The Finite Difference Scheme for the Suspended String Equation with the Nonlinear Damping Term

A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case.

A MATLAB Simulink Library for Transient Flow Simulation of Gas Networks

An efficient transient flow simulation for gas pipelines and networks is presented. The proposed transient flow simulation is based on the transfer function models and MATLABSimulink. The equivalent transfer functions of the nonlinear governing equations are derived for different types of the boundary conditions. Next, a MATLAB-Simulink library is developed and proposed considering any boundary condition type. To verify the accuracy and the computational efficiency of the proposed simulation, the results obtained are compared with those of the conventional finite difference schemes (such as TVD, method of lines, and other finite difference implicit and explicit schemes). The effects of the flow inertia and the pipeline inclination are incorporated in this simulation. It is shown that the proposed simulation has a sufficient accuracy and it is computationally more efficient than the other methods.

A New Method to Solve a Non Linear Differential System

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Photonic Crystal Waveguide 1x3 Flexible Power Splitter for Optical Network

A compact 1x3 power splitter based on Photonic Crystal Waveguides (PCW) with flexible power splitting ratio is presented in this paper. Multimode interference coupler (MMI) is integrated with PCW. The device size reduction compared with the conventional MMI power splitter is attributed to the large dispersion of the PCW. Band Solve tool is used to calculate the band structure of PCW. Finite Difference Time Domain (FDTD) method is adopted to simulate the relevant structure at 1550nm wavelength. The device is polarization insensitive and allows the control of output (o/p) powers within certain percentage points for both polarizations.

Energy Based Temperature Profile for Heat Transfer Analysis of Concrete Section Exposed to Fire on One Side

For fire safety purposes, the fire resistance and the structural behavior of reinforced concrete members are assessed to satisfy specific fire performance criteria. The available prescribed provisions are based on standard fire load. Under various fire scenarios, engineers are in need of both heat transfer analysis and structural analysis. For heat transfer analysis, the study proposed a modified finite difference method to evaluate the temperature profile within a cross section. The research conducted is limited to concrete sections exposed to a fire on their one side. The method is based on the energy conservation principle and a pre-determined power function of the temperature profile. The power value of 2.7 is found to be a suitable value for concrete sections. The temperature profiles of the proposed method are only slightly deviate from those of the experiment, the FEM and the FDM for various fire loads such as ASTM E 119, ASTM 1529, BS EN 1991-1-2 and 550 oC. The proposed method is useful to avoid incontinence of the large matrix system of the typical finite difference method to solve the temperature profile. Furthermore, design engineers can simply apply the proposed method in regular spreadsheet software.

Frequency Response Analysis of Reinforced- Soil Retaining Walls with Polymeric Strips

Few studies have been conducted on polymeric strip and the behavior of soil retaining walls. This paper will present the effect of frequency on the dynamic behavior of reinforced soil retaining walls with polymeric strips. The frequency content describes how the amplitude of a ground motion is distributed among different frequencies. Since the frequency content of an earthquake motion will strongly influence the effects of that motion, the characterization of the motion cannot be completed without the consideration of its frequency content. The maximum axial force of reinforcements and horizontal displacement of the reinforced walls are focused in this research. To clarify the dynamic behavior of reinforced soil retaining walls with polymeric strips, a numerical modeling using Finite Difference Method is benefited. As the results indicate, the frequency of input base acceleration has an important effect on the behavior of these structures. Because of resonant in the system, where the frequency of the input dynamic load is equal to the natural frequency of the system, the maximum horizontal displacement and the maximum axial forces in polymeric strips is occurred. Moreover, they were to increase the structure flexibility because of the main advantages of polymeric strips; i.e. being simple method of construction, having a homogeneous behavior with soils, and possessing long durability, which are of great importance in dynamic analysis.

Stabilization of the Bernoulli-Euler Plate Equation: Numerical Analysis

The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

MEGSOR Iterative Scheme for the Solution of 2D Elliptic PDE's

Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.

Vortex-Shedding Suppression in Mixed Convective Flow past a Heated Square Cylinder

The present study investigates numerically the phenomenon of vortex-shedding and its suppression in twodimensional mixed convective flow past a square cylinder under the joint influence of buoyancy and free-stream orientation with respect to gravity. The numerical experiments have been conducted at a fixed Reynolds number (Re) of 100 and Prandtl number (Pr) of 0.71, while Richardson number (Ri) is varied from 0 to 1.6 and freestream orientation, α, is kept in the range 0o≤ α ≤ 90o, with 0o corresponding to an upward flow and 90o representing a cross-flow scenario, respectively. The continuity, momentum and energy equations, subject to Boussinesq approximation, are discretized using a finite difference method and are solved by a semi-explicit pressure correction scheme. The critical Richardson number, leading to the suppression of the vortex-shedding (Ric), is estimated by using Stuart-Landau theory at various free-stream orientations and the neutral curve is obtained in the Ri-α plane. The neutral curve exhibits an interesting non-monotonic behavior with Ric first increasing with increasing values of α upto 45o and then decreasing till 70o. Beyond 70o, the neutral curve again exhibits a sharp increasing asymptotic trend with Ric approaching very large values as α approaches 90o. The suppression of vortex shedding is not observed at α = 90o (cross-flow). In the unsteady flow regime, the Strouhal number (St) increases with the increase in Richardson number.

Absorption Spectra of Artificial Atoms in Presence of THz Fields

Artificial atoms are growing fields of interest due to their physical and optoelectronicapplications. The absorption spectra of the proposed artificial atom inpresence of Tera-Hertz field is investigated theoretically. We use the non-perturbativeFloquet theory and finite difference method to study the electronic structure of ArtificialAtom. The effect of static electric field on the energy levels of artificial atom is studied.The effect of orientation of static electric field on energy levels and diploe matrix elementsis also highlighted.

Comparison of Finite Difference Schemes for Water Flow in Unsaturated Soils

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of different approximations of moisture capacity function, convergence criteria and time stepping methods were evaluated. Two different infiltration problems were solved to investigate the performance of different schemes. These problems include of vertical water flow in a wet and very dry soils. The numerical solutions of two problems were compared using four evaluation criteria and the results of comparisons showed that fully implicit scheme is better than the other schemes. In addition, utilizing of standard chord slope method for approximation of moisture capacity function, automatic time stepping method and difference between two successive iterations as convergence criterion in the fully implicit scheme can lead to better and more reliable results for simulation of fluid movement in different unsaturated soils.

Improved Plasmonic Demultiplexer Based on Tapered and Rectangular Slot MIM Waveguide

In this paper, we have proposed two novel plasmonic demultiplexing structures based on metal-insulator-metal surfaces which, beside their compact size, have a very good transmission spectrum. The impact of the key internal parameters on the transmission spectrum is numerically analyzed by using the twodimensional (2D) finite difference time domain (FDTD) method. The proposed structures could be used to develop ultra-compact photonic wavelength demultiplexing devices for large-scale photonic integration.

Modeling and Visualizing Seismic Wave Propagation in Elastic Medium Using Multi-Dimension Wave Digital Filtering Approach

A novel PDE solver using the multidimensional wave digital filtering (MDWDF) technique to achieve the solution of a 2D seismic wave system is presented. In essence, the continuous physical system served by a linear Kirchhoff circuit is transformed to an equivalent discrete dynamic system implemented by a MD wave digital filtering (MDWDF) circuit. This amounts to numerically approximating the differential equations used to describe elements of a MD passive electronic circuit by a grid-based difference equations implemented by the so-called state quantities within the passive MDWDF circuit. So the digital model can track the wave field on a dense 3D grid of points. Details about how to transform the continuous system into a desired discrete passive system are addressed. In addition, initial and boundary conditions are properly embedded into the MDWDF circuit in terms of state quantities. Graphic results have clearly demonstrated some physical effects of seismic wave (P-wave and S–wave) propagation including radiation, reflection, and refraction from and across the hard boundaries. Comparison between the MDWDF technique and the finite difference time domain (FDTD) approach is also made in terms of the computational efficiency.

A Mathematical Model for Predicting Isothermal Soil Moisture Profiles Using Finite Difference Method

Subgrade moisture content varies with environmental and soil conditions and has significant influence on pavement performance. Therefore, it is important to establish realistic estimates of expected subgrade moisture contents to account for the effects of this variable on predicted pavement performance during the design stage properly. The initial boundary soil suction profile for a given pavement is a critical factor in determining expected moisture variations in the subgrade for given pavement and climatic and soil conditions. Several numerical models have been developed for predicting water and solute transport in saturated and unsaturated subgrade soils. Soil hydraulic properties are required for quantitatively describing water and chemical transport processes in soils by the numerical models. The required hydraulic properties are hydraulic conductivity, water diffusivity, and specific water capacity. The objective of this paper was to determine isothermal moisture profiles in a soil fill and predict the soil moisture movement above the ground water table using a simple one-dimensional finite difference model.

New Explicit Group Newton's Iterative Methods for the Solutions of Burger's Equation

In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

A Hybrid Differential Transform Approach for Laser Heating of a Double-Layered Thin Film

This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.

Numerical Investigation of a Slender Delta Wing in Combined Force-Pitch and Free-Roll

Numerical investigation of the characteristics of an 80° delta wing in combined force-pitch and free-roll is presented. The implicit, upwind, flux-difference splitting, finite volume scheme and the second-order-accurate finite difference scheme are employed to solve the flow governing equations and Euler rigid-body dynamics equations, respectively. The characteristics of the delta wing in combined free-roll and large amplitude force-pitch is obtained numerically and shows a well agreement with experimental data qualitatively. The motion in combined force-pitch and free-roll significantly reduces the lift force and transverse stabilities of the delta wing, which is closely related to the flying safety. Investigations on sensitive factors indicate that the roll-axis moment of inertia and the structural damping have great influence on the frequency and amplitude, respectively. Moreover, the turbulence model is considered as an influencing factor in the investigation.

Parallel Explicit Group Domain Decomposition Methods for the Telegraph Equation

In a previous work, we presented the numerical solution of the two dimensional second order telegraph partial differential equation discretized by the centred and rotated five-point finite difference discretizations, namely the explicit group (EG) and explicit decoupled group (EDG) iterative methods, respectively. In this paper, we utilize a domain decomposition algorithm on these group schemes to divide the tasks involved in solving the same equation. The objective of this study is to describe the development of the parallel group iterative schemes under OpenMP programming environment as a way to reduce the computational costs of the solution processes using multicore technologies. A detailed performance analysis of the parallel implementations of points and group iterative schemes will be reported and discussed.

Photonic Crystals for Novel Applications in Integrated-Optic Communication Systems and Devices

Photonic Crystal (PhC) based devices are being increasingly used in multifunctional, compact devices in integrated optical communication systems. They provide excellent controllability of light, yet maintaining the small size required for miniaturization. In this paper, the band gap properties of PhCs and their typical applications in optical waveguiding are considered. Novel PhC based applications such as nonlinear switching and tapers are considered and simulation results are shown using the accurate time-domain numerical method based on Finite Difference Time Domain (FDTD) scheme. The suitability of these devices for novel applications is discussed and evaluated.

An Optimal Control of Water Pollution in a Stream Using a Finite Difference Method

Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.