Search results for: simultaneous equations approach

Authors: Luong A. Nguyen, Elihu Deneke, Thomas L. Harman

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This paper describes a multibody dynamics algorithm formulated for parallel implementation on multiprocessor computing platforms using the divide-and-conquer approach. The system of interest is a general topology of rigid and elastic articulated bodies with or without loops. The algorithm is an extension of Featherstone’s divide and conquer approach to include the flexible-body dynamics formulation. The equations of motion, configured for the International Space Station (ISS) with its robotic manipulator arm as a system of articulated flexible bodies, are implemented in separate computer processors. The performance of this divide-and-conquer algorithm implementation in multiple processors is compared with an existing method implemented on a single processor.

Keywords: multibody dynamics, multiple processors, multithreading, divide-and-conquer algorithm, computational efficiency, flexible body dynamics

Procedia PDF Downloads 325

Authors: Mohammadreza Nezamirad, Sepideh Amirahmadian, Nasim Sabetpour, Azadeh Yazdi, Amirmasoud Hamedi

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Cavitation inside the diesel injector nozzle is investigated numerically in this study. Reynolds Stress Navier Stokes set of equations (RANS) are utilized to investigate flow behavior inside the nozzle numerically. Moreover, K-ε turbulent model is found to be a better approach comparing to K-ω turbulent model. Winklhofer rectangular shape nozzle is also simulated in order to verify the current numerical scheme, and with, mass flow rate approach, the current solution is verified. Afterward, a six-hole real-size nozzle was simulated, and it was found that among different fuels used in this study with the same condition, diesel fuel provides the largest length of cavitation. Also, it was found that at the same boundary condition, RME fuel leads to the highest value of discharge coefficient and mass flow rate.

Keywords: cavitation, diesel fuel, CFD, real size nozzle, discharge coefficient

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

Procedia PDF Downloads 326

Authors: Amor Jnifene, Cedric Cocaud

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One of the most constraining problems facing the development of autonomous vehicles is the limitations of current technologies. Guidance and navigation controllers need to be faster and more robust. Communication data links need to be more reliable and secure. For an Unmanned Aerial Vehicles (UAV) to be useful, and fully autonomous, one important feature that needs to be an integral part of the navigation system is autonomous trajectory planning. The work discussed in this paper presents a method for on-line trajectory planning for UAV’s. This method takes into account various constraints of different types including specific vectors of approach close to target points, multiple objectives, and other constraints related to speed, altitude, and obstacle avoidance. The trajectory produced by the proposed method ensures a smooth transition between different segments, satisfies the minimum curvature imposed by the dynamics of the UAV, and finds the optimum velocity based on available atmospheric conditions. Given a set of objective points and waypoints a skeleton of the trajectory is constructed first by linking all waypoints with straight segments based on the order in which they are encountered in the path. Secondly, vectors of approach (VoA) are assigned to objective waypoints and their preceding transitional waypoint if any. Thirdly, the straight segments are replaced by 3D curvilinear trajectories taking into account the aircraft dynamics. In summary, this work presents a method for on-line 3D trajectory generation (TG) of Unmanned Aerial Vehicles (UAVs). The method takes as inputs a series of waypoints and an optional vector of approach for each of the waypoints. Using a dynamic model based on the performance equations of fixed wing aircrafts, the TG computes a set of 3D parametric curves establishing a course between every pair of waypoints, and assembling these sets of curves to construct a complete trajectory. The algorithm ensures geometric continuity at each connection point between two sets of curves. The geometry of the trajectory is optimized according to the dynamic characteristics of the aircraft such that the result translates into a series of dynamically feasible maneuvers. In summary, this work presents a method for on-line 3D trajectory generation (TG) of Unmanned Aerial Vehicles (UAVs). The method takes as inputs a series of waypoints and an optional vector of approach for each of the waypoints. Using a dynamic model based on the performance equations of fixed wing aircraft, the TG computes a set of 3D parametric curves establishing a course between every pair of waypoints, and assembling these sets of curves to construct a complete trajectory. The algorithm ensures geometric continuity at each connection point between two sets of curves. The geometry of the trajectory is optimized according to the dynamic characteristics of the aircraft such that the result translates into a series of dynamically feasible maneuvers.

Keywords: trajectory planning, unmanned autonomous air vehicle, vector of approach, waypoints

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Authors: Cosmas Pandit Pagwiwoko, Ammar Khaled Abdelaziz Abdelsamia

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Flutter as a phenomenon of flow-induced and self-excited vibration has to be recognized considering its harmful effect on the structure especially in a stage of aircraft design. This phenomenon is also important for a wind energy harvester based on the fluttering surface due to its effective operational velocity range. This multi-physics occurrence can be presented by two governing equations in both fluid and structure simultaneously in respecting certain boundary conditions on the surface of the body. In this work, the equations are resolved separately by two distinct solvers, one-time step of each domain. The modelling and simulation of this flow-structure interaction in ANSYS show the effectiveness of this loosely coupled method in representing flutter phenomenon however the process is time-consuming for design purposes. Therefore, another technique using the same weak coupled aero-structure is proposed by using system dynamics approach. In this technique, the aerodynamic forces were calculated using singularity function for a range of frequencies and certain natural mode shapes are transformed into time domain by employing an approximation model of fraction rational function in Laplace variable. The representation of structure in a multi-degree-of-freedom coupled with a transfer function of aerodynamic forces can then be simulated in time domain on a block-diagram platform such as Simulink MATLAB. The dynamic response of flutter at certain velocity can be evaluated with another established flutter calculation in frequency domain k-method. In this method, a parameter of artificial structural damping is inserted in the equation of motion to assure the energy balance of flow and vibrating structure. The simulation in time domain is particularly interested as it enables to apply the structural non-linear factors accurately. Experimental tests on a fluttering airfoil in the wind tunnel are also conducted to validate the method.

Keywords: flutter, flow-induced vibration, flow-structure interaction, non-linear structure

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Authors: Maryam Ebrahimpour, Amir Ebrahimi

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This paper presents the steady-state amplitude analysis of MOS Colpitts oscillator with short channel device. The proposed method is based on a large signal analysis and the nonlinear differential equations that govern the oscillator circuit behaviour. Also, the short channel effects are considered in the proposed analysis and analytical equations for finding the steady-state oscillation amplitude are derived. The output voltage calculated from this analysis is in excellent agreement with simulations for a wide range of circuit parameters.

Keywords: colpitts oscillator, CMOS, electronics, circuits

Procedia PDF Downloads 346

Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin

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This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.

Keywords: CAM, multi-axis milling machining, transformation matrix, rotation angles

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Authors: Ming-Yeh Lu, Shiao-Shing Chen, Saikat Sinha Ray, Hung-Te Hsu

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Recently, anaerobic membrane bioreactors (AnMBRs) has been widely utilized, which combines anaerobic biological treatment process and membrane filtration, that can be present an attractive option for wastewater treatment and water reuse. Conventional AnMBR is having several advantages, such as improving effluent quality, compact space usage, lower sludge yield, without aeration and production of energy. However, the removal of nitrogen and phosphorus in the AnMBR permeate was negligible which become the biggest disadvantage. In recent years, forward osmosis (FO) is an emerging technology that utilizes osmotic pressure as driving force to extract clean water without additional external pressure. The pore size of FO membrane is kindly mentioned the pore size, so nitrogen or phosphorus could effectively improve removal of nitrogen or phosphorus. Anaerobic bioreactor with FO membrane (AnOMBR) can retain the concentrate organic matters and nutrients. However, phosphorus is a non-renewable resource. Due to the high rejection property of FO membrane, the high amount of phosphorus could be recovered from the combination of AnMBR and FO. In this study, development of novel submerged anaerobic osmotic membrane bioreactor integrated with periodic microfiltration (MF) extraction for simultaneous phosphorus and clean water recovery from wastewater was evaluated. A laboratory-scale AnOMBR utilizes cellulose triacetate (CTA) membranes with effective membrane area of 130 cm² was fully submerged into a 5.5 L bioreactor at 30-35℃. Active layer-facing feed stream orientation was utilized, for minimizing fouling and scaling. Additionally, a peristaltic pump was used to circulate draw solution (DS) at a cross flow velocity of 0.7 cm/s. Magnesium sulphate (MgSO₄) solution was used as DS. Microfiltration membrane periodically extracted about 1 L solution when the TDS reaches to 5 g/L to recover phosphorus and simultaneous control the salt accumulation in the bioreactor. During experiment progressed, the average water flux was achieved around 1.6 LMH. The AnOMBR process show greater than 95% removal of soluble chemical oxygen demand (sCOD), nearly 100% of total phosphorous whereas only partial removal of ammonia, and finally average methane production of 0.22 L/g sCOD was obtained. Therefore, AnOMBR system periodically utilizes MF membrane extracted for phosphorus recovery with simultaneous pH adjustment. The overall performance demonstrates that a novel submerged AnOMBR system is having potential for simultaneous wastewater treatment and resource recovery from wastewater, and hence, the new concept of this system can be used to replace for conventional AnMBR in the future.

Keywords: anaerobic treatment, forward osmosis, phosphorus recovery, membrane bioreactor

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Authors: Fatemeh Nemati, Lucinda Leonard, Gwyn Lintern, Richard Thomson

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In this study, we will use modern numerical modeling approaches to estimate tsunami risks to the southern coast of British Columbia from landslides. Wave generation is to be simulated using the NHWAVE model, which solves the Navier-Stokes equations due to the more complex behavior of flow near the landslide source; far-field wave propagation will be simulated using the simpler model FUNWAVE_TVD with high-order Boussinesq-type wave equations, with a focus on the accurate simulation of wave propagation and regional- or coastal-scale inundation predictions.

Keywords: FUNWAVE-TVD, landslide-generated tsunami, NHWAVE, tsunami risk

Procedia PDF Downloads 147

Authors: Azmawati Mohammed Nawi, Siok-Fong Chin, Shamsul Azhar Shah, Rahman Jamal

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In recent years, trace elements have gained importance as biomarkers in many chronic diseases. Unfortunately, the requirement for sample volume increases according to the extent of investigation for diagnosis or elucidating the mechanism of the disease. Here, we describe the method development and validation for simultaneous determination of 25 trace elements (lithium (Li), beryllium (Be), magnesium (Mg), aluminium (Al), vanadium (V), chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), copper (Cu), zinc (Zn), gallium (Ga), arsenic (As), selenium (Se), rubidium (Rb), strontium (Sr), silver (Ag), cadmium (Cd), caesium (Cs), barium (Ba), mercury (Hg), thallium (Tl), lead (Pb), uranium (U)) using just 20 µL of human serum. Serum samples were digested with nitric acid and hydrochloric acid (ratio 1:1, v/v) and analysed using inductively coupled plasma–mass spectrometry (ICP-MS). Seronorm®, a human-derived serum control material was used as quality control samples. The intra-day and inter-day precisions were consistently < 15% for all elements. The validated method was later applied to 30 human serum samples to evaluate its suitability. In conclusion, we have successfully developed and validated a precise and accurate analytical method for determining 25 trace elements requiring very low volume of human serum.

Keywords: acid digestion, ICP-MS, trace element, serum

Procedia PDF Downloads 177

Authors: Ranjith Maniyeri, Ahamed C. Saleel

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Two-dimensional fluid flow over a stationary circular cylinder is one of the bench mark problem in the field of fluid-structure interaction in computational fluid dynamics (CFD). Motivated by this, in the present work, a two-dimensional computational model is developed using an improved version of immersed boundary method which combines the feedback forcing scheme of the virtual boundary method with Peskin’s regularized delta function approach. Lagrangian coordinates are used to represent the cylinder and Eulerian coordinates are used to describe the fluid flow. A two-dimensional Dirac delta function is used to transfer the quantities between the sold to fluid domain. Further, continuity and momentum equations governing the fluid flow are solved using fractional step based finite volume method on a staggered Cartesian grid system. The developed code is validated by comparing the values of drag coefficient obtained for different Reynolds numbers with that of other researcher’s results. Also, through numerical simulations for different Reynolds numbers flow behavior is well captured. The stability analysis of the improved version of immersed boundary method is tested for different values of feedback forcing coefficients.

Keywords: Feedback Forcing Scheme, Finite Volume Method, Immersed Boundary Method, Navier-Stokes Equations

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Alireza Rafie Boldaji, Ahmad Saboonchi

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Chokes are commonly used in oil and gas production systems. A choke is a restriction basically designed to control flow rates of oil and gas wells, to prevent the downstream disturbances from propagating upstream (critical flow), and to protect the surface equipment facilities against slugging at high flowing pressures. There are different methods to calculate the multiphase flow rate, one of the multiphase flow measurement methods is the separation and measurement by on¬e-phaseFlow meter, another common method is the use of movable separator, their operations are very labor-intensive and costly. The current method used is based on the flow differential pressure on both sides of choke. Three groups of correlations describing two-phase flow through wellhead chokes were examined. The first group involved simple empirical equations similar to those of Gilbert, the second group comprised derived equations of two-phase flow incorporating PVT properties, and third group is computational method. In the article we calculate the flow of oil and gas through choke with simulation of this two phase flow bye computational fluid dynamic method, we use Ansys- fluent for this simulation and finally compared results of computational simulation whit empirical equations, the results show good agreement between experimental and numerical results.

Keywords: CFD, two-phase, choke, critical

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Authors: Medine Demir, Volker John

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Fluid equations in a rotating frame of reference have a broad class of important applications in meteorology and oceanography, especially in the large-scale flows considered in ocean and atmosphere, as well as many physical and industrial applications. The Coriolis and the centripetal forces, resulting from the rotation of the earth, play a crucial role in such systems. For such applications it may be required to solve the system in complex three-dimensional geometries. In recent years, the Navier--Stokes equations in a rotating frame have been investigated in a number of papers using the classical inf-sup stable mixed methods, like Taylor-Hood pairs, to contribute to the analysis and the accurate and efficient numerical simulation. Numerical analysis reveals that these classical methods introduce a pressure-dependent contribution in the velocity error bounds that is proportional to some inverse power of the viscosity. Hence, these methods are optimally convergent but small velocity errors might not be achieved for complicated pressures and small viscosity coefficients. Several approaches have been proposed for improving the pressure-robustness of pairs of finite element spaces. In this contribution, a pressure-robust space discretization of the incompressible Navier--Stokes equations in a rotating frame of reference is considered. The discretization employs divergence-free, $H^1$-conforming mixed finite element methods like Scott--Vogelius pairs. However, this approach might come with a modification of the meshes, like the use of barycentric-refined grids in case of Scott--Vogelius pairs. However, this strategy requires the finite element code to have control on the mesh generator which is not realistic in many engineering applications and might also be in conflict with the solver for the linear system. An error estimate for the velocity is derived that tracks the dependency of the error bound on the coefficients of the problem, in particular on the angular velocity. Numerical examples illustrate the theoretical results. The idea of pressure-robust method could be cast on different types of flow problems which would be considered as future studies. As another future research direction, to avoid a modification of the mesh, one may use a very simple parameter-dependent modification of the Scott-Vogelius element, the pressure-wired Stokes element, such that the inf-sup constant is independent of nearly-singular vertices.

Keywords: navier-stokes equations in a rotating frame of refence, coriolis force, pressure-robust error estimate, scott-vogelius pairs of finite element spaces

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Authors: Hassan Youssef Mohamed

Abstract:

In this paper, we show new wave equations, and by using the equations, we concluded that the strong force and the weak force are not fundamental, but they are quantum effects for electromagnetism. This result is different from the current scientific understanding about strong and weak interactions at all. So, we introduce three evidences for our theory. First, we prove the asymptotic freedom phenomenon in the strong force by using our model. Second, we derive the nuclear shell model as an approximation of our model. Third, we prove that the leptons do not participate in the strong interactions, and we prove the short ranges of weak and strong interactions. So, our model is consistent with the current understanding of physics. Finally, we introduce the electron-positron model as the basic ingredients for protons, neutrons, and all matters, so we can study all particles interactions and nuclear interaction as many-body problems of electrons and positrons. Also, we prove the violation of parity conservation in weak interaction as evidence of our theory in the weak interaction. Also, we calculate the average of the binding energy per nucleon.

Keywords: new wave equations, the strong force, the grand unification theory, hydrogen atom, weak force, the nuclear shell model, the asymptotic freedom, electron-positron model, the violation of parity conservation, the binding energy

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Authors: Muhammad Umar Kiani, Muhammad Shahbaz, Hassan Akbar

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Simulation of a high speed inviscid steady ideal air flow around a 2D/axial-symmetry body was carried out by the use of mb_cns code. mb_cns is a program for the time-integration of the Navier-Stokes equations for two-dimensional compressible flows on a multiple-block structured mesh. The flow geometry may be either planar or axisymmetric and multiply-connected domains can be modeled by patching together several blocks. The main simulation code is accompanied by a set of pre and post-processing programs. The pre-processing programs scriptit and mb_prep start with a short script describing the geometry, initial flow state and boundary conditions and produce a discretized version of the initial flow state. The main flow simulation program (or solver as it is sometimes called) is mb_cns. It takes the files prepared by scriptit and mb_prep, integrates the discrete form of the gas flow equations in time and writes the evolved flow data to a set of output files. This output data may consist of the flow state (over the whole domain) at a number of instants in time. After integration in time, the post-processing programs mb_post and mb_cont can be used to reformat the flow state data and produce GIF or postscript plots of flow quantities such as pressure, temperature and Mach number. The current problem is an example of supersonic inviscid flow. The flow domain for the current problem (strake configuration wing) is discretized by a structured grid and a finite-volume approach is used to discretize the conservation equations. The flow field is recorded as cell-average values at cell centers and explicit time stepping is used to update conserved quantities. MUSCL-type interpolation and one of three flux calculation methods (Riemann solver, AUSMDV flux splitting and the Equilibrium Flux Method, EFM) are used to calculate inviscid fluxes across cell faces.

Keywords: steady flow simulation, processing programs, simulation code, inviscid flux

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Authors: Tala Toonsi, Marah Alagha, Lina Alnowaiser, Hala Rajab

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This report is about the Photomath app, which is an AI application that uses image recognition technology, specifically optical character recognition (OCR) algorithms. The (OCR) algorithm translates the images into a mathematical equation, and the app automatically provides a step-by-step solution. The application supports decimals, basic arithmetic, fractions, linear equations, and multiple functions such as logarithms. Testing was conducted to examine the usage of this app, and results were collected by surveying ten participants. Later, the results were analyzed. This paper seeks to answer the question: To what level the artificial intelligence features are accurate and the speed of process in this app. It is hoped this study will inform about the efficiency of AI in Photomath to the users.

Keywords: photomath, image recognition, app, OCR, artificial intelligence, mathematical equations.

Procedia PDF Downloads 165

Authors: Ming-Yeh Lu, Shiao-Shing Chen, Saikat Sinha Ray, Hung-Te Hsu

Abstract:

The submerged anaerobic osmotic membrane bioreactor (AnOMBR) integrated with periodic microfiltration (MF) extraction for simultaneous phosphorus and clean water recovery from wastewater was evaluated. A laboratory-scale AnOMBR used cellulose triacetate (CTA) membranes with effective membrane area of 130 cm² was fully submerged into a 5 L bioreactor at 30-35 ℃. Active layer was orientated to feed stream for minimizing membrane fouling and scaling. Additionally, a peristaltic pump was used to circulate magnesium sulphate (MgSO₄) solution applied as draw solution (DS). Microfiltration membrane periodically extracted about 1 L solution when the TDS reaches to 5 g/L to recover phosphorus and simultaneously control the salt accumulation in the bioreactor. During experiment progress, the average water flux was around 1.6 LMH. The AnOMBR process showed greater than 95% removal of soluble chemical oxygen demand (sCOD), nearly 100% of total phosphorous whereas only partial of ammonia was removed. On the other hand, the average methane production of 0.22 L/g sCOD was obtained. Subsequently, the overall performance demonstrates that a novel submerged AnOMBR system is potential for simultaneous wastewater treatment and resource recovery from wastewater. Therefore, the new concept of this system can be used to replace for the conventional AnMBR in the future.

Keywords: anaerobic treatment, forward osmosis, phosphorus recovery, membrane bioreactor

Procedia PDF Downloads 225

Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

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This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

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Authors: Saeed Otarod

Abstract:

In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Hafiz Muhammad Fazalehaq

Abstract:

This paper documents the results of a longitudinal study done on two bilingual children who speak English and Punjabi simultaneously. Their father is a native English speaker whereas their mother speaks Punjabi. Their mother can speak both the languages (English and Punjabi) whereas their father only speaks English. At the age of six, these children have difficulty in creative thinking and of course creative writing. So, the first task for the researcher is to impress and entice the children to think creatively. Various and different methodologies and techniques were used to entice them to start thinking creatively. Creative thinking leads to creative writing. These children were exposed to numerous sources including videos, photographs, texts and audios at first place in order to have a taste of creative genres (stories in this case). The children were encouraged to create their own stories sometimes with photographs and sometimes by using their favorite toys. At a second stage, they were asked to write about an event or incident. After that, they were motivated to create new stories and write them. Length of their creative writing varies from a few sentences to a two standard page. After this six months’ study, the researcher was able to develop a ten steps methodology for creating and improving/enhancing creative thinking and creative writing skills of the subjects understudy. This ten-step methodology entices and motivates the learner to think creatively for producing a creative piece.

Keywords: bilinguals, creative thinking, creative writing, simultaneous bilingual

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Karim Kheloufi, El Hachemi Amara

Abstract:

In the present study, a three-dimensional transient numerical model was developed to study the temperature field and cutting kerf shape during laser fusion cutting. The finite volume model has been constructed, based on the Navier–Stokes equations and energy conservation equation for the description of momentum and heat transport phenomena, and the Volume of Fluid (VOF) method for free surface tracking. The Fresnel absorption model is used to handle the absorption of the incident wave by the surface of the liquid metal and the enthalpy-porosity technique is employed to account for the latent heat during melting and solidification of the material. To model the physical phenomena occurring at the liquid film/gas interface, including momentum/heat transfer, a new approach is proposed which consists of treating friction force, pressure force applied by the gas jet and the heat absorbed by the cutting front surface as source terms incorporated into the governing equations. All these physics are coupled and solved simultaneously in Fluent CFD®. The main objective of using a transient phase change model in the current case is to simulate the dynamics and geometry of a growing laser-cutting generated kerf until it becomes fully developed. The model is used to investigate the effect of some process parameters on temperature fields and the formed kerf geometry.

Keywords: laser cutting, numerical simulation, heat transfer, fluid flow

Procedia PDF Downloads 327

Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

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Authors: Shahzamani Kiana, Esmaeil Lashgarian Hamed, Merat Shahin

Abstract:

HCV and GBV-C belong to the Flaviviridae family of viruses and GBV-C is the closest virus to HCV genetically. Accumulative research is in progress all over the world to clarify clinical aspects of GBV-C. Possibility of interaction between HCV and GBV-C and also its consequence with other liver diseases are the most important clinical aspects which encourage researchers to develop a technique for simultaneous detection of these viruses. In this study a SYBR Green multiplex real time RT-PCR technique as a new economical and sensitive method was optimized for simultaneous detection of HCV/GBV-C in HCV positive plasma samples. After designing and selection of two pairs of specific primers for HCV and GBV-C, SYBR Green Real time RT-PCR technique optimization was performed separately for each virus. Establishment of multiplex PCR was the next step. Finally our technique was performed on positive and negative plasma samples. 89 cirrhotic HCV positive plasma samples (29 of genotype 3 a and 27 of genotype 1a) were collected from patients before receiving treatment. 14% of genotype 3a and 17.1% of genotype 1a showed HCV/GBV-C co-infection. As a result, 13.48% of 89 samples had HCV/GBV-C co-infection that was compatible with other results from all over the world. Data showed no apparent influence of HGV co-infection on the either clinical or virological aspect of HCV infection. Furthermore, with application of multiplex Real time RT-PCR technique, more time and cost could be saved in clinical-research settings.

Keywords: HCV, GBV-C, cirrhotic patients, multiplex real time RT- PCR

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Chokri Slim

Abstract:

The relative failure of simultaneous equation models in the seventies has led researchers to turn to other approaches that take into account the dynamics of economic and financial systems. In this paper, we use an approach based on vector autoregressive model that is widely used in recent years. Their popularity is due to their flexible nature and ease of use to produce models with useful descriptive characteristics. It is also easy to use them to test economic hypotheses. The standard econometric techniques assume that the series studied are stable over time (stationary hypothesis). Most economic series do not verify this hypothesis, which assumes, when one wishes to study the relationships that bind them to implement specific techniques. This is cointegration which characterizes non-stationary series (integrated) with a linear combination is stationary, will also be presented in this paper. Since the work of Johansen, this approach is generally presented as part of a multivariate analysis and to specify long-term stable relationships while at the same time analyzing the short-term dynamics of the variables considered. In the empirical part, we have applied these concepts to study the dynamics of of the exchange rate in Tunisia, which is one of the most important economic policy of a country open to the outside. According to the results of the empirical study by the cointegration method, there is a cointegration relationship between the exchange rate and its determinants. This relationship shows that the variables have a significant influence in determining the exchange rate in Tunisia.

Keywords: stationarity, cointegration, dynamic models, causality, VECM models

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Authors: Manana Chumburidze

Abstract:

We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method.

Keywords: thermo-piezoelectricity, boundary value problems, Fourier's series, isotropic homogeneous elastic media

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Authors: Ishit Sheth, Chandrasekhar Jinendran, Chinmaya Ranjan Sahu

Abstract:

A fourteen degree of freedom (DOF) ride and handling control mathematical model is developed for a car using generalized boltzmann hamel equation which will create a basis for design of ride and handling controller. Mathematical model developed yield equations of motion for non-holonomic constrained systems in quasi-coordinates. The governing differential equation developed integrates ride and handling control of car. Model-based systems engineering approach is implemented for simulation using matlab/simulink, vehicle’s response in different DOF is examined and later validated using commercial software (ADAMS). This manuscript involves detailed derivation of full car vehicle model which provides response in longitudinal, lateral and yaw motion to demonstrate the advantages of the developed model over the existing dynamic model. The dynamic behaviour of the developed ride and handling model is simulated for different road conditions.

Keywords: Full Vehicle Model, MBSE, Non Holonomic Constraints, Boltzmann Hamel Equation

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Authors: Julien Deborde, Thomas Milcent, Stéphane Glockner, Pierre Lubin

Abstract:

A fully Eulerian method is developed to solve the problem of fluid-elastic structure interactions based on a 1-fluid method. The interface between the fluid and the elastic structure is captured by a level set function, advected by the fluid velocity and solved with a WENO 5 scheme. The elastic deformations are computed in an Eulerian framework thanks to the backward characteristics. We use the Neo Hookean or Mooney Rivlin hyperelastic models and the elastic forces are incorporated as a source term in the incompressible Navier-Stokes equations. The velocity/pressure coupling is solved with a pressure-correction method and the equations are discretized by finite volume schemes on a Cartesian grid. The main difficulty resides in that large deformations in the fluid cause numerical instabilities. In order to avoid these problems, we use a re-initialization process for the level set and linear extrapolation of the backward characteristics. First, we verify and validate our approach on several test cases, including the benchmark of FSI proposed by Turek. Next, we apply this method to study the wave damping phenomenon which is a mean to reduce the waves impact on the coastline. So far, to our knowledge, only simulations with rigid or one dimensional elastic structure has been studied in the literature. We propose to place elastic structures on the seabed and we present results where 50 % of waves energy is absorbed.

Keywords: damping wave, Eulerian formulation, finite volume, fluid structure interaction, hyperelastic material

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