Search results for: mathematical equations

Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: B. Mahfoud, A. Bendjaghlouli

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Natural convection is simulated in a truncated cone filled with nanofluid. Inclined and top walls have constant temperature where the heat source is located on the bottom wall of the conical container which is thermally insulated. A finite volume approach is used to solve the governing equations using the SIMPLE algorithm for different parameters such as Rayleigh number, inclination angle of inclined walls of the enclosure and heat source length. The results showed an enhancement in cooling system by using a nanofluid, when conduction regime is assisted. The inclination angle of inclined sidewall and heat source length affect the heat transfer rate and the maximum temperature.

Keywords: heat source, truncated cone, nanofluid, natural convection

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Authors: Somveer Singh, Vineet Kumar Singh

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This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Y. Yongli, M. H. Aissa

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The purpose of this paper aims for a geotechnical analysis based on experimental physical and mechanical characteristics of Miocene marl situated at Medea region in Algeria. More than 150 soil samples were taken in the investigation part of the North-South Highway which extends over than 53 km from Chiffa in the North to Berrouaghia in the South of Algeria. The analysis of data in terms of Atterberg limits, plasticity index, and clay content reflects an acceptable correlation justified by a high coefficient of regression which was compared with the previous works in the region. Finally, approximated equations that serve as a guideline for geotechnical design locally have been suggested.

Keywords: correlation, geotechnical properties, miocene marl, north-south highway

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Authors: Yasin Tadayonrad

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

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

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Authors: Mostafa Shahriari, Sergio Rojas, David Pardo, Angel Rodriguez- Rozas, Shaaban A. Bakr, Victor M. Calo, Ignacio Muga

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Logging-While Drilling (LWD) is a technique to record down-hole logging measurements while drilling the well. Nowadays, LWD devices (e.g., nuclear, sonic, resistivity) are mostly used commercially for geo-steering applications. Modern borehole resistivity tools are able to measure all components of the magnetic field by incorporating tilted coils. The depth of investigation of LWD tools is limited compared to the thickness of the geological layers. Thus, it is a common practice to approximate the Earth’s subsurface with a sequence of 1D models. For a 1D model, we can reduce the dimensionality of the problem using a Hankel transform. We can solve the resulting system of ordinary differential equations (ODEs) either (a) analytically, which results in a so-called semi-analytic method after performing a numerical inverse Hankel transform, or (b) numerically. Semi-analytic methods are used by the industry due to their high performance. However, they have major limitations, namely: -The analytical solution of the aforementioned system of ODEs exists only for piecewise constant resistivity distributions. For arbitrary resistivity distributions, the solution of the system of ODEs is unknown by today’s knowledge. -In geo-steering, we need to solve inverse problems with respect to the inversion variables (e.g., the constant resistivity value of each layer and bed boundary positions) using a gradient-based inversion method. Thus, we need to compute the corresponding derivatives. However, the analytical derivatives of cross-bedded formation and the analytical derivatives with respect to the bed boundary positions have not been published to the best of our knowledge. The main contribution of this work is to overcome the aforementioned limitations of semi-analytic methods by solving each 1D model (associated with each Hankel mode) using an efficient multi-scale finite element method. The main idea is to divide our computations into two parts: (a) offline computations, which are independent of the tool positions and we precompute only once and use them for all logging positions, and (b) online computations, which depend upon the logging position. With the above method, (a) we can consider arbitrary resistivity distributions along the 1D model, and (b) we can easily and rapidly compute the derivatives with respect to any inversion variable at a negligible additional cost by using an adjoint state formulation. Although the proposed method is slower than semi-analytic methods, its computational efficiency is still high. In the presentation, we shall derive the mathematical variational formulation, describe the proposed multi-scale finite element method, and verify the accuracy and efficiency of our method by performing a wide range of numerical experiments and comparing the numerical solutions to semi-analytic ones when the latest are available.

Keywords: logging-While-Drilling, resistivity measurements, multi-scale finite elements, Hankel transform

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Authors: S. Vivek, Sharad Sharan, R. Arvind, D. V. Praveen, J. Vigneshwar, S. Ajith, V. R. Sanal Kumar

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In this paper numerical studies have been carried out to examine the starting transient flow features of high-performance solid propellant rocket motors with different port geometries but with same propellant loading density. Numerical computations have been carried out using a 3D SST k-ω turbulence model. This code solves standard k-omega turbulence equations with shear flow corrections using a coupled second order implicit unsteady formulation. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-Averaged, Navier-Stokes equations are employed. We have observed from the numerical results that in solid rocket motors with highly loaded propellants having divergent port geometry the hot igniter gases can create pre-ignition thrust oscillations due to flow unsteadiness and recirculation. Under these conditions the convective flux to the surface of the propellant will be enhanced, which will create reattachment point far downstream of the transition region and it will create a situation for secondary ignition and formation of multiple-flame fronts. As a result the effective time required for the complete burning surface area to be ignited comes down drastically giving rise to a high pressurization rate (dp/dt) in the second phase of starting transient. This in effect could lead to starting thrust oscillations and eventually a hard start of the solid rocket motor. We have also observed that the igniter temperature fluctuations will be diminished rapidly and will reach the steady state value faster in the case of solid propellant rocket motors with convergent port than the divergent port irrespective of the igniter total pressure. We have concluded that the thrust oscillations and unexpected thrust spike often observed in solid rockets with non-uniform ports are presumably contributed due to the joint effects of the geometry dependent driving forces, transient burning and the chamber gas dynamics forces. We also concluded that the prudent selection of the port geometry, without altering the propellant loading density, for damping the total temperature fluctuations within the motor is a meaningful objective for the suppression and control of instability and/or pressure/thrust oscillations often observed in solid propellant rocket motors with non-uniform port geometry.

Keywords: ignition transient, solid rockets, starting transient, thrust transient

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

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

Keywords: biomechanics, complaint mechanisms, gonarthrosis, orthoses

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Authors: Nicoly Coelho, Eduardo Vieira Vilas Boas, Paulo Orestes Formigoni

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Faced with the remarkable developments in the various segments of modern engineering, provided by the increasing technological development, professionals of all educational areas need to overcome the difficulties generated due to the good understanding of those who are starting their academic journey. Aiming to overcome these difficulties, this article aims at an introduction to the basic study of numerical methods applied to fluid mechanics and thermodynamics, demonstrating the modeling and simulations with its substance, and a detailed explanation of the fundamental numerical solution for the use of finite difference method, using SCILAB, a free software easily accessible as it is free and can be used for any research center or university, anywhere, both in developed and developing countries. It is known that the Computational Fluid Dynamics (CFD) is a necessary tool for engineers and professionals who study fluid mechanics, however, the teaching of this area of knowledge in undergraduate programs faced some difficulties due to software costs and the degree of difficulty of mathematical problems involved in this way the matter is treated only in postgraduate courses. This work aims to bring the use of DFC low cost in teaching Transport Phenomena for graduation analyzing a small classic case of fundamental thermodynamics with Scilab® program. The study starts from the basic theory involving the equation the partial differential equation governing heat transfer problem, implies the need for mastery of students, discretization processes that include the basic principles of series expansion Taylor responsible for generating a system capable of convergence check equations using the concepts of Sassenfeld, finally coming to be solved by Gauss-Seidel method. In this work we demonstrated processes involving both simple problems solved manually, as well as the complex problems that required computer implementation, for which we use a small algorithm with less than 200 lines in Scilab® in heat transfer study of a heated plate in rectangular shape on four sides with different temperatures on either side, producing a two-dimensional transport with colored graphic simulation. With the spread of computer technology, numerous programs have emerged requiring great researcher programming skills. Thinking that this ability to program DFC is the main problem to be overcome, both by students and by researchers, we present in this article a hint of use of programs with less complex interface, thus enabling less difficulty in producing graphical modeling and simulation for DFC with an extension of the programming area of experience for undergraduates.

Keywords: numerical methods, finite difference method, heat transfer, Scilab

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Authors: J.R.S.S. Kumara, M.A.R.M. Fernando, S.Venkatesh, D.K. Jayaratne

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Protection of heritage monuments against lightning has become extremely important as far as their historical values are concerned. When such structures are large and tall, the risk of lightning initiated from both cloud and ground can be high. This paper presents a lightning risk analysis of three giant stupas in Anuradhapura era (fourth century BC onwards) in Sri Lanka. The three stupas are Jethawaaramaya (269-296 AD), Abayagiriya (88-76 BC) and Ruwanweliseya (161-137 BC), the third, fifth and seventh largest ancient structures in the world. These stupas are solid brick structures consisting of a base, a near hemispherical dome and a conical spire on the top. The ancient stupas constructed with a dielectric crystal on the top and connected to the ground through a conducting material, was considered as the hypothesis for their original lightning protection technique. However, at present, all three stupas are protected with Franklin rod type air termination systems located on top of the spire. First, a risk analysis was carried out according to IEC 62305 by considering the isokeraunic level of the area and the height of the stupas. Then the standard protective angle method and rolling sphere method were used to locate the possible touching points on the surface of the stupas. The study was extended to estimate the critical current which could strike on the unprotected areas of the stupas. The equations proposed by (Uman 2001) and (Cooray2007) were used to find the striking distances. A modified version of rolling sphere method was also applied to see the effects of upward leaders. All these studies were carried out for two scenarios: with original (i.e. ancient) lightning protection system and with present (i.e. new) air termination system. The field distribution on the surface of the stupa in the presence of a downward leader was obtained using finite element based commercial software COMSOL Multiphysics for further investigations of lightning risks. The obtained results were analyzed and compared each other to evaluate the performance of ancient and new lightning protection methods and identify suitable methods to design lightning protection systems for stupas. According to IEC standards, all three stupas with new and ancient lightning protection system has Level IV protection as per protection angle method. However according to rolling sphere method applied with Uman’s equation protection level is III. The same method applied with Cooray’s equation always shows a high risk with respect to Uman’s equation. It was found that there is a risk of lightning strikes on the dome and square chamber of the stupa, and the corresponding critical current values were different with respect to the equations used in the rolling sphere method and modified rolling sphere method.

Keywords: Stupa, heritage, lightning protection, rolling sphere method, protection level

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

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

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

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Authors: Shubham Jaiswal

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In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system.

Keywords: spatial fractional order advection-dispersion equation, second-kind shifted Chebyshev polynomial, collocation method, conservative system, non-conservative system

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Authors: Ilija Plecas, Dalibor Arbutina

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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste

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Authors: Gonzalo García-Reyes

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Conformastat spherically symmetric exact solutions of Einstein's field equations representing matter distributions made of fluid both perfect and anisotropic from given solutions of Poisson's equation of Newtonian gravity are investigated. The approach is used in the construction of new relativistic models of thick spherical shells and three-component models of galaxies (bulge, disk, and dark matter halo), writing, in this case, the metric in cylindrical coordinates. In addition, the circular motion of test particles (rotation curves) along geodesics on the equatorial plane of matter configurations and the stability of the orbits against radial perturbations are studied. The models constructed satisfy all the energy conditions.

Keywords: general relativity, exact solutions, spherical symmetry, galaxy, kinematics and dynamics, dark matter

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Authors: Kaouther Selmi, Alaeddine Sridi, Mohamed Bouallegue, Kais Bouallegue

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Neurons are the fundamental units of the brain and the nervous system. The variable structure model of neurons consists of a system of differential equations with various parameters. By optimizing these parameters, we can create a unique model that describes the dynamic behavior of a single neuron. We introduce a neural network based on neurons with multiple dendrites employing an activation function with a variable structure. In this paper, we present a model for heart behavior. Finally, we showcase our successful simulation of the heart's ECG diagram using our Variable Structure Neuron Model (VSMN). This result could provide valuable insights into cardiology.

Keywords: neural networks, neuron, dendrites, heart behavior, ECG

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Authors: Hamdy M. Youssef, Mowffaq Oreijah, Hunaydi S. Alsharif

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In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

Keywords: thermoelasticity, thermal conductivity, Laplace transforms, Fourier transforms

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Authors: Xiaoyuan Suo

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

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

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Authors: Sreeparna Majee, G. C. Shit

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

Keywords: magnetic nanoparticles, blood flow, atherosclerosis, hyperthermia

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Authors: Marianne Miguet, Gaël Plantard, Yves Jaeger, Vincent Goetz

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The contamination of groundwater is a major concern. A common pollutant, the perchloroethylene, is the target contaminant. Water treatment process as Granular Activated Carbons are very efficient but requires pilot-scale testing to determine the full-scale GAC performance. First, the batch mode was used to get a reliable experimental method to estimate the adsorption capacity of a common volatile compound is settled. The Langmuir model is acceptable to fit the isotherms. Dynamic tests were performed with three columns and different operating conditions. A database of concentration profiles and breakthroughs were obtained. The resolution of the set of differential equations is acceptable to fit the dynamics tests and could be used for a full-scale adsorber.

Keywords: activated carbon, groundwater, perchloroethylene, full-scale

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Authors: Jing Qing-feng, Liu Danmei

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Based on the optimum detection, signal projection and Maximum A Posteriori (MAP) rule, Proakis has deduced the theoretical BER equation of Gray coded MPSK signals. Proakis analyzed the BER theoretical equations mainly based on the projection of signals, which is difficult to be understood. This article solve the same problem based on the signal space, which explains the vectors relations among the sending signals, received signals and noises. The more explicit and easy-deduced process is illustrated in this article based on the signal space, which can illustrated the relations among the signals and noises clearly. This kind of deduction has a univocal geometry meaning. It can explain the correlation between the production and calculation of BER in vector level.

Keywords: MPSK, MAP, signal space, BER

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Authors: Saeid Jalilzadeh

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SVC is one of the most significant devices in FACTS technology which is used in parallel compensation, enhancing the transient stability, limiting the low frequency oscillations and etc. designing a proper controller is effective in operation of svc. In this paper the equations that describe the proposed system have been linearized and then the optimum PID controller has been designed for svc which its optimal coefficients have been earned by chaos algorithm. Quick damping of oscillations of generator is the aim of designing of optimum PID controller for svc whether the input power of generator has been changed suddenly. The system with proposed controller has been simulated for a special disturbance and the dynamic responses of generator have been presented. The simulation results showed that a system composed with proposed controller has suitable operation in fast damping of oscillations of generator.

Keywords: chaos, PID controller, SVC, frequency oscillation

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

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In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

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Authors: H. Aissa, L. Mouzai, M. Bouhadef

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The effects of down slope steepness on soil splash distribution under a water drop impact have been investigated in this study. The equipment used are the burette to simulate a water drop, a splash cup filled with sandy soil which forms the source area and a splash board to collect the ejected particles. The results found in this study have shown that the apparent mass increased with increasing downslope angle following a linear regression equation with high coefficient of determination. In the same way, the radial soil splash distribution over the distance has been analyzed statistically, and an exponential function was the best fit of the relationship for the different slope angles. The curves and the regressions equations validate the well known FSDF and extend the theory of Van Dijk.

Keywords: splash distribution, water drop, slope steepness, soil detachment

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Authors: Verónica Díaz

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

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

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Authors: Eunsu Jang, Kang Park

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In developing an armored ground combat vehicle (AGCV), it is a very important step to analyze the vulnerability (or the survivability) of the AGCV against enemy’s attack. In the vulnerability analysis, the penetration equations are usually used to get the penetration depth and check whether a bullet can penetrate the armor of the AGCV, which causes the damage of internal components or crews. The penetration equations are derived from penetration experiments which require long time and great efforts. However, they usually hold only for the specific material of the target and the specific type of the bullet used in experiments. Thus, penetration simulation using ANSYS can be another option to calculate penetration depth. However, it is very important to model the targets and select the input parameters in order to get an accurate penetration depth. This paper performed a sensitivity analysis of input parameters of ANSYS on the accuracy of the calculated penetration depth. Two conflicting objectives need to be achieved in adopting ANSYS in penetration analysis: maximizing the accuracy of calculation and minimizing the calculation time. To maximize the calculation accuracy, the sensitivity analysis of the input parameters for ANSYS was performed and calculated the RMS error with the experimental data. The input parameters include mesh size, boundary condition, material properties, target diameter are tested and selected to minimize the error between the calculated result from simulation and the experiment data from the papers on the penetration equation. To minimize the calculation time, the parameter values obtained from accuracy analysis are adjusted to get optimized overall performance. As result of analysis, the followings were found: 1) As the mesh size gradually decreases from 0.9 mm to 0.5 mm, both the penetration depth and calculation time increase. 2) As diameters of the target decrease from 250mm to 60 mm, both the penetration depth and calculation time decrease. 3) As the yield stress which is one of the material property of the target decreases, the penetration depth increases. 4) The boundary condition with the fixed side surface of the target gives more penetration depth than that with the fixed side and rear surfaces. By using above finding, the input parameters can be tuned to minimize the error between simulation and experiments. By using simulation tool, ANSYS, with delicately tuned input parameters, penetration analysis can be done on computer without actual experiments. The data of penetration experiments are usually hard to get because of security reasons and only published papers provide them in the limited target material. The next step of this research is to generalize this approach to anticipate the penetration depth by interpolating the known penetration experiments. This result may not be accurate enough to be used to replace the penetration experiments, but those simulations can be used in the early stage of the design process of AGCV in modelling and simulation stage.

Keywords: ANSYS, input parameters, penetration depth, sensitivity analysis

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Authors: Pooja Sharma

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In the present paper the effects of radiation is studied on unsteady flow of viscous incompressible electrically conducting fluid past a vertical porous plate embedded in the porous medium in the presence of constant heat flux. A uniform Transverse Magnetic field is considered and induced magnetic field is supposed as negligible. The non-linear governing equations are solved numerically. Numerical results of the velocity and temperature fields are shown through graphs. The results illustrates that the appropriator combination of regulated values of thermo-physical parameters is expedient for controlling the flow system.

Keywords: heat transfer, radiation, MHD flow, porous medium

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Authors: Stefano M. Spagocci

Abstract:

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

Procedia PDF Downloads 68

Authors: Mahdi Goharrokhi, Rasool Shiri, Eiraj Naser

Abstract:

A depropanizer column of a particular refinery was redesigned in this work. That is, minimum reflux ratio, minimum number of trays, feed tray location and the hydraulic characteristics of the tower were calculated and compared with the actual values of the existing tower. To Design review of the tower, fundamental equations were used to develop software which its results were compared with two commercial software results. In each case PR EOS was used. Based on the total energy consumption in reboiler and condenser, feed tray location was also determined using case study definition for tower.

Keywords: column, hydraulic design, pressure drop, energy consumption

Procedia PDF Downloads 424

Authors: Tomohiko Utsuki, Kyoka Sato

Abstract:

In emergency medicine, it is recognized that brain resuscitation is very important for the reduction of mortality rate and neurological sequelae. Especially, the control of brain temperature (BT), intracranial pressure (ICP), and cerebral blood flow (CBF) are most required for stabilizing brain’s physiological state in the treatment for such as brain injury, stroke, and encephalopathy. However, the manual control of BT, ICP, and CBF frequently requires the decision and operation of medical staff, relevant to medication and the setting of therapeutic apparatus. Thus, the integration and the automation of the control of those is very effective for not only improving therapeutic effect but also reducing staff burden and medical cost. For realizing such integration and automation, a mathematical model of brain physiological state is necessary as the controlled object in simulations, because the performance test of a prototype of the control system using patients is not ethically allowed. A model of cerebral blood circulation has already been constructed, which is the most basic part of brain physiological state. Also, a migration model of extracellular fluid in brain has been constructed, however the condition that the total volume of intracranial cavity is almost changeless due to the hardness of cranial bone has not been considered in that model. Therefore, in this research, the dynamic migration model of extracellular fluid in brain was constructed on the consideration of the changelessness of intracranial cavity’s total volume. This model is connectable to the cerebral blood circulation model. The constructed model consists of fourteen compartments, twelve of which corresponds to perfused area of bilateral anterior, middle and posterior cerebral arteries, the others corresponds to cerebral ventricles and subarachnoid space. This model enable to calculate the migration of tissue fluid from capillaries to gray matter and white matter, the flow of tissue fluid between compartments, the production and absorption of cerebrospinal fluid at choroid plexus and arachnoid granulation, and the production of metabolic water. Further, the volume, the colloid concentration, and the tissue pressure of/in each compartment are also calculable by solving 40-dimensional non-linear simultaneous differential equations. In this research, the obtained model was analyzed for its validation under the four condition of a normal adult, an adult with higher cerebral capillary pressure, an adult with lower cerebral capillary pressure, and an adult with lower colloid concentration in cerebral capillary. In the result, calculated fluid flow, tissue volume, colloid concentration, and tissue pressure were all converged to suitable value for the set condition within 60 minutes at a maximum. Also, because these results were not conflict with prior knowledge, it is certain that the model can enough represent physiological state of brain under such limited conditions at least. One of next challenges is to integrate this model and the already constructed cerebral blood circulation model. This modification enable to simulate CBF and ICP more precisely due to calculating the effect of blood pressure change to extracellular fluid migration and that of ICP change to CBF.

Keywords: dynamic model, cerebral extracellular migration, brain resuscitation, automatic control

Procedia PDF Downloads 156

Authors: Abdulali Bashir Ben Saleh

Abstract:

The powdered beet red roots (PBRR) were used as an adsorbent to remove dyes namely methylene blue dye (as a typical cationic or basic dye) from aqueous solutions. The present study shows that used beet red roots powder exhibit adsorption trend for the dye. The adsorption processes were carried out at various conditions of concentrations, processing time and a wide range of pH between 2.5-11. Adsorption isotherm equations such as Freundlich, and Langmuir were applied to calculate the values of respective constants. Adsorption study was found that the currently introduced adsorbent can be used to remove cationic dyes such as methylene blue from aqueous solutions.

Keywords: beet red root, removal of deys, methylene blue, adsorption

Procedia PDF Downloads 333