Papers by Keyword: Finite Difference

Abstract: Recently, theoretical analysis of the electronic properties of quantum dot has attracted a great attention when modern nanotechnology has made it possible to fabricate a realistic quantum dots in laboratory [. Quantum dot structures which provide electron confinement in three dimensions can be grown by the so called self-assembly effect or Stranski-Krastanov growth mode. Particular interest attracts ordering effects in StranskiKrastanow growth which proceeds on a lattice-mismatched substrate via formation of essentially three-dimensional islands. This is especially true for the InAs-GaAs system where the lattice mismatch is high and the nucleation process is rapid. Although, quantum dots have being studied experimentally but large amount of numerical studies of electron confined states also have been developed to simulate electronic and optical properties in quantum dots. The single band effective mass is one of the formalism of envelope function which has been widely used to solve quantum dot systems. However, the effective mass m^* is usually position dependent in semiconductor heterostrutures. Consequently, the concerning about the form of the boundary conditions to impose on different material interface arisen [3]. According to the present works [2, , the position dependent Hamiltonian is given by: . where m = m (r) is the position dependent effective mass of an electron in conduction band. The constant α, β, and γ is arbitrary set to satisfy α + β + γ = -1. Various approximations regarding the actual constant of α, β, and γ in position dependent effective mass have been observed, example Gora & William (by putting α = -1 and β = γ = 0), Zhu & Kroemer (α = γ = -1/2 and β = 0), and BenDaniel-Duke (α = γ = 0 and β = -1). Among them, β = 1 (known as the Ben DanielDuke Hamiltonian [) is most popular method for solving mass continuity problem on the classic Hamiltonian [. Extensively, these interface condition was been used to solved most of the heterostructure problem such as quantum dots [. However, there is a qualitative argument based upon the Ben DanielDuke choice violates the Heisenberg uncertainty principle and the issue of the correct effective-mass equation was further questioned by Pistol, M. E. which he claims that all the possible equations lead to the same interfacial conditions on the envelope function [. In this paper, we will investigate the effect of discontinuity mass within interface of two semiconductor materials inside InAs-GaAs quantum dot by using the classic constant mass Hamiltonian (CH), position dependent effective mass Hamiltonian (PDH) and Ben Daniel and Duke Hamiltonian (BDH). The most common analytic methods are solving the transcendental equation obtained by matching the interface boundary condition on the envelope function. But this kind of method will suffer from complexity of model quantum dots that contain multiple layer or geometry that unable to derive into analytic formulation. Thus, this study will focus on comparison between difference finite difference formalism to illustrate the mass discontinuity effect on the numerical solution.

Abstract: This work aims to solve the 1D Burgers equation, which represents a simplification of the Navier-Stokes equation, supposing the yielding only at x-direction and without pressure gradient. For such a solution, an implicit scheme (Cranck-Nicolson method) with a fourth order precision in space is utilized. The main contribution of this work is the application of a linearization technique of the non-linear term (advective term), and then, towards the analytical and numerical results from literature, validate and demonstrate it as being highly satisfactory.

Abstract: Based on the elastic wave equation, high-order finite-difference schemes for reverse-time extrapolation in the space of staggered grid and the perfectly matched layer (PML) absorbing boundary condition for the equation are derived. Prestack reverse-time depth migration (RTM) of elastic wave equation using the excitation time imaging condition and normalized cross-correlation imaging condition is carried out. Numerical experiments show that reverse-time migration is not limited for the angle of incidence and dramatic changes in lateral velocity. The reverse-time migration results of normalized cross-correlation imaging condition give the better effect than that of excitation time imaging condition.

Abstract: The aim of this study is to present a mathematical model for the wave pressure in the Diesel injection system. The method of characteristics and the finite difference method have been used to solve the governing equations. Recent studies show that finite difference method is superior to the method of characteristics concerning computation time and nonlinearity. The injection process of a high-speed Diesel engine was studied in detail, using an original computer program developed in MATLAB. The governing equations are solved by the use of the finite difference method with central pattern at space coordinate in combination with the separation of flux vector. The fuel injection system is divided into pump, pipe and nozzle component to model the entire system. When forming equations of continuity and motion the following assumptions are considered: all the equations have 1D spatial resolution, temperature change due to pressure and time during the cycle is not considered, the vapors pressure of the fuel is small compared to the level of the pressure injection system, it is assumed that cavitation will not occur and elastic deformation in the injection system is not considered. The experiment is carried out to measure the fuel consumption, in-cylinder pressure, the fuel injection pipe pressure near the injection valve and needle lift for several regimes of the working domain of a Diesel engine. The experimental set-up includes a 4 stroke cycle 4 cylinder Diesel engine T684 made by Tractorul Brasov Romania. Simulations show satisfactory results, in principal for regime of low speed, for regime of high speed it is important to take into account cavitation and the elasticity of the component; but improvements are possible. Since the models are developed for certain conditions it was not expected to be valid for all working conditions. Targets for further research related to the present work is to improve the model attaching submodels for cavitation and elasticity of the component

Abstract: As more and more electric transmission lines have to go through the mining area, if we can fully realize the collapse and deformation characteristics of mined-out area, and master the scientific laws of its occurrence and development, we may take reasonable measures to avoid the happening of accidents, ensure the line to run in a reliable way, and greatly improve the construction quality and economic benefits. For different location conditions of coal mine worked out section to the surface of the power transmission tower, we use finite difference software FLAC3D to analyze mutual influence and interaction between underground worked out section and surface iron tower foundation. The conclusion in this paper can be used as a reference to mining site. The influence range can be estimated before mining, as far as possible avoiding influence within the scope of strata. It is the key to ensure the safety of power transmission tower, people life and property.

Abstract: Nonlinear liquid sloshing problems in a vertically excited tank are numerically simulated by using a finite difference method. First, the irregular liquid domain is mapped onto a rectangular area by σ-transformation. Then, in the process of time iteration, the free surface is forecasted to estimate the boundary of the next time layer; and some nonlinear terms are approximated to derive linear equations. Free surface elevation and sloshing forces in the vertical sloshing process can be calculated precisely by this method.

Abstract: This paper introduces several methods in solving the wave equations for a loudspeaker. The separation of variables method is very common for solving constant coefficient linear partial differential problems. The finite difference method has been the main method of numerical computation in early work. The direct method is to formulate the boundary integral equation and can be solved using a direct time integration procedure. There are also some transform methods such as Fourier, Laplaces and wavelet transforms etc. to solve the wave equations. The retarded potential technique to solve the wave problems numerically was first used in the early 1960s. Since then, many authors have worked on the method and its applications.

Abstract: High pressure (HP) fuel pipeline is one of the major components of Combination Electronic Unit Pump (CEUP) diesel fuel injection system and has significant contribution in building up of high pressure required during fuel injection cycle. A MATLAB numerical model of pressure wave inside HP fuel pipeline of CEUP system using damped wave equation has been developed in MATLAB to study and simulate pressure wave propagation through fuel pipeline at various operating conditions of diesel engine. Finite Difference method has been applied to model and simulate pressure equation at various equidistant locations of fuel pipeline. Dynamic variations of fuel properties as a function of varying pressure have also been incorporated. The MATLAB model has been validated by comparing simulated pressures with those of experimentally validated AMESim numerical model of CEUP fuel injection system. Quantitative comparisons were also done using Root Mean Square Error (RMSE) and Index of Agreement (IA). Results show that MATLAB numerical model is quite accurate especially at low cam rotational speeds and low cam angles.

Abstract: According to a new version of equations of elasodynamics of quasicrystals suggested by Ref, a finite difference method of the anti-plane elastic dynamic equations of 1D hexagonal and 3D icosahedral quasicrystals is developed. Further the dynamic behaviour of the material with a model III crack under impact loading is given.The results show dynamic stress intensity factor of the crack tip, in which the similar and different features with conventional materials are discussed, especially the phonon,phason and phonon-phason coupling effects are explored.

Abstract: In this paper, finite difference method and finite volume method are applied to incompressible viscous driven cavity flow problems, and their results are analyzed and compared. As for the finite difference method, second-order upwind and second-order central difference format are applied to the discretization of the convection and diffusion items respectively. For the finite volume method, three different ways are utilized to discretize the control equations: QUICK, second-order central difference and third-order upwind formats. The results show that computing time as well as calculation accuracy exponentially depends on Reynolds number, discrete formats and grid numbers.