Search results for: mathematical transmission modeling

Authors: Ayse Ozturk

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The study extends the prior research on modeling competencies by positioning students’ cognitive and language resources as the fundamentals for pursuing their own inquiry and expression lines through mathematical modeling. This strategy aims to answer the question that guides this study, “How do students’ group approaches to modeling tasks affect their modeling competencies over a unit of instruction?” Six bilingual tenth-grade students worked on open-ended modeling problems along with the content focused on quantities over six weeks. Each group was found to have a unique cognitive approach for solving these problems. Three different problem-solving strategies affected how the groups’ modeling competencies changed. The results provide evidence that the discussion around groups’ solutions, coupled with their reflections, advances group interpreting and validating competencies in the mathematical modeling process

Keywords: cognition, collective learning, mathematical modeling competencies, problem-solving

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Authors: Endrik Mifta Shaiful, Firman Riyudha

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Acquired Immunodeficiency Syndrome (AIDS) is one of the world's deadliest diseases caused by the Human Immunodeficiency Virus (HIV) that infects white blood cells and cause a decline in the immune system. AIDS quickly became a world epidemic disease that affects almost all countries. Therefore, mathematical modeling approach to the spread of HIV and AIDS is needed to anticipate the spread of HIV and AIDS which are widespread. The purpose of this study is to determine the parameter estimation on mathematical models of HIV transmission and AIDS using cumulative data of people with HIV and AIDS each year in Indonesia. In this model, there are parameters of r ∈ [0,1) which is the effectiveness of the treatment in patients with HIV. If the value of r is close to 1, the number of people with HIV and AIDS will decline toward zero. The estimation results indicate when the value of r is close to unity, there will be a significant decline in HIV patients, whereas in AIDS patients constantly decreases towards zero.

Keywords: HIV, AIDS, parameter estimation, mathematical models

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Authors: A. Torokhti

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A new method of mathematical modeling of the distributed nonlinear system is developed. The system is represented by a combination of the set of spatially distributed sensors and the fusion center. Its mathematical model is obtained from the iterative procedure that converges to the model which is optimal in the sense of minimizing an associated cost function.

Keywords: mathematical modeling, non-linear system, spatially distributed sensors, fusion center

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

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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

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Authors: Paras Ram, Vikas Kumar

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The transmission of Malaria with seasonal were studied through the use of mathematical models. The data from the annual number of Malaria cases reported to the Division of Epidemiology, Ministry of Public Health, Thailand during the period 1997-2011 were analyzed. The transmission of Malaria with seasonal was studied by formulating a mathematical model which had been modified to describe different situations encountered in the transmission of Malaria. In our model, the population was separated into two groups: the human and vector groups, and then constructed a system of nonlinear differential equations. Each human group was divided into susceptible, infectious in hot season, infectious in rainy season, infectious in cool season and recovered classes. The vector population was separated into two classes only: susceptible and infectious vectors. The analysis of the models was given by the standard dynamical modeling.

Keywords: ferrofluid, magnetic field, porous medium, rotating disk, Neuringer-Rosensweig Model

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Authors: Amit Sharma, J. N. Sharma

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This paper deals with the study of reflection and transmission characteristics of acoustic waves at the interface of a semiconductor halfspace and elastic solid. The amplitude ratios (reflection and transmission coefficients) of reflected and transmitted waves to that of incident wave varying with the incident angles have been examined for the case of quasi-longitudinal wave. The special cases of normal and grazing incidence have also been derived with the help of Gauss elimination method. The mathematical model consisting of governing partial differential equations of motion and charge carriers diffusion of n-type semiconductors and elastic solid has been solved both analytically and numerically in the study. The numerical computations of reflection and transmission coefficients has been carried out by using MATLAB programming software for silicon (Si) semiconductor and copper elastic solid. The computer simulated results have been plotted graphically for Si semiconductors. The study may be useful in semiconductors, geology, and seismology in addition to surface acoustic wave (SAW) devices.

Keywords: quasilongitudinal, reflection and transmission, semiconductors, acoustics

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Authors: Sanyka Banerjee, Saikat Nandi, P. K. Dan

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Synchronizers as an integral part of gearbox is a key element in the transmission system in automotive. The performance of synchronizer affects transmission efficiency and driving comfort. Synchronizing mechanism as a major component of transmission system must be capable of preventing vibration and noise in the gears. Gear shifting efficiency improvement with an aim to achieve smooth, quick and energy efficient power transmission remains a challenge for the automotive industry. Performance of the synchronizer is dependent on the features and characteristics of its sub-components and therefore analysis of the contribution of such characteristics is necessary. An important exercise involved is to identify all such characteristics or factors which are associated with the modeling and analysis and for this purpose the literature was reviewed, rather extensively, to study the mathematical models, formulated considering such. It has been observed that certain factors are rather common across models; however, there are few factors which have specifically been selected for individual models, as reported. In order to obtain a more realistic model, an attempt here has been made to identify and assimilate practically all possible factors which may be considered in formulating the model more comprehensively. A simulation study, formulated as a block model, for such analysis has been carried out in a reliable environment like MATLAB. Lower synchronization time is desirable and hence, it has been considered here as the output factors in the simulation modeling for evaluating transmission efficiency. An improved synchronizer model requires optimized values of sub-component design parameters. A parametric optimization utilizing Taguchi’s design of experiment based response data and their analysis has been carried out for this purpose. The effectiveness of the optimized parameters for the improved synchronizer performance has been validated by the simulation study of the synchronizer block model with improved parameter values as input parameters for better transmission efficiency and driver comfort.

Keywords: design of experiments, modeling, parametric optimization, simulation, synchronizer

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Authors: Selahattin Gultekin

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Today, in engineering departments, mathematics courses such as calculus, linear algebra and differential equations are generally taught by mathematicians. Therefore, during mathematicians’ classroom teaching there are few or no applications of the concepts to real world problems at all. Most of the times, students do not know whether the concepts or rules taught in these courses will be used extensively in their majors or not. This situation holds true of for all engineering and science disciplines. The general trend toward these mathematic courses is not good. The real-life application of mathematics will be appreciated by students when mathematical modeling of real-world problems are tackled. So, students do not like abstract mathematics, rather they prefer a solid application of the concepts to our daily life problems. The author highly recommends that mathematical modeling is to be taught starting in high schools all over the world In this paper, some mathematical concepts such as limit, derivative, integral, Taylor Series, differential equations and mean-value-theorem are chosen and their applications with graphical representations to real problems are emphasized.

Keywords: applied mathematics, engineering mathematics, mathematical concepts, mathematical modeling

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Authors: N. Ibrahim-Rassoul, A. Kessi, E. K. Si-Ahmed, N. Djilali, J. Legrand

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The static and dynamic formation of liquid water bridges is analyzed using a combination of visualization experiments in a microchannel with a mathematical model. This paper presents experimental and theoretical findings of water plug/capillary bridge formation in a 250 μm squared microchannel. The approach combines mathematical and numerical modeling with experimental visualization and measurements. The generality of the model is also illustrated for flow conditions encountered in manipulation of polymeric materials and formation of liquid bridges between patterned surfaces. The predictions of the model agree favorably the observations as well as with the experimental recordings.

Keywords: green energy, mathematical modeling, fuel cell, water plug, gas diffusion layer, surface of revolution

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: Arpan Dwivedi, Yogesh Pahariya

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In this paper, optimal design of hybrid standalone power supply system (SAPS) is done for off grid applications in remote areas where transmission of power is difficult. The hybrid SAPS system uses two primary energy sources, wind and solar, and in addition to these diesel generator is also connected to meet the load demand in case of failure of wind and solar system. This paper presents mathematical modeling of 1.4 MW hybrid SAPS system for rural electrification. This paper firstly focuses on mathematical modeling of PV module connected in a string, secondly focuses on modeling of permanent magnet wind turbine generator (PMWTG). The hybrid controller is also designed for selection of power from the source available as per the load demand. The power output of hybrid SAPS system is analyzed for meeting load demands at urban as well as for rural areas.

Keywords: SAPS, DG, PMWTG, rural area, off-grid, PV module

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Authors: Mauricio George Miguel Jardini, Jose Antonio Jardini

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Transmission power utilities participate with kilometers of circuits, many with particularities in terms of vegetation growth. To control these rights-of-way, maintenance teams perform ground, and air inspections, and the identification method is subjective (indirect). On a ground inspection, when identifying an irregularity, for example, high vegetation threatening contact with the conductor cable, pruning or suppression is performed immediately. In an aerial inspection, the suppression team is mobilized to the identified point. This work investigates the use of 3D modeling of a transmission line segment using RGB (red, blue, and green) images and LiDAR (Light Detection and Ranging) sensor data. Both sensors are coupled to unmanned aerial vehicle. The goal is the accurate and timely detection of vegetation along the right-of-way that can cause shutdowns.

Keywords: 3D modeling, LiDAR, right-of-way, transmission lines, vegetation

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Authors: Zahira Anane, Abdelhafid Bayadi

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Corona in the HV overhead transmission lines is an important source of attenuation and distortion of overvoltage surges. This phenomenon of distortion, which is superimposed on the distortion by skin effect, is due to the dissipation of energy by injection of space charges around the conductor, this process with place as soon as the instantaneous voltage exceeds the threshold voltage of the corona effect conductors. This paper presents a mathematical model to determine the corona inception voltage, the critical electric field and the corona radius, to predict the capacitive changes at conductor of transmission line due to corona. This model has been incorporated into the Alternative Transients Program version of the Electromagnetic Transients Program (ATP/EMTP) as a user defined component, using the MODELS interface with NORTON TYPE94 of this program and using the foreign subroutine. For obtained the displacement of corona charge hell, dichotomy mathematical method is used for this computation. The present corona model can be used for computing of distortion and attenuation of transient overvoltage waves being propagated in a transmission line of the very high voltage electric power.

Keywords: high voltage, corona, Type94 NORTON, dichotomy, ATP/EMTP, MODELS, distortion, foreign model

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Authors: Sadia Arshad

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

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

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A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An in-compressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping

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Authors: Rafayel Azizyan, Valeri Arakelyan, Aram Gevorgyan, Varduhi Balayan, Emil Gevorgyan

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Currently, mathematical and computer modeling are widely used in different biological studies to predict or assess behavior of such complex systems as biological ones. This study deals with mathematical and computer modeling of bi-substrate enzymatic reactions, which play an important role in different biochemical pathways. The main objective of this study is to represent the results from in silico investigation of bi-substrate enzymatic reactions in the presence of uncompetitive inhibitors, as well as to describe in details the inhibition effects. Four models of uncompetitive inhibition were designed using different software packages. Particularly, uncompetitive inhibitor to the first [ES1] and the second ([ES1S2]; [FS2]) enzyme-substrate complexes have been studied. The simulation, using the same kinetic parameters for all models allowed investigating the behavior of reactions as well as determined some interesting aspects concerning influence of different cases of uncompetitive inhibition. Besides that shown, that uncompetitive inhibitors exhibit specific selectivity depending on mechanism of bi-substrate enzymatic reaction.

Keywords: mathematical modeling, bi-substrate enzymatic reactions, reversible inhibition

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Authors: A. Kojah, A. Nacaroğlu

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Single phase transmission lines are used to transfer data or energy between two users. Transient conditions such as switching operations and short circuit faults cause the generation of the fluctuation on the waveform to be transmitted. Spatial voltage distribution on the single phase transmission line may change owing to the position and duration of the short circuit fault in the system. In this paper, the state space representation of the single phase transmission line for short circuit fault and for various types of terminations is given. Since the transmission line is modeled in time domain using distributed parametric elements, the mathematical representation of the event is given in state space (time domain) differential equation form. It also makes easy to solve the problem because of the time and space dependent characteristics of the voltage variations on the distributed parametrically modeled transmission line.

Keywords: energy transmission, transient effects, transmission line, transient voltage, RLC short circuit, single phase

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Authors: Juliana A. Knocikova, Yann Bouret, Médéric Argentina, Laurent Counillon

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Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.

Keywords: eukaryotic cell, mathematical modeling, osmosis, volume alterations

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

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

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

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Authors: Hanbey Hazar, Hakan Gul

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In this study; piston, exhaust, and suction valves of a diesel engine were coated in 300 mm thickness with Tungsten Carbide (WC) by using the HVOF coating method. Mathematical modeling of a coated and uncoated (standardized) engine was performed by using ANN (Artificial Neural Networks). The purpose was to decrease the number of repetitions of tests and reduce the test cost through mathematical modeling of engines by using ANN. The results obtained from the tests were entered in ANN and therefore engines' values at all speeds were estimated. Results obtained from the tests were compared with those obtained from ANN and they were observed to be compatible. It was also observed that, with thermal barrier coating, hydrocarbon (HC), carbon monoxide (CO), and smoke density values of the diesel engine decreased; but nitrogen oxides (NOx) increased. Furthermore, it was determined that results obtained through mathematical modeling by means of ANN reduced the number of test repetitions. Therefore, it was understood that time, fuel and labor could be saved in this way.

Keywords: Artificial Neural Network, Diesel Engine, Mathematical Modelling, Thermal Barrier Coating

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Authors: Zahid Ullah, Atlas Khan

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This abstract focuses on the advancements in mathematical modeling and optimization techniques that play a crucial role in enhancing the efficiency, reliability, and performance of these systems. In this era of rapidly evolving technology, mathematical modeling and optimization offer powerful tools to tackle the complex challenges faced by control, signal processing, and energy systems. This abstract presents the latest research and developments in mathematical methodologies, encompassing areas such as control theory, system identification, signal processing algorithms, and energy optimization. The abstract highlights the interdisciplinary nature of mathematical modeling and optimization, showcasing their applications in a wide range of domains, including power systems, communication networks, industrial automation, and renewable energy. It explores key mathematical techniques, such as linear and nonlinear programming, convex optimization, stochastic modeling, and numerical algorithms, that enable the design, analysis, and optimization of complex control and signal processing systems. Furthermore, the abstract emphasizes the importance of addressing real-world challenges in control, signal processing, and energy systems through innovative mathematical approaches. It discusses the integration of mathematical models with data-driven approaches, machine learning, and artificial intelligence to enhance system performance, adaptability, and decision-making capabilities. The abstract also underscores the significance of bridging the gap between theoretical advancements and practical applications. It recognizes the need for practical implementation of mathematical models and optimization algorithms in real-world systems, considering factors such as scalability, computational efficiency, and robustness. In summary, this abstract showcases the advancements in mathematical modeling and optimization techniques for control, signal processing, and energy systems. It highlights the interdisciplinary nature of these techniques, their applications across various domains, and their potential to address real-world challenges. The abstract emphasizes the importance of practical implementation and integration with emerging technologies to drive innovation and improve the performance of control, signal processing, and energy.

Keywords: mathematical modeling, optimization, control systems, signal processing, energy systems, interdisciplinary applications, system identification, numerical algorithms

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Authors: Marcio S. da Silva, Jose Mauricio de B. Bezerra, Antonio E. de A. Nogueira

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This paper aims to make a performance analysis of shield wire transmission lines against atmospheric discharges when it is made the option of sectioning the shield wire and verify if the tolerability of the change. As a goal of this work, it was established to make complete modeling of a transmission line in the ATPDraw program with shield wire grounded in all the towers and in some towers. The methodology used to make the proposed evaluation was to choose an actual transmission line that served as a case study. From the choice of transmission line and verification of all its topology and materials, complete modeling of the line using the ATPDraw software was performed. Then several atmospheric discharges were simulated by striking the grounded shield wires in each tower. These simulations served to identify the behavior of the existing line against atmospheric discharges. After this first analysis, the same line was reconsidered with shield wire segmentation. The shielding wire segmentation technique aims to reduce induced losses in shield wires and is adopted in some transmission lines in Brazil. With the same conditions of atmospheric discharge the transmission line, this time with shield wire segmentation was again evaluated. The results obtained showed that it is possible to obtain similar performances against atmospheric discharges between a shield wired line in multiple towers and the same line with shield wire segmentation if some precautions are adopted as verification of the ground resistance of the wire segmented shield, adequacy of the maximum length of the segmented gap, evaluation of the separation length of the electrodes of the insulator spark, among others. As a conclusion, it is verified that since the correct assessment and adopted the correct criteria of adjustment a transmission line with shielded wire segmentation can perform very similar to the traditional use with multiple earths. This solution contributes in a very important way to the reduction of energy losses in transmission lines.

Keywords: atmospheric discharges, ATPDraw, shield wire, transmission lines

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Authors: Giovanni Incerti

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In this paper the dynamic behavior of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the mathematical model here proposed also takes into consideration the electrical behaviour of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations of the mathematical model without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the abovementioned software.

Keywords: belt drive, vibrations, startup, DC motor

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Authors: Ujwal Kishor Zore, Shankar Balajirao Kausley, Aniruddha Bhalchandra Pandit

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There are some important design parameters of activated sludge process (ASP) for wastewater treatment and they must be optimally defined to have the optimized plant working. To know them, developing a mathematical model is a way out as it is nearly commensurate the real world works. In this study, a mathematical model was developed for ASP, solved under activated sludge model no 1 (ASM 1) conditions and MATLAB tool was used to solve the mathematical equations. For its real-life validation, the developed model was tested for the inputs from the municipal wastewater treatment plant and the results were quite promising. Additionally, the most cardinal assumptions required to design the treatment plant are discussed in this paper. With the need for computerization and digitalization surging in every aspect of engineering, this mathematical model developed might prove to be a boon to many biological wastewater treatment plants as now they can in no time know the design parameters which are required for a particular type of wastewater treatment.

Keywords: waste water treatment, activated sludge process, mathematical modeling, optimization

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Authors: Ketan Naik, P. H. Bhathawala

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The purpose of this work is to develop a mathematical model of Human Cardiovascular System using lumped parameter method. The model is divided in three parts: Systemic Circulation, Pulmonary Circulation and the Heart. The established mathematical model has been simulated by MATLAB software. The innovation of this study is in describing the system based on the vessel diameters and simulating mathematical equations with active electrical elements. Terminology of human physical body and required physical data like vessel’s radius, thickness etc., which are required to calculate circuit parameters like resistance, inductance and capacitance, are proceeds from well-known medical books. The developed model is useful to understand the anatomic of human cardiovascular system and related syndromes. The model is deal with vessel’s pressure and blood flow at certain time.

Keywords: cardiovascular system, lumped parameter method, mathematical modeling, simulation

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Authors: Chen Yong, Bi Wangyang, Zang Libin, Li Jinkai, Cheng Xiaowei, Liu Jinmin, Yu Miao

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New energy vehicle power transmission systems continue to develop in the direction of high torque, high speed, and high efficiency. The cooling and lubrication of the motor and the transmission system are integrated, and new requirements are placed on the lubricants for the transmission system. The effects of traditional lubricants and special lubricants for new energy vehicles on transmission efficiency were studied through experiments and simulation methods. A mathematical model of the transmission efficiency of the lubricating oil in the gearbox was established. The power loss of each part was analyzed according to the working conditions. The relationship between the speed and the characteristics of different lubricating oil products on the power loss of the stirring oil was discussed. The minimum oil film thickness was required for the life of the gearbox. The accuracy of the calculation results was verified by the transmission efficiency test conducted on the two-motor integrated test bench. The results show that the efficiency increases first and then decreases with the increase of the speed and decreases with the increase of the kinematic viscosity of the lubricant. The increase of the kinematic viscosity amplifies the transmission power loss caused by the high speed. New energy vehicle special lubricants have less attenuation of transmission efficiency in the range above mid-speed. The research results provide a theoretical basis and guidance for the evaluation and selection of transmission efficiency of gearbox lubricants for new energy vehicles.

Keywords: new energy vehicles, lubricants, transmission efficiency, kinematic viscosity, test and simulation

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Authors: Muleya Nqobile, Winston Garira

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We presented a compartmental deterministic multi-scale model which encompass internal plant defensive mechanism and pathogen interaction, then we consider nesting the model into the epidemiological model. The objective was to improve our understanding of the transmission dynamics of within host and between host of Guignardia citricapa Kiely. The inflow of infected class was scaled down to individual level while the outflow was scaled up to average population level. Conceptual model and mathematical model were constructed to display a theoretical framework which can be used for predicting or identify disease pattern.

Keywords: epidemiological model, mathematical modelling, multi-scale modelling, immunological model

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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: Ofosuhene O. Apenteng, Noor Azina Ismail

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Recently tourism is a major foreign exchange earner in the World. In this paper, we propose the mathematical model to study the impact of tourists on the spread of HIV incidences using compartmental differential equation models. Simulation studies of reproduction number are used to demonstrate new insights on the spread of HIV disease. The periodogram analysis of a time series was used to determine the speed at which the disease is spread. The results indicate that with the persistent flow of tourism into a country, the disease status has increased the epidemic rate. The result suggests that the government must put more control on illegal prostitution, unprotected sexual activity as well as to emphasis on prevention policies that include the safe sexual activity through the campaign by the tourism board.

Keywords: HIV/AIDS, mathematical transmission modeling, tourists, stability, simulation

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Authors: Benaliouche Hana, Abdessemed Djamal, Meniai Abdessalem, Lesage Geoffroy, Heran Marc

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This paper presents a dynamic mathematical model of activated sludge which is able to predict the formation and degradation kinetics of SMP (Soluble microbial products) in membrane bioreactor systems. The model is based on a calibrated version of ASM1 with the theory of production and degradation of SMP. The model was calibrated on the experimental data from MBR (Mathematical modeling Membrane bioreactor) pilot plant. Analytical expressions have been developed, describing the concentrations of the main state variables present in the sludge matrix, with the inclusion of only six additional linear differential equations. The objective is to present a new dynamic mathematical model of activated sludge capable of predicting the formation and degradation kinetics of SMP (UAP and BAP) from the submerged membrane bioreactor (BRMI), operating at low organic load (C / N = 3.5), for two sludge retention times (SRT) fixed at 40 days and 60 days, to study their impact on membrane fouling, The modeling study was carried out under the steady-state condition. Analytical expressions were then validated by comparing their results with those obtained by simulations using GPS-X-Hydromantis software. These equations made it possible, by means of modeling approaches (ASM1), to identify the operating and kinetic parameters and help to predict membrane fouling.

Keywords: Activated Sludge Model No. 1 (ASM1), mathematical modeling membrane bioreactor, soluble microbial products, UAP, BAP, Modeling SMP, MBR, heterotrophic biomass

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