different concourse layouts in order to check its performance in different scenarios. Results revealed that terminal layout pattern is a significant parameter in airport and that the proposed model is capable of dealing with key constraints and objectives, which supports its practical usability for future decision making tools. Potential solution techniques were also suggested in this study for future works.

Keywords: airport management, terminal layout, gate assignment problem, mathematical modeling

Procedia PDF Downloads 229

Authors: S. Belhour, A. K. Ferouani, C. Azizi

Abstract:

In recent years, a considerable effort (experience, numerical simulation, and theoretical prediction models) has characterised by high efficiency and low cost. Then an improved physics analytical model for simulating is proposed. The performance of GaAs MESFETs has been developed for use in device design for high frequency. This model is based on mathematical analysis, and a new approach for the standard model is proposed, this approach allowed to conceive applicable model for MESFET’s operating in the turn-one or pinch-off region and valid for the short-channel and the long channel MESFET’s in which the two dimensional potential distribution contributed by the depletion layer under the gate is obtained by conventional approximation. More ever, comparisons between the analytical models with different values of mobility are proposed, and a good agreement is obtained.

Keywords: analytical, gallium arsenide, MESFET, mobility, models

Procedia PDF Downloads 74