Search results for: implicit equation

Authors: Sarun Phibanchon, Yuttakarn Rattanachai

Abstract:

The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

Procedia PDF Downloads 379

Authors: Olukunle C. Olawole, Dilip Kumar De

Abstract:

We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.

Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density

Procedia PDF Downloads 343

Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci

Abstract:

In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.

Keywords: crossover model, critical region, fundamental equation, n-heptane

Procedia PDF Downloads 441

Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

Abstract:

We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

Procedia PDF Downloads 403

Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

Abstract:

Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

Procedia PDF Downloads 369

Authors: A. A. Soliman

Abstract:

The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

Procedia PDF Downloads 272

Authors: M. A. Riurean, S. Heijnen, C. A. Knott, J. Makinde, D. Gotti, J. VD. Kamp

Abstract:

Objectives: The current study is done in preparation for a randomized controlled study investigating the effects of an implicit motor learning protocol implemented using an extension-supporting glove. It will explore different protocols to find out which is preferred when studying motor learn-ing in the chronic stroke population that struggles with hand spasticity. Design: This exploratory study will follow 24 individuals who have a chronic stroke (> 6 months) during their usual care journey. We will record the results of two 9-Hole Peg Tests (9HPT) done during their therapy ses-sions with a physiotherapist or in their home before and after 4 weeks of them wearing an exten-sion-supporting glove used to employ the to-be-studied protocols. The participants will wear the glove 3 times/week for one hour while performing their activities of daily living and record the times they wore it in a diary. Their experience will be monitored through telecommunication once every week. Subjects: Individuals that have had a stroke at least 6 months prior to participation, hand spasticity measured on the modified Ashworth Scale of maximum 3, and finger flexion motor control measured on the Motricity Index of at least 19/33. Exclusion criteria: extreme hemi-neglect. Methods: The participants will be randomly divided into 3 groups: one group using the glove in a pre-set way of decreasing support (implicit motor learning), one group using the glove in a self-controlled way of decreasing support (autonomous motor learning), and the third using the glove with constant support (as control). Before and after the 4-week period, there will be an intake session and a post-assessment session. Analysis: We will compare the results of the two 9HPTs to check whether the protocols were effective. Furthermore, we will compare the results between the three groups to find the preferred one. A qualitative analysis will be run of the experience of participants throughout the 4-week period. Expected results: We expect that the group using the implicit learning protocol will show superior results.

Keywords: implicit learning, hand spasticity, stroke, error minimization, motor task

Procedia PDF Downloads 31

Authors: Hamid Hamli Benzahar

Abstract:

The main goal of this research is to study the deflection of a composite beam CB taking into account the effect of shear deformation. The structure is made up of two beams of different sections, joined together by thin adhesive, subjected to end moments and a distributed load. The fundamental differential equation of CB can be obtained from the total energy equation while considering the shear deformation. The differential equation found will be compared with those found in CB, where the shear deformation is zero. The CB system is numerically modeled by the finite element method, where the numerical results of deflection will be compared with those found theoretically.

Keywords: composite beam, shear deformation, moments, finites elements

Procedia PDF Downloads 42

Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

Procedia PDF Downloads 105

Authors: Zsuzsa Szakaly

Abstract:

Several constitutions have explicit or implicit eternity clauses in the European Union, their classic roles were analyzed so far, albeit there are new possibilities emerging in relation to the identity of the constitutions of the Member States. The aim of the study is to look at the practice of the Constitutional Courts of the Member States in detail regarding eternity clauses where limiting constitutional amendment has practical bearing, and to examine the influence of such practice on Europeanization. There are some states that apply explicit eternity clauses embedded in the text of the constitution, e.g., Italy, Germany, and Romania. In other states, the Constitutional Court 'unearthed' the implicit eternity clauses from the text of the basic law, e.g., Slovakia and Croatia. By using comparative analysis to examine the explicit or implicit clauses of the concerned constitutions, taking into consideration the new trends of the judicial opinions of the Member States and the fresh scientific studies, the main questions are: How to wield the double-edged sword of eternity clauses? To support European Integration or to support the sovereignty of the Member State? To help Europeanization or to act against it? Eternity clauses can easily find themselves between a rock and a hard place, the law of the European Union and the law of a Member State, with more possible interpretations. As more and more Constitutional Courts started to declare elements of their Member States’ constitutional identities, these began to interfere with the eternity clauses. Will this trend eventually work against Europeanization? As a result of the research, it can be stated that a lowest common denominator exists in the practice of European Constitutional Courts regarding eternity clauses. The chance of a European model and the possibility of this model influencing the status quo between the European Union and the Member States will be examined by looking at the answers these courts have found so far.

Keywords: constitutional court, constitutional identity, eternity clause, European Integration

Procedia PDF Downloads 113

Authors: Jiya Mohammed, Ibrahim Ismail Giwa

Abstract:

Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

Procedia PDF Downloads 438

Authors: Makhlouf Mourad, Medkour Mihoub, Bouchher Omar, Messabih Sidi Mohamed, Benrachedi Khaled

Abstract:

This work is the modeling and simulation of fluid flow (liquid) through porous media. This type of flow occurs in many situations of interest in applied sciences and engineering, fluid (oil) consists of several individual substances in pure, single-phase flow is incompressible and isothermal. The porous medium is isotropic, homogeneous optionally, with the rectangular format and the flow is two-dimensional. Modeling of hydrodynamic phenomena incorporates Darcy's law and the equation of mass conservation. Correlations are used to model the density and viscosity of the fluid. A finite volume code is used in the discretization of differential equations. The nonlinearity is treated by Newton's method with relaxation coefficient. The results of the simulation of the pressure and the mobility of liquid flowing through porous media are presented, analyzed, and illustrated.

Keywords: Darcy equation, middle porous, continuity equation, Peng Robinson equation, mobility

Procedia PDF Downloads 177

Authors: Alexander Zibenberg, Rima’a Da’As

Abstract:

According to the author’s knowledge, individuals are naturally inclined to classify people as leaders and followers. Individuals utilize cognitive structures or prototypes specifying the traits and abilities that characterize the effective leader (implicit leadership theories) and effective follower in an organization (implicit followership theories). Thus, the present study offers insights into understanding how teachers' personal values (self-enhancement and self-transcendence) explain the preference for styles of effective leader (i.e., principal) and assumptions about the traits and behaviors that characterize effective followers (i.e., student). Beyond the direct effect on perceptions of effective types of leader and follower, the present study argues that values may also interact with organizational and personal contexts in influencing perceptions. Thus authors suggest that teachers' managerial position may moderate the relationships between personal values and perception of the effective leader and follower. Specifically, two key questions are addressed in the present research: (1) Is there a relationship between personal values and perceptions of the effective leader and effective follower? and (2) Are these relationships stable or could they change across different contexts? Two hundred fifty-five Israeli teachers participated in this study, completing questionnaires – about the effective student and effective principal. Results of structural equations modeling (SEM) with maximum likelihood estimation showed: first: the model fit the data well. Second: researchers found a positive relationship between self-enhancement and anti-prototype of the effective principal and anti-prototype of the effective student. The relationship between self-transcendence value and both perceptions were found significant as well. Self-transcendence positively related to the way the teacher perceives the prototype of the effective principal and effective student. Besides, authors found that teachers' managerial position moderates these relationships. The article contributes to the literature both on perceptions and on personal values. Although several earlier studies explored issues of implicit leadership theories and implicit followership theories, personality characteristics (values) have garnered less attention in this matter. This study shows that personal values which are deeply rooted, abstract motivations that guide justify or explain attitudes, norms, opinions and actions explain differences in perception of the effective leader and follower. The results advance the theoretical understanding of the relationship between personal values and individuals’ perceptions in organizations. An additional contribution of this study is the application of the teacher's managerial position to explain a potential boundary condition of the translation of personal values into outcomes. The findings suggest that through the management process in the organization, teachers acquire knowledge and skills which augment their ability (beyond their personal values) to predict perceptions of ideal types of principal and student. The study elucidates the unique role of personal values in understanding an organizational thinking in organization. It seems that personal values might explain the differences in individual preferences of the organizational paradigm (mechanistic vs organic).

Keywords: implicit leadership theories, implicit followership theories, organizational paradigms, personal values

Procedia PDF Downloads 132

Authors: E. V. Krishnan

Abstract:

In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.

Keywords: travelling wave solutions, Jacobi elliptic functions, solitary wave solutions, Korteweg-de Vries equation

Procedia PDF Downloads 302

Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

Abstract:

In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

Procedia PDF Downloads 71

Authors: Tai-Ping Chang

Abstract:

In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

Procedia PDF Downloads 290

Authors: Mahtab Makaremi Masouleh, Günter Wozniak

Abstract:

This research is part of an interdisciplinary project, promoting the design of a light temporary installable textile defence system against flood. In case river water levels increase abruptly especially in winter time, one can expect massive extra load on a textile protective structure in term of impact as a result of floating debris and even tree trunks. Estimation of this impulsive force on such structures is of a great importance, as it can ensure the reliability of the design in critical cases. This fact provides the motivation for the numerical analysis of a fluid structure interaction application, comprising flexible slender shaped and free-surface water flow, where an accelerated heavy flotsam tends to approach the membrane. In this context, the analysis on both the behavior of the flexible membrane and its interaction with moving flotsam is conducted by finite elements based solvers of the explicit solver and implicit Abacus solver available as products of SIMULIA software. On the other hand, a study on how free surface water flow behaves in response to moving structures, has been investigated using the finite volume solver of Star CCM+ from Siemens PLM Software. An automatic communication tool (CSE, SIMULIA Co-Simulation Engine) and the implementation of an effective partitioned strategy in form of an implicit coupling algorithm makes it possible for partitioned domains to be interconnected powerfully. The applied procedure ensures stability and convergence in the solution of these complicated issues, albeit with high computational cost; however, the other complexity of this study stems from mesh criterion in the fluid domain, where the two structures approach each other. This contribution presents the approaches for the establishment of a convergent numerical solution and compares the results with experimental findings.

Keywords: co-simulation, flexible thin structure, fluid-structure interaction, implicit coupling algorithm, moving flotsam

Procedia PDF Downloads 359

Authors: P. Srinivas, P. V. N. Prasad

Abstract:

Since torque ripple is the main cause of noise and vibrations, the performance of Switched Reluctance Motor (SRM) can be improved by minimizing its torque ripple using a novel control technique called Direct Torque Control (DTC). In DTC technique, torque is controlled directly through control of magnitude of the flux and change in speed of the stator flux vector. The flux and torque are maintained within set hysteresis bands. The DTC of SRM is analysed by two methods. In one of the methods, the actual torque is computed by conducting Finite Element Analysis (FEA) on the design specifications of the motor. In the other method, the torque is computed by Simplified Torque Equation. The variation of peak current, average current, torque ripple and speed settling time with Simplified Torque Equation model is compared with FEA based model.

Keywords: direct toque control, simplified torque equation, finite element analysis, torque ripple

Procedia PDF Downloads 454

Authors: Sreeparna Majee, G. C. Shit

Abstract:

Unsteady blood flow has been numerically investigated through stenosed arteries to achieve an idea about the physiological blood flow pattern in diseased arteries. The blood is treated as Newtonian fluid and the arterial wall is considered to be rigid having deposition of plaque in its lumen. For direct numerical simulation, vorticity-stream function formulation has been adopted to solve the problem using implicit finite difference method by developing well known Peaceman-Rachford Alternating Direction Implicit (ADI) scheme. The effects of magnetic parameter and Reynolds number on velocity and wall shear stress are being studied and presented quantitatively over the entire arterial segment. The streamlines have been plotted to understand the flow pattern in the stenosed artery, which has significant alterations in the downstream of the stenosis in the presence of magnetic field. The results show that there are nominal changes in the flow pattern when magnetic field strength is enhanced upto 8T which can have remarkable usage to MRI machines.

Keywords: magnetohydrodynamics, blood flow, stenosis, energy dissipation

Procedia PDF Downloads 253

Authors: Abdel-Maksoud Abdel-Kader Soliman

Abstract:

The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

Procedia PDF Downloads 464

Authors: Elisha Kyirem

Abstract:

Undoubtedly, climate change is a major global challenge that could threaten the very foundation upon which life on earth is anchored, with its impacts on human mobility attracting the attention of policy makers and researchers. There is an increasing body of literature and case studies suggesting that migration could be a way through which the vulnerable move away from areas exposed to climate extreme events to improve their lives and that of their families. This presents migration as a way through which people voluntarily move to seek opportunities that could help reduce their exposure and avoid danger from climate events. Thus, migration is seen as a proactive adaptation strategy aimed at building resilience and improving livelihoods to enable people to adapt to future changing events. However, there has not been any mathematical equation linking migration and climate change adaptation. Drawing from literature in development studies, this paper develops an equation that seeks to link the relationship between migration and climate change adaptation. The mathematical equation establishes the linkages between migration, resilience, poverty reduction and vulnerability, and these the paper maintains, are the key variables for conceptualizing the migration-climate change adaptation nexus. The paper then tests the validity of the equation using the sustainable livelihood framework and publicly available data on migration and tourism in Ghana.

Keywords: migration, adaptation, climate change, adaptation, poverty reduction

Procedia PDF Downloads 356

Authors: Satyanarayana Engu, Ahmed Mohd, V. Murugan

Abstract:

We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time.

Keywords: Burgers equation, Cole-Hopf transformation, Hermite polynomials, large time asymptotics

Procedia PDF Downloads 295

Authors: Saeed Ghali, Hoda El-Faramawy, Mamdouh Eissa, Michael Mishreky

Abstract:

Scale-resistant austenitic stainless steel, X45CrNiW 18-9, has been developed, and modified steels produced through partial and total nickel replacement by nitrogen. These modified steels were produced in a 10 kg induction furnace under different nitrogen pressures and were cast into ingots. The produced modified stainless steels were forged, followed by air cooling. The phases of modified stainless steels have been investigated using the Schaeffler diagram, dilatometer, and microstructure observations. Both partial and total replacement of nickel using 0.33-0.50% nitrogen are effective in producing fully austenitic stainless steels. The nitrogen contents were determined and compared with those calculated using the Institute of Metal Science (IMS) equation. The results showed great deviations between the actual nitrogen contents and predicted values through IMS equation. So, an equation has been derived based on chemical composition, pressure, and temperature at 1600oC. [N%] = 0.0078 + 0.0406*X, where X is a function of chemical composition and nitrogen pressure. The derived equation has been used to calculate the nitrogen content of different steels using published data. The results reveal the difficulty of deriving a general equation for the prediction of nitrogen content covering different steel compositions. So, it is necessary to use a narrow composition range.

Keywords: solubility, nitrogen, stainless steel, Schaeffler

Procedia PDF Downloads 205

Authors: Azad A. Mohammed, Dunyazad K. Assi, Alan S. Abdulrahman

Abstract:

Current ACI 318 Code provides two limits for minimum steel ratio for concrete beams. When concrete compressive strength be larger than 31 MPa the limit of √(fc')/4fy usually governs. In this paper shortcomings related to using this limit was fairly discussed and showed that the limit is based on 90% safety factor and was derived based on modulus of rupture equation suitable for concretes of compressive strength lower than 31 MPa. Accordingly, the limit is nor suitable and critical for concretes of higher compressive strength. An alternative equation was proposed for minimum steel ratio of rectangular beams and was found that the proposed limit is accurate for beams of wide range of concrete compressive strength. Shortcomings of the current ACI 318 Code equation and accuracy of the proposed equation were supported by test data obtained from testing six reinforced concrete beams.

Keywords: concrete beam, compressive strength, minimum steel ratio, modulus of rupture

Procedia PDF Downloads 513

Authors: Guesh Simretab Gebremedhin, Saumya Rajan Jena

Abstract:

In this work, a septic B-spline scheme has been used to simplify the process of solving an approximate solution of the generalized Rosenau-regularized long-wave equation (GR-RLWE) with initial boundary conditions. The resulting system of first-order ODEs has dealt with Butcher’s fifth order Runge-Kutta (BFRK) approach without using finite difference techniques for discretizing the time-dependent variables at each time level. Here, no transformation or any kind of linearization technique is employed to tackle the nonlinearity of the equation. Two test problems have been selected for numerical justifications and comparisons with other researchers on the basis of efficiency, accuracy, and results of the two invariants Mᵢ (mass) and Eᵢ (energy) of some motion that has been used to test the conservative properties of the proposed scheme.

Keywords: septic B-spline scheme, Butcher's fifth order Runge-Kutta approach, error norms, generalized Rosenau-RLW equation

Procedia PDF Downloads 32

Authors: Jian-Ping Yu, Wen-Xiu Ma, Yong-Li Sun, Chaudry Masood Khalique

Abstract:

In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions.

Keywords: 2d Toda equation, Hirota bilinear method, Lump-type solution, multiple-lump-type solution

Procedia PDF Downloads 191

Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

Abstract:

According to the increasing volume of traffic, lane changing plays a crucial role in traffic flow. Lane changing in traffic depends on several factors including road geometrical design, speed, drivers’ behavioral characteristics, etc. A great deal of research has been carried out regarding these fields. Despite of the other significant factors, the drivers’ behavioral characteristics of lane changing has been emphasized in this paper. This paper has predicted the effective equation based on personal characteristics of lane changing by regression models.

Keywords: effective equation, lane changing, drivers’ behavioral characteristics, regression models

Procedia PDF Downloads 420

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

Abstract:

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

Procedia PDF Downloads 176

Authors: A. R. Nezamabadi, M. Veiskarami

Abstract:

This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration

Procedia PDF Downloads 445

Authors: Somveer Singh, Vineet Kumar Singh

Abstract:

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

Procedia PDF Downloads 404