Search results for: mathematical equations.

Authors: Michaela Chovancova, Jakub Elcner

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

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

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Authors: Yasser El-Henawy, M. Abd El-Kader, Gamal H. Moustafa

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A theoretical study of a humidification dehumidification solar desalination unit has been carried out to increase understanding the effect of weather conditions on the unit productivity. A humidification-dehumidification (HD) solar desalination unit has been designed to provide fresh water for population in remote arid areas. It consists of solar water collector and air collector; to provide the hot water and air to the desalination chamber. The desalination chamber is divided into humidification and dehumidification towers. The circulation of air between the two towers is maintained by the forced convection. A mathematical model has been formulated, in which the thermodynamic relations were used to study the flow, heat and mass transfer inside the humidifier and dehumidifier. The present technique is performed in order to increase the unit performance. Heat and mass balance has been done and a set of governing equations has been solved using the finite difference technique. The unit productivity has been calculated along the working day during the summer and winter sessions and has compared with the available experimental results. The average accumulative productivity of the system in winter has been ranged between 2.5 to 4 kg/m2.day, while the average summer productivity has been found between 8 to 12 kg/m2 day.

Keywords: solar desalination, solar collector, humidification and dehumidification, simulation, finite difference, water productivity

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Authors: Abdelkhalek Bakkari

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

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

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Authors: Nini Johana Marín Rodríguez, William Fernando Oquendo Patino

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In this work, we model a coupled system where we explore the effects of steady and random behavior on a linear system like an extension of the classic Strogatz model. This is exemplified by modeling a couple love dynamics as a linear system of two coupled differential equations and studying its stability for four types of lovers chosen as CC='Cautious- Cautious', OO='Only other feelings', OP='Opposites' and RR='Romeo the Robot'. We explore the effects of, first, introducing saturation, and second, adding a random variation to one of the CC-type lover, which will shape his character by trying to model how its variability influences the dynamics between love and hate in couple in a long run relationship. This work could also be useful to model other kind of systems where interactions can be modeled as linear systems with external or internal random influence. We found the final results are not easy to predict and a strong dependence on initial conditions appear, which a signature of chaos.

Keywords: differential equations, dynamical systems, linear system, love dynamics

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Authors: Anuar Ishak

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The characteristics of stagnation point flow of a nanofluid towards a stretching/shrinking sheet are investigated. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. The numerical results show that dual (upper and lower branch) solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. It is found that the skin friction decreases when the sheet is stretched, but increases when the suction effect is increased. It is also found that increasing the thermophoresis parameter reduces the heat transfer rate at the surface, while increasing the Brownian motion parameter increases the mass transfer rate at the surface.

Keywords: dual solutions, heat transfer, forced convection, nanofluid, stability analysis

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Authors: Riccardo Zanni, Maria Galvez-Llompart, Ramon Garcia-Domenech, Jorge Galvez

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Biopesticides, such as naturally occurring chemicals, pheromones, fungi, bacteria and insect predators are often a winning choice in crop protection because of their environmental friendly profile. They are considered to have lower toxicity than traditional pesticides. After almost a century of pesticides use, resistances to traditional insecticides are wide spread, while those to bioinsecticides have raised less attention, and resistance management is frequently neglected. This seems to be a crucial mistake since resistances have already occurred for many marketed biopesticides. With an eye to the future, we present here a selection of new natural occurring chemicals as potential bioinsecticides. The molecules were selected using a consolidated mathematical paradigm called molecular topology. Several QSAR equations were depicted and subsequently applied for the virtual screening of hundred thousands molecules of natural origin, which resulted in the selection of new potential bioinsecticides. The most innovative aspect of this work does not only reside in the importance of the identification of new molecules overcoming biopesticides’ resistances, but on the possibility to promote shared knowledge in the field of green chemistry through this unique in silico discipline named molecular topology.

Keywords: green chemistry, QSAR, molecular topology, biopesticide

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Sarwat Jahan, Asker Rajin Rahman

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

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

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Authors: Emhimed Saffor

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

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

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Authors: Nessa-Amie T. Peñaflor, Antonio Cinto

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

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

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Authors: Atara Shriki, Ilana Lavy

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

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

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Authors: A. T. Kuda, J. J. Dayya, A. Jimoh

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This paper investigates the fault detection and Isolation technique of measurement data sets from a three tank system using analytical model-based temporal redundancy which is based on residual generation using parity equations/space approach. It further briefly outlines other approaches of model-based residual generation. The basic idea of parity space residual generation in temporal redundancy is dynamic relationship between sensor outputs and actuator inputs (input-output model). These residuals where then used to detect whether or not the system is faulty and indicate the location of the fault when it is faulty. The method obtains good results by detecting and isolating faults from the considered data sets measurements generated from the system.

Keywords: fault detection, fault isolation, disturbing influences, system failure, parity equation/relation, structured parity equations

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: P. C. Tewari, Parveen Kumar

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The paper describes the availability analysis of milling system of a rice milling plant using probabilistic approach. The subsystems under study are special purpose machines. The availability analysis of the system is carried out to determine the effect of failure and repair rates of each subsystem on overall performance (i.e. steady state availability) of system concerned. Further, on the basis of effect of repair rates on the system availability, maintenance repair priorities have been suggested. The problem is formulated using Markov Birth-Death process taking exponential distribution for probable failures and repair rates. The first order differential equations associated with transition diagram are developed by using mnemonic rule. These equations are solved using normalizing conditions and recursive method to drive out the steady state availability expression of the system. The findings of the paper are presented and discussed with the plant personnel to adopt a suitable maintenance policy to increase the productivity of the rice milling plant.

Keywords: availability modeling, Markov process, milling system, rice milling plant

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Authors: Yohannes Yirga, Daniel Tesfay

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The convective heat and mass transfer in nanofluid flow through a porous media due to a permeable stretching sheet with magnetic field, viscous dissipation, and chemical reaction and Soret effects are numerically investigated. Two types of nanofluids, namely Cu-water and Ag-water were studied. The governing boundary layer equations are formulated and reduced to a set of ordinary differential equations using similarity transformations and then solved numerically using the Keller box method. Numerical results are obtained for the skin friction coefficient, Nusselt number and Sherwood number as well as for the velocity, temperature and concentration profiles for selected values of the governing parameters. Excellent validation of the present numerical results has been achieved with the earlier linearly stretching sheet problems in the literature.

Keywords: heat and mass transfer, magnetohydrodynamics, nanofluid, fluid dynamics

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Authors: Quznetsov Gunn

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In the study of the logical foundations of probability theory, it was found that the terms and equations of the fundamental theoretical physics represent terms and theorems of the classical probability theory, more precisely, of that part of this theory, which considers the probability of dot events in the 3 + 1 space-time. In particular, the masses, moments, energies, spins, etc. turn out of parameters of probability distributions such events. The terms and the equations of the electroweak and of the quark-gluon theories turn out the theoretical-probabilistic terms and theorems. Here the relation of a neutrino to his lepton becomes clear, the W and Z bosons masses turn out dynamic ones, the cause of the asymmetry between particles and antiparticles is the impossibility of the birth of single antiparticles. In addition, phenomena such as confinement and asymptotic freedom receive their probabilistic explanation. And here we have the logical foundations of the gravity theory with phenomena dark energy and dark matter.

Keywords: classical theory of probability, logical foundation of fundamental theoretical physics, masses, moments, energies, spins

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Authors: Hamid Maidat, Khedidja Bouhadef, Djamel Eddine Ameziani, Azzedine Abdedou

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This work consists of a numerical simulation of convective heat transfer in a vertical plane channel filled with a heat generating porous medium, in the absence of local thermal equilibrium. The walls are maintained to a constant temperature and the inlet velocity is uniform. The dynamic range is described by the Darcy-Brinkman model and the thermal field by two energy equations model. A dimensionless formulation is developed for performing a parametric study based on certain dimensionless groups such as, the Biot interstitial number, the thermal conductivity ratio and the volumetric heat generation. The governing equations are solved using the finite volume method, gave rise to a multitude of results concerning in particular the thermal field in the porous channel and the existence or not of the local thermal equilibrium.

Keywords: local thermal non equilibrium model, mixed convection, porous medium, power generation

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Authors: Valentina Narvaez Gaitan, Laura Valentina Rodriguez Leguizamon, Ruben Dario Hernandez B.

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This work describes a physiological signal emulation system that uses electromyography (EMG) signals obtained from muscle sensors in the first instance. These signals are used to extract their characteristics to model and emulate specific arm movements. The main objective of this effort is to develop a new biomedical software system capable of generating physiological signals through the use of embedded systems by establishing the characteristics of the acquired signals. The acquisition system used was Biosignals, which contains two EMG electrodes used to acquire signals from the forearm muscles placed on the extensor and flexor muscles. Processing algorithms were implemented to classify the signals generated by the arm muscles when performing specific movements such as wrist flexion extension, palmar grip, and wrist pronation-supination. Matlab software was used to condition and preprocess the signals for subsequent classification. Subsequently, the mathematical modeling of each signal is performed to be generated by the embedded system, with a validation of the accuracy of the obtained signal using the percentage of cross-correlation, obtaining a precision of 96%. The equations are then discretized to be emulated in the embedded system, obtaining a system capable of generating physiological signals according to the characteristics of medical analysis.

Keywords: classification, electromyography, embedded system, emulation, physiological signals

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Authors: Mohammad R. Jalali, Mohammad M. Jalali

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The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.

Keywords: Green–Naghdi equations, nonlinearity, numerical prediction, sloshing waves, solitary waves

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

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

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

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Authors: Vikas Kumar

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The present study is carried out to investigate the magneto-viscous effects on incompressible ferrofluid flow over a porous rotating disc with suction or injection on the surface of the disc subjected to a magnetic field. The flow under consideration is axi-symmetric steady ferrofluid flow of electrically non-conducting fluid. Karman’s transformation is used to convert the governing boundary layer equations involved in the problem to a system of non linear coupled differential equations. The solution of this system is obtained by using power series approximation. The flow characteristics i.e. radial, tangential, axial velocities and boundary layer displacement thickness are calculated for various values of MFD (magnetic field dependent) viscosity and for different values of suction injection parameter. Besides this, skin friction coefficients are also calculated on the surface of the disk. Thus, the obtained results are presented numerically and graphically in the paper.

Keywords: axi-symmetric, ferrofluid, magnetic field, porous rotating disk

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Authors: Jianyang Zhu, Lin Jiang, Tixian Tian

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Inspired by the increasing interesting on the wind power associated with production of clear electric power, a numerical experiment is applied to investigate the aerodynamic performance of straight type vertical axis wind turbine with different thickness and solidity, where the incompressible Navier-Stokes (N-S) equations coupled with dynamic mesh technique is solved. By analyzing the flow field, as well as energy coefficient of different thickness and solidity turbine, it is found that the thickness and solidity can significantly influence the performance of vertical axis wind turbine. For the turbine under low tip speed, the mean energy coefficient increase with the increasing of thickness and solidity, which may improve the self starting performance of the turbine. However for the turbine under high tip speed, the appropriate thickness and smaller solidity turbine possesses better performance. In addition, delay stall and no interaction of the blade and previous separated vortex are observed around appropriate thickness and solidity turbine, therefore lead better performance characteristics.

Keywords: vertical axis wind turbine, N-S equations, dynamic mesh technique, thickness, solidity

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Authors: Titinan Pothong, Prasit Wangpakapattanawong, Stephen Elliott

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Shifting cultivation is an indigenous agricultural practice among upland people and has long been one of the major land-use systems in Southeast Asia. As a result, fallows and secondary forests have come to cover a large part of the region. However, they are increasingly being replaced by monocultures, such as corn cultivation. This is believed to be a main driver of deforestation and forest degradation, and one of the reasons behind the recurring winter smog crisis in Thailand and around Southeast Asia. Accurate biomass estimation of trees is important to quantify valuable carbon stocks and changes to these stocks in case of land use change. However, presently, Thailand lacks proper tools and optimal equations to quantify its carbon stocks, especially for secondary evergreen forests, including fallow areas after shifting cultivation and smaller trees with a diameter at breast height (DBH) of less than 5 cm. Developing new allometric equations to estimate biomass is urgently needed to accurately estimate and manage carbon storage in tropical secondary forests. This study established new equations using a destructive method at three study sites: approximately 50-year-old secondary forest, 4-year-old fallow, and 7-year-old fallow. Tree biomass was collected by harvesting 136 individual trees (including coppiced trees) from 23 species, with a DBH ranging from 1 to 31 cm. Oven-dried samples were sent for carbon analysis. Wood density was calculated from disk samples and samples collected with an increment borer from 79 species, including 35 species currently missing from the Global Wood Densities database. Several models were developed, showing that aboveground biomass (AGB) was strongly related to DBH, height (H), and wood density (WD). Including WD in the model was found to improve the accuracy of the AGB estimation. This study provides insights for reforestation management, and can be used to prepare baseline data for Thailand’s carbon stocks for the REDD+ and other carbon trading schemes. These may provide monetary incentives to stop illegal logging and deforestation for monoculture.

Keywords: aboveground biomass, allometric equation, carbon stock, secondary forest

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Authors: F. Rahimi Dehgolan, S. E. Khadem, S. Bab, M. Najafee

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Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.

Keywords: rotating shaft, flexible blades, centrifugal stiffness, stability

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Authors: Win Ko Ko, A. N. Temnov

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The problem of nonlinear oscillations of a two-layer liquid completely filling a limited volume is considered. Using two basic asymmetric harmonics excited in two mutually perpendicular planes, ordinary differential equations of nonlinear oscillations of the interface of a two-layer liquid are investigated. In this paper, hydrodynamic coefficients of linear and nonlinear problems in integral relations were determined. As a result, the instability regions of forced oscillations of a two-layered liquid in a cylindrical tank occurring in the plane of action of the disturbing force are constructed, as well as the dynamic instability regions of the parametric resonance for different ratios of densities of the upper and lower liquids depending on the amplitudes of liquids from the excitations frequencies. Steady-state regimes of fluid motion were found in the regions of dynamic instability of the initial oscillation form. The Bubnov-Galerkin method is used to construct instability regions for approximate solution of nonlinear differential equations.

Keywords: nonlinear oscillations, two-layered liquid, instability region, hydrodynamic coefficients, resonance frequency

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Authors: M. Ahmed, Javed Mallick, Mohammad Abul Hasan

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The flexural tensile strength of concrete is an important parameter for determining cracking behavior of concrete structure and to compute deflection under flexure. Many factors have been shown to influence the flexural tensile strength, particularly the level of concrete strength, size of member, age of concrete and confinement to flexure member etc. Empirical equations have been suggested to relate the flexural tensile strength and compressive strength. Limited literature is available for relationship between flexural tensile strength and compressive strength giving consideration to the factors affecting the flexural tensile strength specially the concrete confinement factor. The concrete member such as slabs, beams and columns critical locations are under confinement effects. The paper presents the experimental study to predict the flexural tensile strength and compressive strength empirical relations using statistical procedures considering the effect of confinement and age of concrete for wide range of concrete strength (from 35 to about 100 MPa). It is concluded from study that due consideration of confinement should be given in deriving the flexural tensile strength and compressive strength proportionality equations.

Keywords: compressive strength, flexural tensile strength, modulus of rupture, statistical procedures, concrete confinement

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Authors: Alicia Kamischke, Souhail Elhouar, Yasser Khodair

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The American Institute of Steel Construction (AISC) Specification (360-10) provides equations for calculating the capacity of a W-shaped steel member to resist concentrated forces applied to its flange. In the case of flange local bending, the capacity equations were primarily formulated for an interior point along the member, which is defined to be at a distance larger than ten flange thicknesses away from the member’s end. When a concentrated load is applied within ten flange thicknesses from the member’s end, AISC requires a fifty percent reduction to be applied to the flange bending capacity. This reduction, however, is not supported by any research. In this study, finite element modeling is used to investigate the actual reduction in capacity near the end of such a steel member. The results indicate that the AISC equation for flange local bending is quite conservative for forces applied at less than ten flange thicknesses from the member’s end and a new equation is suggested for the evaluation of available flange local bending capacity within that distance.

Keywords: flange local bending, concentrated forces, column, flange capacity

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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: Ozgul Kartal, Wade Tillett, Lyn D. English

Abstract:

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

Procedia PDF Downloads 65

Authors: Abdulrahman Abdulrahman

Abstract:

The specific energy equation has many applications in practical channels, such as exponential channels. In this paper, the governing equation of alternate depth ratio for exponential channels, in general, was investigated towards obtaining analytical solution for the alternate depth ratio in three exponential channel shapes, viz., rectangular, triangular, and parabolic channels. The alternate depth ratio for rectangular channels is quadratic; hence it is very simple to solve. While for parabolic and triangular channels, the alternate depth ratio is cubic and quartic equations, respectively, analytical solution for these equations may be achieved easily for a given Froud number. Different examples are solved to prove the efficiency of the proposed solution. Such analytical solution can be easily used in natural rivers and most of practical channels.

Keywords: alternate depth, analytical solution, specific energy, parabolic channel, rectangular channel, triangular channel, open channel flow

Procedia PDF Downloads 199