Search results for: incompressible navier-stokes equations

Authors: Magdy G. Asaad

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Solitons are among the most beneficial solutions for science and technology for their applicability in physical applications including plasma, energy transport along protein molecules, wave transport along poly-acetylene molecules, ocean waves, constructing optical communication systems, transmission of information through optical fibers and Josephson junctions. In this talk, we will apply the bilinear technique to generate a class of soliton solutions to the (3+1)-dimensional nonlinear soliton equation of Jimbo-Miwa type. Examples of the resulting soliton solutions are computed and a few solutions are plotted.

Keywords: Pfaffian solutions, N-soliton solutions, soliton equations, Jimbo-Miwa

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Authors: Vandana N. Purav

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Fibonacci and Lucas polynomials are special cases of Chebyshev polynomial. There are two types of Chebyshev polynomials, a Chebyshev polynomial of first kind and a Chebyshev polynomial of second kind. Chebyshev polynomial of second kind can be derived from the Chebyshev polynomial of first kind. Chebyshev polynomial is a polynomial of degree n and satisfies a second order homogenous differential equation. We consider the difference equations which are related with Chebyshev, Fibonacci and Lucas polynomias. Thus Chebyshev polynomial of second kind play an important role in finding the recurrence relations with Fibonacci and Lucas polynomials.

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Authors: Shahin A. Abdel-Naby, James P. Colgan, Michael S. Pindzola

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A time-dependent close-coupling method is developed to calculate a total, double and triple autoionization rates for hollow atomic ions of four-electron systems. This work was motivated by recent observations of the four-electron Auger process in near K-edge photoionization of C+ ions. The time-dependent close-coupled equations are solved using lattice techniques to obtain a discrete representation of radial wave functions and all operators on a four-dimensional grid with uniform spacing. Initial excited states are obtained by relaxation of the Schrodinger equation in imaginary time using a Schmidt orthogonalization method involving interior subshells. The radial wave function grids are partitioned over the cores on a massively parallel computer, which is essential due to the large memory requirements needed to store the coupled-wave functions and the long run times needed to reach the convergence of the ionization process. Total, double, and triple autoionization rates are obtained by the propagation of the time-dependent close-coupled equations in real-time using integration over bound and continuum single-particle states. These states are generated by matrix diagonalization of one-electron Hamiltonians. The total autoionization rates for each L excited state is found to be slightly above the single autoionization rate for the excited configuration using configuration-average distorted-wave theory. As expected, we find the double and triple autoionization rates to be much smaller than the total autoionization rates. Future work can be extended to study electron-impact triple ionization of atoms or ions. The work was supported in part by grants from the American University of Sharjah and the US Department of Energy. Computational work was carried out at the National Energy Research Scientific Computing Center (NERSC) in Berkeley, California, USA.

Keywords: hollow atoms, autoionization, auger rates, time-dependent close-coupling method

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Authors: S. Kohestani, R. Amrollahi, P. Daryabor

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Microwave diagnostics such as reflectometry are receiving growing attention in magnetic confinement fusionresearch. In order to obtain the better understanding of plasma confinement physics, more detailed measurements on density profile and its fluctuations might be required. A 2D full-wave simulation of ordinary mode propagation has been written in an effort to model effects seen in reflectometry experiment. The code uses the finite-difference-time-domain method with a perfectly-matched-layer absorption boundary to solve Maxwell’s equations.The code has been used to simulate the reflectometer measurement in Alborz Tokamak.

Keywords: reflectometry, simulation, ordinary mode, tokamak

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Authors: N. Smaoui, B. Chentouf

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The boundary stabilization problem of the rotating disk-beam system is a topic of interest in research studies. This system involves a flexible beam attached to the center of a disk, and the control and stabilization of this system have been extensively studied. This research focuses on the case where the center of mass is fixed in an inertial frame, and the rotation of the center is non-uniform. The system is represented by a set of nonlinear coupled partial differential equations and ordinary differential equations. The boundary stabilization problem of this system via a delayed boundary control is considered. We assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. The aim of this research is threefold: First, we demonstrate that the rotating disk-beam system is well-posed in an appropriate functional space. Then, we establish the exponential stability property of the system. Finally, we provide numerical simulations that illustrate the theoretical findings. The research utilizes the semigroup theory to establish the well-posedness of the system. The resolvent method is then employed to prove the exponential stability property. Finally, the finite element method is used to demonstrate the theoretical results through numerical simulations. The research findings indicate that the rotating disk-beam system can be stabilized using a boundary control with a time delay. The proof of stability is based on the resolvent method and a variation of constants formula. The numerical simulations further illustrate the theoretical results. The findings have potential implications for the design and implementation of control strategies in similar systems. In conclusion, this research demonstrates that the rotating disk-beam system can be stabilized using a boundary control with time delay. The well-posedness and exponential stability properties are established through theoretical analysis, and these findings are further supported by numerical simulations. The research contributes to the understanding and practical application of control strategies for flexible structures, providing insights into the stability of rotating disk-beam systems.

Keywords: rotating disk-beam, delayed force control, delayed moment control, torque control, exponential stability

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Authors: S. Kopylov, C. Z. Bo

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This study is aimed at exploring the possibility of energy recovery through the suppression of vibrations. The article describes design of electromagnetic dynamic damper. The magnetic part of the device performs the function of a tuned mass damper, thereby providing both energy regeneration and damping properties to the protected mass. According to the theory of tuned mass damper, equations of mathematical models were obtained. Then, under given properties of current system, amplitude frequency response was investigated. Therefore, main ideas and methods for further research were defined.

Keywords: electromagnetic damper, oscillations with two degrees of freedom, regeneration systems, tuned mass damper

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Authors: Lukas Vierus, Thomas Schuster

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A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.

Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions

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Authors: Angelo I. Aquino, Luis Ma. T. Bo-ot

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We use the Homotopy Analysis Method (HAM) to solve the system of equations modeling the two-level system and extract results which will pinpoint to turbulent behavior. We look at multi-valued solutions as indicative of turbulence or turbulent-like behavior. We take dierent specic cases which result in multi-valued velocities. The solutions are in series form and application of HAM ensures convergence in some region.

Keywords: multivalued solutions, homotopy analysis method, two-level system, equation

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Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale

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This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.

Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories

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Authors: Roger Yu

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A numerical scheme has been developed to solve wave equations for chaotic systems such as stadium-shaped cavity. The same numerical method can also be used for finding wave properties of rectangle cavities with randomly placed obstacles. About 30k eigenvalues have been obtained accurately on a normal circumstance. For comparison, we also initiated an experimental study which determines both eigenfrequencies and eigenfunctions of a stadium-shaped cavity using pulse and normal mode analyzing techniques. The acoustic cavity was made adjustable so that the transition from nonchaotic (circle) to chaotic (stadium) waves can be investigated.

Keywords: quantum dot, chaos, numerical method, eigenvalues

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Authors: Maja Andrić, Josip Pečarić

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Over the last five decades, an enormous amount of work has been done on Opial’s integral inequality, dealing with new proofs, various generalizations, extensions and discrete analogs. The Opial inequality is recognized as a fundamental result in the analysis of qualitative properties of solution of differential equations. We use submultiplicative convex functions, appropriate representations of functions and inequalities involving means to obtain generalizations and extensions of certain known multidimensional integral and discrete Opial-type inequalities.

Keywords: Opial's inequality, Jensen's inequality, integral inequality, discrete inequality

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Authors: Aziza Altaibayeva, Ertan Güdekli, Ratbay Myrzakulov

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In this letter, we explore exact solutions for the Horava-Lifshitz gravity. We use of an extension of this theory with first order dynamical lapse function. The equations of motion have been derived in a fully consistent scenario. We assume that there are some spherically symmetric families of exact solutions of this extended theory of gravity. We obtain exact solutions and investigate the singularity structures of these solutions. Specially, an exact solution with the regular horizon is found.

Keywords: quantum gravity, Horava-Lifshitz gravity, black hole, spherically symmetric space times

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Authors: Abdulatif Abdulsalam Mohamed Shaban

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A.C motors, in general, have superior performance characteristics to their d.c. counterparts. However, despite these advantage a.c. motors lack the controllability and simplicity and so d.c. motors retain a competitive edge where precise control is required. As part of an overall project to develop an improved cycloconverter control strategy for induction motors. Simulation and modelling techniques have been developed. This contribution describes a method used to simulate an induction motor drive using the SIMULINK toolbox within MATLAB software. The cycloconverter fed induction motor is principally modelled using the d-q axis equations. Results of the simulation for a given set of induction motor parameters are also presented.

Keywords: simulation, converter, motor, cycloconverter

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Authors: A. M. Tahsini, S. A. Hosseini

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In the present study, the surface temperature history of the adaptor part in a two-stage supersonic launch vehicle is accurately predicted. The full Navier-Stokes equations are used to estimate the aerodynamic heat flux. The one-dimensional heat conduction in solid phase is used to compute the temperature history. The instantaneous surface temperature is used to improve the applied heat flux, to improve the accuracy of the results.

Keywords: aerodynamic heating, heat conduction, numerical simulation, supersonic flight, launch vehicle

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: stochastic integrals, single–server queue model, catastrophes, busy period

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Authors: M. Salih Taci, N. Tayebi, I. Bozkır

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This paper investigates the operation of a sinusoidal supplied autotransformer on the different states of magnetic polarity of primary and secondary terminals for four different step-up and step-down analytical conditions. In this paper, a new analytical modeling and equations for dot-marked and polarity-based step-up and step-down autotransformer are presented. These models are validated by the simulation of current and voltage waveforms for each state. PSpice environment was used for simulation.

Keywords: autotransformer modeling, autotransformer simulation, step-up autotransformer, step-down autotransformer, polarity

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Authors: Nam-Hee Kim, Jang-Hoon Ko, Kwon-Hee Lee

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A relief valve is a mechanical element to keep safety by controlling high pressure. Usually, the high pressure is relieved by using the spring force and letting the fluid to flow from another way out of system. When its normal pressure is reached, the relief valve can return to initial state. The relief valve in this study has been applied for pressure vessel, evaporator, piping line, etc. The relief valve should be designed for smooth operation and should satisfy the structural safety requirement under operating condition. In general, the structural analysis is performed by following fluid flow analysis. In this process, the FSI (Fluid-Structure Interaction) is required to input the force obtained from the output of the flow analysis. Firstly, this study predicts the velocity profile and the pressure distribution in the given system. In this study, the assumptions for flow analysis are as follows: • The flow is steady-state and three-dimensional. • The fluid is Newtonian and incompressible. • The walls of the pipe and valve are smooth. The flow characteristics in this relief valve does not induce any problem. The commercial software ANSYS/CFX is utilized for flow analysis. On the contrary, very high pressure may cause structural problem due to severe stress. The relief valve is made of body, bonnet, guide, piston and nozzle, and its material is stainless steel. To investigate its structural safety, the worst case loading is considered as the pressure of 700 bar. The load is applied to inside the valve, which is greater than the load obtained from FSI. The maximum stress is calculated as 378 MPa by performing the finite element analysis. However, the value is greater than its allowable value. Thus, an alternative design is suggested to improve the structural performance through case study. We found that the sensitive design variable to the strength is the shape of the nozzle. The case study is to vary the size of the nozzle. Finally, it can be seen that the suggested design satisfy the structural design requirement. The FE analysis is performed by using the commercial software ANSYS/Workbench.

Keywords: relief valve, structural analysis, structural design, strength, safety factor

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Zaki Abiza, Miguel Chavez, David M. Holman, Ruddy Brionnaud

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In this paper, the prediction of the aerodynamic behavior of the flow around a Finned Projectile will be validated using a Computational Fluid Dynamics (CFD) solution, XFlow, based on the Lattice-Boltzmann Method (LBM). XFlow is an innovative CFD software developed by Next Limit Dynamics. It is based on a state-of-the-art Lattice-Boltzmann Method which uses a proprietary particle-based kinetic solver and a LES turbulent model coupled with the generalized law of the wall (WMLES). The Lattice-Boltzmann method discretizes the continuous Boltzmann equation, a transport equation for the particle probability distribution function. From the Boltzmann transport equation, and by means of the Chapman-Enskog expansion, the compressible Navier-Stokes equations can be recovered. However to simulate compressible flows, this method has a Mach number limitation because of the lattice discretization. Thanks to this flexible particle-based approach the traditional meshing process is avoided, the discretization stage is strongly accelerated reducing engineering costs, and computations on complex geometries are affordable in a straightforward way. The projectile that will be used in this work is the Army-Navy Basic Finned Missile (ANF) with a caliber of 0.03 m. The analysis will consist in varying the Mach number from M=0.5 comparing the axial force coefficient, normal force slope coefficient and the pitch moment slope coefficient of the Finned Projectile obtained by XFlow with the experimental data. The slope coefficients will be obtained using finite difference techniques in the linear range of the polar curve. The aim of such an analysis is to find out the limiting Mach number value starting from which the effects of high fluid compressibility (related to transonic flow regime) lead the XFlow simulations to differ from the experimental results. This will allow identifying the critical Mach number which limits the validity of the isothermal formulation of XFlow and beyond which a fully compressible solver implementing a coupled momentum-energy equations would be required.

Keywords: CFD, computational fluid dynamics, drag, finned projectile, lattice-boltzmann method, LBM, lift, mach, pitch

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Authors: Hamidreza Bayat, Arash Mirabdolah Lavasani, Meysam Bolhasani, Sajad Moosavi

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Flow around a flat tube is studied numerically. Reynolds number is defined base on equivalent circular tube and it is varied in range of 100 to 300. Equations are solved by using finite volume method and results are presented in form of drag and lift coefficient. Results show that drag coefficient of flat tube is up to 66% lower than circular tube with equivalent diameter. In addition, by increasing l/D from 1 to 2, the drag coefficient of flat tube is decreased about 14-27%.

Keywords: laminar flow, flat-tube, drag coefficient, cross-flow, heat exchanger

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Authors: Ahmed I. Raheem

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In this thesis, stratified and stratified wavy flow regimes have been investigated numerically for the oil (1.57 mPa s viscosity and 780 kg/m3 density) and water twophase flow in small and large horizontal steel pipes with a diameter between 0.0254 to 0.508 m by ANSYS Fluent software. Volume of fluid (VOF) with two phases flows using two equations family models (Realizable k-

Keywords: CFD, two-phase flow, pressure gradient, volume of fluid, large diameter, horizontal pipe, oil-water stratified and stratified wavy flow

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Authors: Esther Cabezas-Rivas

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Ordinary differential equations (ODE) are a fundamental part of the curriculum for most engineering degrees, and students typically have difficulties in the subsequent abstract mathematical calculations. To enhance their motivation and profit that they are digital natives, we propose a teamwork project that includes the creation of a video. It should explain how to model mathematically a real-world problem transforming it into an ODE, which should then be solved using the tools learned in the lectures. This idea was indeed implemented with first-year students of a BSc in Engineering and Management during the period of online learning caused by the outbreak of COVID-19 in Spain. Each group of 4 students was assigned a different topic: model a hot water heater, search for the shortest path, design the quickest route for delivery, cooling a computer chip, the shape of the hanging cables of the Golden Gate, detecting land mines, rocket trajectories, etc. These topics should be worked out through two complementary channels: a written report describing the problem and a 10-15 min video on the subject. The report includes the following items: description of the problem to be modeled, detailed obtention of the ODE that models the problem, its complete solution, and interpretation in the context of the original problem. We report the outcomes of this teaching in context and active learning experience, including the feedback received by the students. They highlighted the encouragement of creativity and originality, which are skills that they do not typically relate to mathematics. Additionally, the video format (unlike a common presentation) has the advantage of allowing them to critically review and self-assess the recording, repeating some parts until the result is satisfactory. As a side effect, they felt more confident about their oral abilities. In short, students agreed that they had fun preparing the video. They recognized that it was tricky to combine deep mathematical contents with entertainment since, without the latter, it is impossible to engage people to view the video till the end. Despite this difficulty, after the activity, they claimed to understand better the material, and they enjoyed showing the videos to family and friends during and after the project.

Keywords: active learning, contextual teaching, models in differential equations, student-produced videos

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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

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Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics.

Keywords: conserved quantities, fokas-lenells equation, landau-lifshitz equation, lax pair

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Devinder Singh, Arvind Kumar, Rajneesh Kumar

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The general solution of the equations for a homogeneous isotropic microstretch thermo elastic medium with mass diffusion for two dimensional problems is obtained due to normal and tangential forces. The integral transform technique is used to obtain the components of displacements, microrotation, stress and mass concentration, temperature change and mass concentration. A particular case of interest is deduced from the present investigation.

Keywords: normal force, tangential force, microstretch, thermoelastic, the integral transform technique, deforming force, microstress force, boundary value problem

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Authors: Arcady Ponosov

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A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

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Authors: Gyo Woo Lee, Man Young Kim

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The blocked-off formulations for the analysis of radiative heat transfer are formulated and examined in order to find the solutions in a two-dimensional complex enclosure. The final discretization equations using the step scheme for spatial differencing practice are proposed with the additional source term to incorporate the blocked-off procedure. After introducing the implementation for inactive region into the general discretization equation, three different problems are examined to find the performance of the solution methods.

Keywords: radiative heat transfer, Finite Volume Method (FVM), blocked-off solution procedure, body-fitted coordinate

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Authors: Waleed Al-Nuaimy, Luke Anastassiou, Manjinder Kainth

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As the process of teaching has evolved with the advent of new technologies over the ages, so has the process of learning. Educators have perpetually found themselves on the lookout for new technology-enhanced methods of teaching in order to increase learning efficiency and decrease ever expanding workloads. Shortly after the invention of the internet, web-based learning started to pick up in the late 1990s and educators quickly found that the process of providing learning material and marking assignments could change thanks to the connectivity offered by the internet. With the creation of early web-based virtual learning environments (VLEs) such as SPIDER and Blackboard, it soon became apparent that VLEs resulted in higher reported computer self-efficacy among students, but at the cost of students being less satisfied with the learning process . It may be argued that the impersonal nature of VLEs, and their limited functionality may have been the leading factors contributing to this reported dissatisfaction. To this day, often faced with the prospects of assigning colossal engineering cohorts their homework and assessments, educators may frequently choose optimally curated assessment formats, such as multiple-choice quizzes and numerical answer input boxes, so that automated grading software embedded in the VLEs can save time and mark student submissions instantaneously. A crucial skill that is meant to be learnt during most science and engineering undergraduate degrees is gaining the confidence in using, solving and deriving mathematical equations. Equations underpin a significant portion of the topics taught in many STEM subjects, and it is in homework assignments and assessments that this understanding is tested. It is not hard to see that this can become challenging if the majority of assignment formats students are engaging with are multiple-choice questions, and educators end up with a reduced perspective of their students’ ability to manipulate equations. Artificial intelligence (AI) has in recent times been shown to be an important consideration for many technologies. In our paper, we explore the use of new AI based software designed to work in conjunction with current VLEs. Using our experience with the software, we discuss its potential to solve a selection of problems ranging from impersonality to the reduction of educator workloads by speeding up the marking process. We examine the software’s potential to increase learning efficiency through its features which claim to allow more customized and higher-quality feedback. We investigate the usability of features allowing students to input equation derivations in a range of different forms, and discuss relevant observations associated with these input methods. Furthermore, we make ethical considerations and discuss potential drawbacks to the software, including the extent to which optical character recognition (OCR) could play a part in the perpetuation of errors and create disagreements between student intent and their submitted assignment answers. It is the intention of the authors that this study will be useful as an example of the implementation of AI in a practical assessment scenario insofar as serving as a springboard for further considerations and studies that utilise AI in the setting and marking of science and engineering assignments.

Keywords: engineering education, assessment, artificial intelligence, optical character recognition (OCR)

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Authors: Mohammed A. Hajeeh

Abstract:

This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.

Keywords: repairable models, imperfect, availability, exponential distribution

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