Search results for: Diffusion equation

Authors: Giulio Mangano, Alberto De Marco, Giovanni Zenezini

Abstract:

The concept of City Logistics (CL) has emerged to improve the impacts of last mile freight distribution in urban areas. In this paper, a System Dynamics (SD) model exploring the dynamics of the diffusion of a ICT platform for CL management across different populations is proposed. For the development of the model two sources have been used. On the one hand, the major diffusion variables and feedback loops are derived from a literature review of existing diffusion models. On the other hand, the parameters are represented by the value propositions delivered by the platform as a response to some of the users’ needs. To extract the most important value propositions the Business Model Canvas approach has been used. Such approach in fact focuses on understanding how a company can create value for her target customers. These variables and parameters are thus translated into a SD diffusion model with three different populations namely municipalities, logistics service providers, and own account carriers. Results show that, the three populations under analysis fully adopt the platform within the simulation time frame, highlighting a strong demand by different stakeholders for CL projects aiming at carrying out more efficient urban logistics operations.

Keywords: City logistics, simulation, system dynamics, business model.

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Authors: F. Bayatbabolghani, K. Parand

Abstract:

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faster convergence in this problem.

Keywords: Collocation method, Hermite function, Semi-infinite, Thomas-Fermi equation.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang, Yu Li

Abstract:

Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, controlled by the optimum smoothing time. In this scheme, the anisotropic diffusion is governed by the local coordinate transformation and the first and the second order normal derivatives of the image, while the edge enhancement is done by the hyperbolic tangent function. Experiments on real ultrasonic images indicate effective preservation of edges, local details and ultrasonic echoic bright strips on denoising by our scheme.

Keywords: anisotropic diffusion, coordinate transformationdirectional derivatives, edge enhancement, hyperbolic tangentfunction, image denoising.

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieh

Abstract:

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: Polynomial constitutive equation, solitary.

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Authors: Chantawan Noisri, Robert Harold Buchanan Exell

Abstract:

A simple model for studying convectional lifting processes in the tropics is described in this paper with some tests of the model in dry air. The model consists of the density equation, the wind equation, the vertical velocity equation, and the temperature equation. The model domain is two-dimensional with length 100 km and height 17.5 km. Plan for experiments to investigate the effects of the heating surface, the deep convection approximation and the treatment of velocities at the boundaries are discussed. Equations for the simplified treatment of moisture in the atmosphere in future numerical experiments are also given.

Keywords: Numerical weather prediction, Finite differences, Convection lifting.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang, Yu Li

Abstract:

Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, controlled by the optimum smoothing time. In this scheme, the anisotropic diffusion is governed by the local coordinate transformation and the first and the second order normal derivatives of the image, while the edge enhancement is done by the hyperbolic tangent function. Experiments on real ultrasonic images indicate effective preservation of edges, local details and ultrasonic echoic bright strips on denoising by our scheme.

Keywords: anisotropic diffusion, coordinate transformation, directional derivatives, edge enhancement, hyperbolic tangent function, image denoising.

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Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

Abstract:

As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

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Authors: Tanapat Brikshavana, Anirut Luadsong

Abstract:

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating propagation velocity terms are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting modified donorcell scheme for avoiding stability problems and prove that it is consistent to the modified donor-cell scheme with same accuracy. The splitting modified donor-cell scheme was adopted to split the wave spectral action balance equation into four one-dimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-cores computer.

Keywords: donor-cell scheme, parallel algorithm, spectral action balance equation, splitting method.

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

Abstract:

In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: Diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix.

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Authors: Kannanut Chamsri

Abstract:

Darcy’s Law is a well-known constitutive equation describing the flow of a fluid through a porous medium. The equation shows a relationship between the superficial or Darcy velocity and the pressure gradient which was first experimentally observed by Henry Darcy in 1855-1856. In this study, we apply homogenization method to Stokes equation in order to derive Darcy’s Law. The process of deriving the equation is complicated, especially in multidimensional domain. Thus, for the sake of simplicity, we use the indicial notation as well as the homogenization. This combination provides a smooth, simple and easy technique to derive Darcy’s Law.

Keywords: Darcy’s Law, Homogenization method, Indicial notation

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Authors: Qiang Zhao, Yina Shi, Guangwei Yuan, Zhiwei Dong

Abstract:

A cell-centered finite volume scheme for discretizing diffusion operators on distorted quadrilateral meshes has recently been designed and added to APMFCG to enable that code to be used as a tool for studying explosive magnetic flux compression generators. This paper describes this scheme. Comparisons with analytic results for 2-D test cases are presented, as well as 2-D results from a test of a "realistic" generator configuration.

Keywords: Cell-centered FVM, distorted meshes, diffusion scheme, MFCG.

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Authors: Reza Abazari, Rasool Abazari

Abstract:

In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.

Keywords: Coupled Korteweg-de Vries(KdV) equation, Coupled Burgers equation, Coupled Schrödinger equation, differential transformation method.

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Authors: N. Khatiashvili, K. Pirumova, D. Janjgava

Abstract:

The Stokes equation connected with the fluid flow over the axisymmetric bodies in a cylindrical area is considered. The equation is studied in a moving coordinate system with the appropriate boundary conditions. Effective formulas for the velocity components are obtained. The graphs of the velocity components and velocity profile are plotted.

Keywords: Stokes system, viscous fluid.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually the effects of blurred edges and jagged artifacts in the image to some extent. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to sharpen edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (“jaggies") along the tangent directions. In order to preserve image features such as edges, corners and textures, the nonlinear diffusion coefficients are locally adjusted according to the directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directional derivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Ahmet Tekcan

Abstract:

Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations

Keywords: Pell equation, solutions of Pell equation.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang

Abstract:

Image interpolation is a common problem in imaging applications. However, most interpolation algorithms in existence suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This paper presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts (''jaggies'') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first and second order directional derivatives of the image. Experimental results on synthetic images and nature images demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Keywords: anisotropic diffusion, bidirectional flow, directionalderivatives, edge enhancement, image interpolation, inverse flow, shock filter.

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Authors: Michael Tupý, Vít Petránek

Abstract:

The paper is focused on testing of the poly(vinyl butyral) (PVB) layer which had the function of a CO₂ insulating protection against concrete and mortar carbonation. The barrier efficiency of PVB was verified by the measurement of diffusion characteristics. Two different types of PVB were tested; original extruded PVB sheet and PVB sheet made from PVB dispersion which was obtained from recycled windshields. The work deals with the testing CO₂ diffusion when polymer sheets were exposed to a CO₂ atmosphere (10% v/v CO₂) with 0% RH. The excellent barrier capability against CO₂ permeability of original and also recycled types of PVB layers was observed. This application of PVB waste can bring advantageous use in civil engineering and significant environmental contribution.

Keywords: Windshield, Poly(vinyl butyral), Mortar, Diffusion, Carbonatation, Polymer waste.

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Authors: Wan Nural Jawahir Wan Yussof, Hans Burkhardt

Abstract:

Liver segmentation is the first significant process for liver diagnosis of the Computed Tomography. It segments the liver structure from other abdominal organs. Sophisticated filtering techniques are indispensable for a proper segmentation. In this paper, we employ a 3D anisotropic diffusion as a preprocessing step. While removing image noise, this technique preserve the significant parts of the image, typically edges, lines or other details that are important for the interpretation of the image. The segmentation task is done by using thresholding with automatic threshold values selection and finally the false liver region is eliminated using 3D connected component. The result shows that by employing the 3D anisotropic filtering, better liver segmentation results could be achieved eventhough simple segmentation technique is used.

Keywords: 3D Anisotropic Diffusion, non-linear filtering, CT Liver.

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Authors: Mohammad Taghi Darvishi, Mohammad Najafi

Abstract:

By means of the extended homoclinic test approach (shortly EHTA) with the aid of a symbolic computation system such as Maple, some complexiton type solutions for the (3+1)-dimensional Jimbo-Miwa equation are presented.

Keywords: Jimbo-Miwa equation, painleve analysis, Hirota's bilinear form, computerized symbolic computation.

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Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: Felix Che Shu

Abstract:

We give an explicit formula for the general solution of a one dimensional linear delay differential equation with multiple delays, which are integer multiples of the smallest delay. For an equation of this class with two delays, we derive two equations with single delays, whose stability is sufficient for the stability of the equation with two delays. This presents a new approach to the study of the stability of such systems. This approach avoids requirement of the knowledge of the location of the characteristic roots of the equation with multiple delays which are generally more difficult to determine, compared to the location of the characteristic roots of equations with a single delay.

Keywords: Delay Differential Equation, Explicit Solution, Exponential Stability, Lyapunov Exponents, Multiple Delays.

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Authors: Masoud Abedini, Azrul A. Mutalib, Shahrizan Baharom, Hong Hao

Abstract:

This study was conducted published to investigate there liability of the equation pressure-impulse (PI) reinforced concrete column inprevious studies. Equation involves three different levels of damage criteria known as D =0. 2, D =0. 5 and D =0. 8.The damage criteria known as a minor when 0-0.2, 0.2-0.5is known as moderate damage, high damage known as 0.5-0.8, and 0.8-1 of the structure is considered a failure. In this study, two types of reliability analyzes conducted. First, using pressure-impulse equation with different parameters. The parameters involved are the concrete strength, depth, width, and height column, the ratio of longitudinal reinforcement and transverse reinforcement ratio. In the first analysis of the reliability of this new equation is derived to improve the previous equations. The second reliability analysis involves three types of columns used to derive the PI curve diagram using the derived equation to compare with the equation derived from other researchers and graph minimum standoff versus weapon yield Federal Emergency Management Agency (FEMA). The results showed that the derived equation is more accurate with FEMA standards than previous researchers.

Keywords: Blast load, RC column, P-I curve, Analytical formulae, Standard FEMA.

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

Abstract:

The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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Authors: Ehsan Mahdavi

Abstract:

In this paper, we apply the Exp-function method to Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara equation is the combination of the Rosenau and standard Kawahara equations and Rosenau-KdV equation is the combination of the Rosenau and standard KdV equations. These equations are nonlinear partial differential equations (NPDE) which play an important role in mathematical physics. Exp-function method is easy, succinct and powerful to implement to nonlinear partial differential equations arising in mathematical physics. We mainly try to present an application of Exp-function method and offer solutions for common errors wich occur during some of the recent works.

Keywords: Exp-function method, Rosenau Kawahara equation, Rosenau Korteweg-de Vries equation, nonlinear partial differential equation.

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Authors: H. Ozbasaran

Abstract:

IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: Cantilever, IPN, IPE, lateral torsional buckling

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Authors: Zdravka Aljinović, Snježana Pivac, Boško Šego

Abstract:

According to the interaction of inflation and unemployment, expectation of the rate of inflation in Croatia is estimated. The interaction between inflation and unemployment is shown by model based on three first-order differential i.e. difference equations: Phillips relation, adaptive expectations equation and monetary-policy equation. The resulting equation is second order differential i.e. difference equation which describes the time path of inflation. The data of the rate of inflation and the rate of unemployment are used for parameters estimation. On the basis of the estimated time paths, the stability and convergence analysis is done for the rate of inflation.

Keywords: Differencing, inflation, time path, unemployment.

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Authors: N. Kumaresan , J. Kavikumar, Kuru Ratnavelu

Abstract:

In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method.

Keywords: Fuzzy differential equation, Generalized differentiability, H-difference and Simulink.

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Authors: A. R. Shahani, E. Mahdavi, M. Amidpour

Abstract:

Environment-assisted cracking (EAC) is one of the most serious causes of structural failure over a broad range of industrial applications including offshore structures. In EAC condition there is not a definite relation such as Paris equation in Linear Elastic Fracture Mechanics (LEFM). According to studying and searching a lot what the researchers said either a material has contact with hydrogen or any other corrosive environment, phenomenon of electrical and chemical reactions of material with its environment will be happened. In the literature, there are many different works to consider fatigue crack growing and solve it but they are experimental works. Thus, in this paper, authors have an aim to evaluate mathematically the pervious works in LEFM. Obviously, if an environment is more sour and corrosive, the changes of stress intensity factor is more and the calculation of stress intensity factor is difficult. A mathematical relation to deal with the stress intensity factor during the diffusion of sour environment especially hydrogen in a marine pipeline is presented. By using this relation having and some experimental relation an analytical formulation will be presented which enables the fatigue crack growth and critical crack length under cyclic loading to be predicted. In addition, we can calculate KSCC and stress intensity factor in the pipeline caused by EAC.

Keywords: Embrittlement, Fracture mechanics, Hydrogen diffusion, Stress intensity factor.

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Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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