Search results for: non-linear differential equations

Authors: Ahmed Alghurabi, Mysara Mohyaldinn, Shiferaw Jufar, Obai Younis, Abdullah Abduljabbar

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Erosion modeling equations were typically acquired from regulated experimental trials for solid particles entrained in single-phase or multi-phase flows. Evidently, those equations were later employed to predict the erosion damage caused by the continuous impacts of solid particles entrained in streamflow. It is also well-known that the particle impact angle and velocity do not change drastically in gas-sand flow erosion prediction; hence an accurate prediction of erosion can be projected. On the contrary, high-density fluid flows, such as water flow, through complex geometries, such as sand screens, greatly affect the sand particles’ trajectories/tracks and consequently impact the erosion rate predictions. Particle tracking models and erosion equations are frequently applied simultaneously as a method to improve erosion visualization and estimation. In the present work, computational fluid dynamic (CFD)-based erosion modeling was performed using a commercially available software; ANSYS Fluent. The continuous phase (water flow) behavior was simulated using the realizable K-epsilon model, and the secondary phase (solid particles), having a 5% flow concentration, was tracked with the help of the discrete phase model (DPM). To accomplish a successful erosion modeling, three erosion equations from the literature were utilized and introduced to the ANSYS Fluent software to predict the screen wire-slot velocity surge and estimate the maximum erosion rates on the screen surface. Results of turbulent kinetic energy, turbulence intensity, dissipation rate, the total pressure on the screen, screen wall shear stress, and flow velocity vectors were presented and discussed. Moreover, the particle tracks and path-lines were also demonstrated based on their residence time, velocity magnitude, and flow turbulence. On one hand, results from the utilized erosion equations have shown similarities in screen erosion patterns, locations, and DPM concentrations. On the other hand, the model equations estimated slightly different values of maximum erosion rates of the wire-wrapped screen. This is solely based on the fact that the utilized erosion equations were developed with some assumptions that are controlled by the experimental lab conditions.

Keywords: CFD simulation, erosion rate prediction, material loss due to erosion, water-sand flow

Procedia PDF Downloads 163

Authors: Christopher Spiewak, M. R. Islam, Mohammad Arifur Rahaman, Mohammad H. Rahman, Roger Smith, Maarouf Saad

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For those who have lost the ability to move their hand, going through repetitious motions with the assistance of a therapist is the main method of recovery. We have been developed a robotic assistive device to rehabilitate the hand motions in place of the traditional therapy. The developed assistive device (RAD-HR) is comprised of four degrees of freedom enabling basic movements, hand function, and assists in supporting the hand during rehabilitation. We used a nonlinear computed torque control technique to control the RAD-HR. The accuracy of the controller was evaluated in simulations (MATLAB/Simulink environment). To see the robustness of the controller external disturbance as modelling uncertainty (±10% of joint torques) were added in each joints.

Keywords: biorobotics, rehabilitation, robotic assistive device, exoskeleton, nonlinear control

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Authors: X. Wang, J. S. Kuang

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The Fixed-angle Softened Truss Model with Tension-stiffening (FASTMT) has a superior performance in predicting the shear behaviour of reinforced concrete (RC) membrane elements, especially for the post-cracking behaviour. Nevertheless, massive computational work is inevitable due to the multiple transcendental equations involved in the stress-strain relationship. In this paper, an iterative root-finding technique is introduced to FASTMT for solving quickly the transcendental equations of the tension-stiffening effect of RC membrane elements. This fast FASTMT, which performs in MATLAB, uses the bisection method to calculate the tensile stress of the membranes. By adopting the simplification, the elapsed time of each loop is reduced significantly and the transcendental equations can be solved accurately. Owing to the high efficiency and good accuracy as compared with FASTMT, the fast FASTMT can be further applied in quick prediction of shear behaviour of complex large-scale RC structures.

Keywords: bisection method, FASTMT, iterative root-finding technique, reinforced concrete membrane

Procedia PDF Downloads 271

Authors: Tahseen Saad, Halim Ceylan, Jonathan Weaver, Osman Nuri Çelik, Onur Gungor Sahin

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A new concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. To control the coordination problem, which depends on offset selection and to estimate uniform delay based on the offset choice in a traffic signal network. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and are compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show new model minimizes the total uniform delay to almost half compared to conventional models. The mathematical objective function is robust. The algorithm convergence time is fast.

Keywords: area traffic control, traffic flow, differential evolution, sinusoidal periodic function, uniform delay, offset variable

Procedia PDF Downloads 276

Authors: T. Watanabe

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Combustion analysis of suspended sodium droplet is performed by solving numerically the Navier-Stokes equations and the energy conservation equations. The combustion model consists of the pre-ignition and post-ignition models. The reaction rate for the pre-ignition model is based on the chemical kinetics, while that for the post-ignition model is based on the mass transfer rate of oxygen. The calculated droplet temperature is shown to be in good agreement with the existing experimental data. The temperature field in and around the droplet is obtained as well as the droplet shape variation, and the present numerical model is confirmed to be effective for the combustion analysis.

Keywords: analysis, combustion, droplet, sodium

Procedia PDF Downloads 211

Authors: Eddegdag Nasser, Naamane Azzeddine, Radouani Mohammed, Ensam Meknes

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In this study, we are interested in the asymptotic modeling of the two-dimensional stationary supersonic flow of a viscous compressible fluid around wing airfoil. The aim of this article is to solve the partial differential equations of the flow far from the leading edge and near the wall using the triple-deck technique is what brought again in precision according to the principle of least degeneration. In order to validate our theoretical model, these obtained results will be compared with the experimental results. The comparison of the results of our model with experimentation has shown that they are quantitatively acceptable compared to the obtained experimental results. The experimental study was conducted using the AF300 supersonic wind tunnel and a NACA Reduced airfoil model with two pressure Taps on extrados. In this experiment, we have considered the incident upstream supersonic Mach number over a dissymmetric NACA airfoil wing. The validation and the accuracy of the results support our model.

Keywords: supersonic, viscous, triple deck technique, asymptotic methods, AF300 supersonic wind tunnel, reduced airfoil model

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Authors: Mengxiao Li, Johnson Zhang

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Currently, topology optimization technique is widely used to define the layout design of structures that are presented as truss-like topologies. However, due to the difficulty in combining optimization technique with more realistic material models where their nonlinear properties should be considered, the achieved optimized topologies are commonly unable to apply straight towards the practical design problems. This study presented an optimization procedure of composite structures where different elastic stiffness, yield criteria, and hardening models are assumed for the candidate materials. From the results, it can be concluded that a more explicit modeling has the significant influence on the resulting topologies. Also, the isotropic or kinematic hardening is important for elastoplastic structural optimization design. The capability of the proposed optimization procedure is shown through several cases.

Keywords: topology optimization, material composition, nonlinear modeling, hardening rules

Procedia PDF Downloads 482

Authors: Basant Singh Sikarwar, Mukesh Roy, Ayush Goyal, Priya Ranjan

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This work combines two bodies of knowledge which includes biomedical basis of blood stain formation and fluid communities’ wisdom that such formation of blood stain depends heavily on physical properties. Moreover biomedical research tells that different patterns in stains of blood are robust indicator of blood donor’s health or lack thereof. Based on these valuable insights an innovative screening tool is proposed which can act as an aide in the diagnosis of diseases such Anemia, Hyperlipidaemia, Tuberculosis, Blood cancer, Leukemia, Malaria etc., with enhanced confidence in the proposed analysis. To realize this powerful technique, simple, robust and low-cost micro-fluidic devices, a micro-capillary viscometer and a pendant drop tensiometer are designed and proposed to be fabricated to measure the viscosity, surface tension and wettability of various blood samples. Once prognosis and diagnosis data has been generated, automated linear and nonlinear classifiers have been applied into the automated reasoning and presentation of results. A support vector machine (SVM) classifies data on a linear fashion. Discriminant analysis and nonlinear embedding’s are coupled with nonlinear manifold detection in data and detected decisions are made accordingly. In this way, physical properties can be used, using linear and non-linear classification techniques, for screening of various diseases in humans and cattle. Experiments are carried out to validate the physical properties measurement devices. This framework can be further developed towards a real life portable disease screening cum diagnostics tool. Small-scale production of screening cum diagnostic devices is proposed to carry out independent test.

Keywords: blood, physical properties, diagnostic, nonlinear, classifier, device, surface tension, viscosity, wettability

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Authors: Bo Liu, Liangtian Gao, Idrees Qasim

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The impact of the storm leads to accidents even in the case of vessels that meet the computed safety criteria for stability. That is why, in order to clarify the causes of the accident and shipwreck, it is necessary to study the dynamics of the ship under the complex sudden impact of external forces. The task is to determine the movement and landing of the ship in the complex and sudden impact of external forces, i.e. when the ship's load changes over a relatively short period of time. For the solution, a technique was used to study the ship's dynamics, which is based on the compilation of a system of differential equations of motion. A coordinate system was adopted for the equation of motion of the hull and the determination of external forces. As a numerical method of integration, the 4^th order Runge-Kutta method was chosen. The results of the calculation show that dynamic deviations were lower for high-altitude vessels. The study of the movement of the hull under a difficult situation is performed: receiving of cargo, impact of a flurry of wind and subsequent displacement of the cargo. The risk of overturning and flooding was assessed.

Keywords: dynamics, statics, roll, trim, vertical displacement, dynamic load, tilt

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Authors: Partha P. Gopmandal, S. Bhattacharyya

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We investigate the thermal end effect on the pseudo-steady state behavior of the isotachophoretic transport of ionic species in a 2-D microchannel. Both ends of the channel are kept at a constant temperature which may lead to significant changes in electrophoretic migration speed. A mathematical model based on Nernst-Planck equations for transport of ions coupled with the equation for temperature field is considered. In addition, the charge conservation equations govern the potential field due to the external electric field. We have computed the equations for ion transport, potential and temperature in a coupled manner through the finite volume method. The diffusive terms are discretized via central difference scheme, while QUICK (Quadratic Upwind Interpolation Convection Kinematics) scheme is used to discretize the convective terms. We find that the thermal end effect has significant effect on the isotachophoretic (ITP) migration speed of the analyte. Our result shows that the ITP velocity for temperature dependent case no longer varies linearly with the applied electric field. A detailed analysis has been made to provide a range of the key parameters to minimize the Joule heating effect on ITP transport of analytes.

Keywords: finite volume method, isotachophoresis, QUICK scheme, thermal effect

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Authors: Julia Zimmerman, Gaurav Savant

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This study aims to evaluate the efficacy of the U.S. Army Corp of Engineers’ River Analysis System (HEC-RAS) application to modeling the hydraulics of estuaries. HEC-RAS has been broadly used for a variety of riverine applications. However, it has not been widely applied to the study of circulation in estuaries. This report details the model development and validation of a combined 1D/2D unsteady flow hydraulic model using HEC-RAS for estuaries and they are associated with tidally influenced rivers. Two estuaries, Galveston Bay and Delaware Bay, were used as case studies. Galveston Bay, a bar-built, vertically mixed estuary, was modeled for the 2005 calendar year. Delaware Bay, a drowned river valley estuary, was modeled from October 22, 2019, to November 5, 2019. Water surface elevation was used to validate both models by comparing simulation results to NOAA’s Center for Operational Oceanographic Products and Services (CO-OPS) gauge data. Simulations were run using the Diffusion Wave Equations (DW), the Shallow Water Equations, Eulerian-Lagrangian Method (SWE-ELM), and the Shallow Water Equations Eulerian Method (SWE-EM) and compared for both accuracy and computational resources required. In general, the Diffusion Wave Equations results were found to be comparable to the two Shallow Water equations sets while requiring less computational power. The 1D/2D combined approach was valid for study areas within the 2D flow area, with the 1D flow serving mainly as an inflow boundary condition. Within the Delaware Bay estuary, the HEC-RAS DW model ran in 22 minutes and had an average R² value of 0.94 within the 2-D mesh. The Galveston Bay HEC-RAS DW ran in 6 hours and 47 minutes and had an average R² value of 0.83 within the 2-D mesh. The longer run time and lower R² for Galveston Bay can be attributed to the increased length of the time frame modeled and the greater complexity of the estuarine system. The models did not accurately capture tidal effects within the 1D flow area.

Keywords: Delaware bay, estuarine hydraulics, Galveston bay, HEC-RAS, one-dimensional modeling, two-dimensional modeling

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Authors: Marcelo Jesus Kato Avila, Joao Da Costa Pantoja

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Differential settlement of foundations is a serious pathology in buildings that put at risk lives and property. A common reason for the occurrence of this specific pathology in central Brazil is the presence of collapsible clay, a typical soil in the region. In this study, the foundation of a condemned building erected above this soil is analyzed. The aim is to prevent problems in new constructions, to predict which buildings may be subjected to damages, and to make possible a more precise treatment in less advanced differential settlements observed in the buildings of the vicinity, which includes a hospital, a Military School, an indoor sporting arena, the Police Academy, and the Military Police Headquarters. The methodology consists of visual inspection, photographic report of the main pathologies, analysis of the existing foundations, determination of the soil properties, the study of the cracking level and assessment of structural failure risk of the building. The findings show that the presence of water weaken the soil structure on which the foundation rest, being the main cause of the pathologic settlement, indicating that even in a one store building it was necessary to consider deeper digging, other categories of foundations, and more elaborated and detailed foundation plans when the soil presents this behavior.

Keywords: building cracks, collapsible clay, differential settlement, structural failure risk

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Authors: Salma Parvin, M. A. Alim

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The convective and radiative heat transfer performance and entropy generation on forced convection through a direct absorption solar collector (DASC) is investigated numerically. Four different fluids, including Cu-water nanofluid, Al₂O₃-waternanofluid, TiO₂-waternanofluid, and pure water are used as the working fluid. Entropy production has been taken into account in addition to the collector efficiency and heat transfer enhancement. Penalty finite element method with Galerkin’s weighted residual technique is used to solve the governing non-linear partial differential equations. Numerical simulations are performed for the variation of mass flow rate. The outcomes are presented in the form of isotherms, average output temperature, the average Nusselt number, collector efficiency, average entropy generation, and Bejan number. The results present that the rate of heat transfer and collector efficiency enhance significantly for raising the values of m up to a certain range.

Keywords: DASC, forced convection, mass flow rate, nanofluid

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Authors: Evans Iyamu

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Genes encoding hydrophobins play distinct roles at different stages of the life cycle of fungi, and they foster hyphal attachment to surfaces. The hydrophobin Sc4 is known to provide a hydrophobic membrane lining of the gas channels within Schizophyllum commune fruiting bodies. Here, we cultivated non-fruiting, monokaryotic S. commune 12-43 on glass surfaces that could be verified by micrography. Differential gene expression profiling of nine hydrophobin genes and the hydrophobin-like sc15 gene by quantitative PCR showed significant up-regulation of sc4 when S. commune was attached to glass surfaces, also confirmed with RNA-Seq data analysis. Another silicate, namely quartz sand, was investigated, and induction of sc4 was seen as well. The up-regulation of the hydrophobin gene sc4 may indicate involvement in S. commune hyphal attachment to glass as well as quartz surfaces. We propose that the covering of hyphae by Sc4 allows for direct interaction with the hydrophobic surfaces of silicates and that differential functions of specific hydrophobin genes depend on the surface interface involved. This study could help with the clarification of the biological functions of hydrophobins in natural surroundings, including hydrophobic surface attachment. Therefore, the analysis of growth on glass serves as a basis for understanding S. commune interaction with glass surfaces while providing the possibility to visualize the interaction microscopically.

Keywords: hydrophobin, structured glass surfaces, differential gene expression, quartz sand

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Authors: Sergey Kuznetsov, Yuri Urman

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We present an approach to investigate non-linear dynamical effects occurring in the noncontact superconducting and diamagnetic suspensions, when levitated body has finite size. This approach is based on the calculation of interaction energy between spherical finite size superconducting or diamagnetic body with external magnetic field. Effects of small deviations from spherical shape may be also taken into account by introducing small corrections to the energy. This model allows investigating dynamical effects important for practical applications, such as nonlinear resonances, change of vibration plane, coupling of rotational and translational motions etc. We also show how the geometry of suspension affects various dynamical effects and how an inverse problem may be formulated to enforce or diminish various dynamical effects.

Keywords: levitation, non-linear dynamics, superconducting, diamagnetic stability

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Authors: Mohammed Farag, Mina Attari, S. Andrew Gadsden, Saeid R. Habibi

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Battery state of charge (SOC) estimation is an important parameter as it measures the total amount of electrical energy stored at a current time. The SOC percentage acts as a fuel gauge if it is compared with a conventional vehicle. Estimating the SOC is, therefore, essential for monitoring the amount of useful life remaining in the battery system. This paper looks at the implementation of three nonlinear estimation strategies for Li-Ion battery SOC estimation. One of the most common behavioral battery models is the one state hysteresis (OSH) model. The extended Kalman filter (EKF), the smooth variable structure filter (SVSF), and the time-varying smoothing boundary layer SVSF are applied on this model, and the results are compared.

Keywords: state of charge estimation, battery modeling, one-state hysteresis, filtering and estimation

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Authors: Munawwar Mohabuth, Andrei Kotousov, Ching-Tai Ng

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On the basis of the finite deformation theory, the effect of homogeneous stress on the propagation of Lamb waves in an initially isotropic hyperelastic plate is analysed. The equations governing the propagation of small amplitude waves in the prestressed plate are derived using the theory of small deformations superimposed on large deformations. By enforcing traction free boundary conditions at the upper and lower surfaces of the plate, acoustoelastic dispersion equations for Lamb wave propagation are obtained, which are solved numerically. Results are given for an aluminum plate subjected to a range of applied stresses.

Keywords: acoustoelasticity, dispersion, finite deformation, lamb waves

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Authors: Danladi Ali

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In this paper, we measured GSM signal strength in the Dnepropetrovsk city in order to predict path loss in study area using nonlinear autoregressive neural network prediction and we also, used neural network clustering to determine average GSM signal strength receive at the study area. The nonlinear auto-regressive neural network predicted that the GSM signal is attenuated with the mean square error (MSE) of 2.6748dB, this attenuation value is used to modify the COST 231 Hata and the Okumura-Hata models. The neural network clustering revealed that -75dB to -95dB is received more frequently. This means that the signal strength received at the study is mostly weak signal

Keywords: one-dimensional multilevel wavelets, path loss, GSM signal strength, propagation, urban environment and model

Procedia PDF Downloads 382

Authors: Gonzalez Carlos, Martinez Fransisco

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There are various types of analysis that allow us to involve seismic phenomena that cause strong requirements for structures that are designed by society; one of them is a probabilistic analysis which works from prediction equations that have been created based on metadata seismic compiled in different regions. These equations form models that are used to describe the 5% damped pseudo spectra response for the various zones considering some easily known input parameters. The biggest problem for the creation of these models requires data with great robust statistics that support the results, and there are several places where this type of information is not available, for which the use of alternative methodologies helps to achieve adjustments to different models of seismic prediction.

Keywords: GMPM, 5% damped pseudo-response spectra, models of seismic prediction, PSHA

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Authors: Ewelina Nowak, Anna Wisla-Swider

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Deoxyribonucleic acid (DNA) is a biomolecule which exhibits an electro-optic properties. These features are related with structure of double-stranded helix. Modification of DNA with ionic liquids allows intensify these properties. The aim of our study was synthesis of ionic liquids that are used the formation of DNA-surfactant complexes in order to obtain new materials with potential application for nonlinear optics. Complexes were achieved through the ion exchange reactions of carbazole-based and imidazole-based ionic liquids with H+ ions from salmon DNA. To examination the properties of obtained complexes DNA-ionic liquids there were investigated using circular dichroism (CD), UV-Vis spectra and infrared spectroscopy (IR). Additionally, the resulting DNA-surfactant complexes were characterized in terms of solubility in common organic solvents and water.

Keywords: deoxyribonucleic acid, biomolecule, carbazole, imidazole, ionic liquids, ion exchange reactions

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Authors: Rasikh Tariq, Fatima Z. Benarab

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Evaporative coolers has a minimum potential to reach the wet-bulb temperature of intake air which is not enough to handle a large cooling load; therefore, it is not a feasible option to overcome cooling requirement of a building. The invention of Maisotsenko (M) cycle has led evaporative cooling technology to reach the sub-wet-bulb temperature of the intake air; therefore, it brings an innovation in evaporative cooling techniques. In this work, we developed a mathematical model of the Maisotsenko based air cooler by applying energy and mass balance laws on different air channels. The governing ordinary differential equations are discretized and simulated on MATLAB. The temperature and the humidity plots are shown in the simulation results. A parametric study is conducted by varying working air inlet conditions (temperature and humidity), inlet air velocity, geometric parameters and water temperature. The influence of these aforementioned parameters on the cooling effectiveness of the HMX is reported.  Results have shown that the effectiveness of the M-Cycle is increased by increasing the ambient temperature and decreasing absolute humidity. An air velocity of 0.5 m/sec and a channel height of 6-8mm is recommended.

Keywords: HMX, maisotsenko cycle, mathematical modeling, numerical simulation, parametric study

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Authors: Sun Lim, Kyun Jung

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In this paper, we describe the control strategy of high speed parallel robot system with EtherCAT network. This work deals the parallel robot system with centralized control on the real-time operating system such as window TwinCAT3. Most control scheme and algorithm is implemented master platform on the PC, the input and output interface is ported on the slave side. The data is transferred by maximum 20usecond with 1000byte. EtherCAT is very high speed and stable industrial network. The control strategy with EtherCAT is very useful and robust on Ethernet network environment. The developed parallel robot is controlled pre-design nonlinear controller for 6G/0.43 cycle time of pick and place motion tracking. The experiment shows the good design and validation of the controller.

Keywords: parallel robot control, etherCAT, nonlinear control, parallel robot inverse kinematic

Procedia PDF Downloads 571

Authors: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

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So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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Authors: Kobamelo Mashaba

Abstract:

The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry.

Keywords: delayed partial differential equation, modified Crank-Nicolson Method, molten slag, heat recovery, parabolic equation

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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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

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Authors: Imil Hamda Imran, Sami El Ferik

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This paper deals with adaptive cooperative control of non holonomic mobile robot moved together in a given formation. The controller is designed based on the Immersion and Invariance (I&I) approach. I&I is a framework for adaptive stabilization of nonlinear systems with uncertain parameters. We investigate the tracking control of non holonomic mobile robot with uncertainties in The I&I-based adaptive controller regulates the angular and linear velocity of non holonomic mobile robot. The results demonstrate that the ability of I&I-based adaptive cooperative control in tracking the position of non holonomic mobile robot.

Keywords: nonholonomic mobile robot, immersion and invariance, adaptive control, uncertain nonlinear systems

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Authors: Khedidja Bouhadef, Imene Said Kouadri, Omar Rahli

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In this paper numerical investigation is performed to analyze natural convection heat transfer characteristics within a wavy-wall enclosure filled with fluid-saturated porous medium. The bottom wall which has the wavy geometry is maintained at a constant high temperature, while the top wall is straight and is maintained at a constant lower temperature. The left and right walls of the enclosure are both straight and insulated. The governing differential equations are solved by Finite-volume approach and grid generation is used to transform the physical complex domain to a computational regular space. The aim is to examine flow field, temperature distribution and heat transfer evolutions inside the cavity when Darcy number, Rayleigh number and undulations number values are varied. The results mainly indicate that the heat transfer is rather affected by the permeability and Rayleigh number values since increasing these values enhance the Nusselt number; although the exchanges are not highly affected by the undulations number.

Keywords: grid generation, natural convection, porous medium, wavy wall enclosure

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Authors: K. Khadidja

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Solitons are stable solution of nonlinear Schrodinger equation. Their stability is due to the exact combination between nonlinearity and dispersion which causes pulse broadening. Higher order solitons are born when nonlinear length is N multiple of dispersive length. Soliton order is determined by the number N itself. In this paper, evolution of higher order solitons is illustrated by simulation using Matlab. Results show that higher order solitons change their shape periodically, the reason why they are bad for transmission comparing to fundamental solitons which are constant. Partial analysis of a soliton of higher order explains that the periodic shape is due to the interplay between nonlinearity and dispersion which are not equal during a period. This class of solitons has many applications such as generation of supercontinuum and the impulse compression on the Femtosecond scale. As a conclusion, the periodicity which is harmful to transmission can be beneficial in other applications.

Keywords: dispersion, nonlinearity, optical fiber, soliton

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Authors: Hassan Youssef Mohamed

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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

Procedia PDF Downloads 185