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boundary conditions</title> <meta name="description" content="Search results for: second-order boundary conditions"> <meta name="keywords" content="second-order boundary conditions"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="second-order boundary conditions"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 10639</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: second-order boundary conditions</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10639</span> Fourier Galerkin Approach to Wave Equation with Absorbing Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexandra%20Leukauf">Alexandra Leukauf</a>, <a href="https://publications.waset.org/abstracts/search?q=Alexander%20Schirrer"> Alexander Schirrer</a>, <a href="https://publications.waset.org/abstracts/search?q=Emir%20Talic"> Emir Talic</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=absorbing%20boundary%20conditions" title="absorbing boundary conditions">absorbing boundary conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20control" title=" boundary control"> boundary control</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20Galerkin%20approach" title=" Fourier Galerkin approach"> Fourier Galerkin approach</a>, <a href="https://publications.waset.org/abstracts/search?q=modal%20approach" title=" modal approach"> modal approach</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20equation" title=" wave equation"> wave equation</a> </p> <a href="https://publications.waset.org/abstracts/65648/fourier-galerkin-approach-to-wave-equation-with-absorbing-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65648.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">396</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10638</span> Magnetohydrodynamic 3D Maxwell Fluid Flow Towards a Horizontal Stretched Surface with Convective Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Y.%20Malika">M. Y. Malika</a>, <a href="https://publications.waset.org/abstracts/search?q=Farzana"> Farzana</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdul%20Rehman"> Abdul Rehman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study deals with the steady, 3D MHD boundary layer flow of a non-Newtonian Maxwell fluid flow due to a horizontal surface stretched exponentially in two lateral directions. The temperature at the boundary is assumed to be distributed exponentially and possesses convective boundary conditions. The governing nonlinear system of partial differential equations along with associated boundary conditions is simplified using a suitable transformation and the obtained set of ordinary differential equations is solved through numerical techniques. The effects of important involved parameters associated with fluid flow and heat flux are shown through graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20layer%20flow" title="boundary layer flow">boundary layer flow</a>, <a href="https://publications.waset.org/abstracts/search?q=exponentially%20stretched%20surface" title=" exponentially stretched surface"> exponentially stretched surface</a>, <a href="https://publications.waset.org/abstracts/search?q=Maxwell%20fluid" title=" Maxwell fluid"> Maxwell fluid</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a> </p> <a href="https://publications.waset.org/abstracts/23186/magnetohydrodynamic-3d-maxwell-fluid-flow-towards-a-horizontal-stretched-surface-with-convective-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23186.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">588</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10637</span> Collocation Method for Coupled System of Boundary Value Problems with Cubic B-Splines </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20N.%20S.%20Kasi%20Viswanadham">K. N. S. Kasi Viswanadham </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=coupled%20system" title=" coupled system"> coupled system</a>, <a href="https://publications.waset.org/abstracts/search?q=cubic%20b-splines" title=" cubic b-splines"> cubic b-splines</a>, <a href="https://publications.waset.org/abstracts/search?q=mesh%20points" title=" mesh points"> mesh points</a> </p> <a href="https://publications.waset.org/abstracts/54713/collocation-method-for-coupled-system-of-boundary-value-problems-with-cubic-b-splines" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54713.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">209</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10636</span> 1D Klein-Gordon Equation in an Infinite Square Well with PT Symmetry Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Suleiman%20Bashir%20Adamu">Suleiman Bashir Adamu</a>, <a href="https://publications.waset.org/abstracts/search?q=Lawan%20Sani%20Taura"> Lawan Sani Taura</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schr枚dinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eigenvalues" title="Eigenvalues">Eigenvalues</a>, <a href="https://publications.waset.org/abstracts/search?q=Eigenfunction" title=" Eigenfunction"> Eigenfunction</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamiltonian" title=" Hamiltonian"> Hamiltonian</a>, <a href="https://publications.waset.org/abstracts/search?q=Klein-%20Gordon%20equation" title=" Klein- Gordon equation"> Klein- Gordon equation</a>, <a href="https://publications.waset.org/abstracts/search?q=PT-symmetric%20quantum%20mechanics" title=" PT-symmetric quantum mechanics"> PT-symmetric quantum mechanics</a> </p> <a href="https://publications.waset.org/abstracts/50876/1d-klein-gordon-equation-in-an-infinite-square-well-with-pt-symmetry-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50876.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">383</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10635</span> A Numerical Study of Force-Based Boundary Conditions in Multiparticle Collision Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arturo%20Ayala-Hernandez">Arturo Ayala-Hernandez</a>, <a href="https://publications.waset.org/abstracts/search?q=Humberto%20Hijar"> Humberto Hijar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We propose a new alternative method for imposing fluid-solid boundary conditions in simulations of Multiparticle Collision Dynamics. Our method is based on the introduction of an explicit potential force acting between the fluid particles and a surface representing a solid boundary. We show that our method can be used in simulations of plane Poiseuille flows. Important quantities characterizing the flow and the fluid-solid interaction like the slip coefficient at the solid boundary and the effective viscosity of the fluid, are measured in terms of the set of independent parameters defining the numerical implementation. We find that our method can be used to simulate the correct hydrodynamic flow within a wide range of values of these parameters. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Multiparticle%20Collision%20Dynamics" title="Multiparticle Collision Dynamics">Multiparticle Collision Dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=fluid-solid" title=" fluid-solid"> fluid-solid</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20conditions" title=" boundary conditions"> boundary conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=molecular%20dynamics" title=" molecular dynamics"> molecular dynamics</a> </p> <a href="https://publications.waset.org/abstracts/17569/a-numerical-study-of-force-based-boundary-conditions-in-multiparticle-collision-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17569.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">538</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10634</span> Boundary Conditions for 2D Site Response Analysis in OpenSees</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Eskandarighadi">M. Eskandarighadi</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20R.%20McGann"> C. R. McGann</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is observed from past experiences of earthquakes that local site conditions can significantly affect the strong ground motion characteristicssuch as frequency content, amplitude, and duration of seismic waves. The most common method for investigating site response is one-dimensional seismic site response analysis. The infinite horizontal length of the model and the homogeneous characteristic of the soil are crucial assumptions of this method. One boundary condition that can be used in the sides is tying the sides horizontally for vertical 1D wave propagation. However, 1D analysis cannot account for the 2D nature of wave propagation in the condition where the soil profile is not fully horizontal or has heterogeneity within layers. Therefore, 2D seismic site response analysis can be used to take all of these limitations into account for a better understanding of local site conditions. Different types of boundary conditions can be appliedin 2D site response models, such as tied boundary condition, massive columns, and free-field boundary condition. The tied boundary condition has been used in 1D analysis, which is useful for 1D wave propagation. Employing two massive columns at the sides is another approach for capturing the 2D nature of wave propagation. Free-field boundary condition can simulate the free-field motion that would exist far from the domain of interest. The goal for free-field boundary condition is to minimize the unwanted reflection from sides. This research focuses on the comparison between these methods with examples and discusses the details and limitations of each of these boundary conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20condition" title="boundary condition">boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=free-field" title=" free-field"> free-field</a>, <a href="https://publications.waset.org/abstracts/search?q=massive%20columns" title=" massive columns"> massive columns</a>, <a href="https://publications.waset.org/abstracts/search?q=opensees" title=" opensees"> opensees</a>, <a href="https://publications.waset.org/abstracts/search?q=site%20response%20analysis" title=" site response analysis"> site response analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20propagation" title=" wave propagation"> wave propagation</a> </p> <a href="https://publications.waset.org/abstracts/158091/boundary-conditions-for-2d-site-response-analysis-in-opensees" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/158091.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">183</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10633</span> Differential Transform Method: Some Important Examples</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Jamil%20Amir">M. Jamil Amir</a>, <a href="https://publications.waset.org/abstracts/search?q=Rabia%20Iqbal"> Rabia Iqbal</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Yaseen"> M. Yaseen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> 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. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=differential%20transform%20method" title="differential transform method">differential transform method</a>, <a href="https://publications.waset.org/abstracts/search?q=laplace%20equation" title=" laplace equation"> laplace equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Dirichlet%20boundary%20conditions" title=" Dirichlet boundary conditions"> Dirichlet boundary conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=Neumann%20boundary%20conditions" title=" Neumann boundary conditions"> Neumann boundary conditions</a> </p> <a href="https://publications.waset.org/abstracts/18605/differential-transform-method-some-important-examples" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18605.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">537</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10632</span> A Non-Standard Finite Difference Scheme for the Solution of Laplace Equation with Dirichlet Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khaled%20Moaddy">Khaled Moaddy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=standard%20finite%20difference%20schemes" title="standard finite difference schemes">standard finite difference schemes</a>, <a href="https://publications.waset.org/abstracts/search?q=non-standard%20schemes" title=" non-standard schemes"> non-standard schemes</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplace%20equation" title=" Laplace equation"> Laplace equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Dirichlet%20boundary%20conditions" title=" Dirichlet boundary conditions"> Dirichlet boundary conditions</a> </p> <a href="https://publications.waset.org/abstracts/119718/a-non-standard-finite-difference-scheme-for-the-solution-of-laplace-equation-with-dirichlet-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/119718.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">132</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10631</span> Effect of Boundary Condition on Granular Pressure of Gas-Solid Flow in a Rotating Drum</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rezwana%20Rahman">Rezwana Rahman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various simulations have been conducted to understand the particle's macroscopic behavior in the solid-gas multiphase flow in rotating drums in the past. In these studies, the particle-wall no-slip boundary condition was usually adopted. However, the non-slip boundary condition is rarely encountered in real systems. A little effort has been made to investigate the particle behavior at slip boundary conditions. The paper represents a study of the gas-solid flow in a horizontal rotating drum at a slip boundary wall condition. Two different sizes of particles with the same density have been considered. The Eulerian鈥揈ulerian multiphase model with the kinetic theory of granular flow was used in the simulations. The granular pressure at the rolling flow regime with specularity coefficient 1 was examined and compared with that obtained based on the no-slip boundary condition. The results reveal that the profiles of granular pressure distribution on the transverse plane of the drum are similar for both boundary conditions. But, overall, compared with those for the no-slip boundary condition, the values of granular pressure for specularity coefficient 1 are larger for the larger particle and smaller for the smaller particle. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20condition" title="boundary condition">boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=eulerian%E2%80%93eulerian" title=" eulerian鈥揺ulerian"> eulerian鈥揺ulerian</a>, <a href="https://publications.waset.org/abstracts/search?q=multiphase" title=" multiphase"> multiphase</a>, <a href="https://publications.waset.org/abstracts/search?q=specularity%20coefficient" title=" specularity coefficient"> specularity coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=transverse%20plane" title=" transverse plane"> transverse plane</a> </p> <a href="https://publications.waset.org/abstracts/138424/effect-of-boundary-condition-on-granular-pressure-of-gas-solid-flow-in-a-rotating-drum" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/138424.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">219</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10630</span> Theoretical Modal Analysis of Freely and Simply Supported RC Slabs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20S.%20Ahmed">M. S. Ahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20A.%20Mohammad"> F. A. Mohammad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper focuses on the dynamic behavior of reinforced concrete (RC) slabs. Therefore, the theoretical modal analysis was performed using two different types of boundary conditions. Modal analysis method is the most important dynamic analyses. The analysis would be modal case when there is no external force on the structure. By using this method in this paper, the effects of freely and simply supported boundary conditions on the frequencies and mode shapes of RC square slabs are studied. ANSYS software was employed to derive the finite element model to determine the natural frequencies and mode shapes of the slabs. Then, the obtained results through numerical analysis (finite element analysis) would be compared with an exact solution. The main goal of the research study is to predict how the boundary conditions change the behavior of the slab structures prior to performing experimental modal analysis. Based on the results, it is concluded that simply support boundary condition has obvious influence to increase the natural frequencies and change the shape of mode when it is compared with freely supported boundary condition of slabs. This means that such support conditions have direct influence on the dynamic behavior of the slabs. Thus, it is suggested to use free-free boundary condition in experimental modal analysis to precisely reflect the properties of the structure. By using free-free boundary conditions, the influence of poorly defined supports is interrupted. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=natural%20frequencies" title="natural frequencies">natural frequencies</a>, <a href="https://publications.waset.org/abstracts/search?q=mode%20shapes" title=" mode shapes"> mode shapes</a>, <a href="https://publications.waset.org/abstracts/search?q=modal%20analysis" title=" modal analysis"> modal analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=ANSYS%20software" title=" ANSYS software"> ANSYS software</a>, <a href="https://publications.waset.org/abstracts/search?q=RC%20slabs" title=" RC slabs"> RC slabs</a> </p> <a href="https://publications.waset.org/abstracts/17461/theoretical-modal-analysis-of-freely-and-simply-supported-rc-slabs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17461.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">457</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10629</span> Degeneracy and Defectiveness in Non-Hermitian Systems with Open Boundary</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yongxu%20Fu">Yongxu Fu</a>, <a href="https://publications.waset.org/abstracts/search?q=Shaolong%20Wan"> Shaolong Wan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study the band degeneracy, defectiveness, as well as exceptional points of non-Hermitian systems and materials analytically. We elaborate on the energy bands, the band degeneracy, and the defectiveness of eigenstates under open boundary conditions based on developing a general theory of one-dimensional (1D) non-Hermitian systems. We research the presence of the exceptional points in a generalized non-Hermitian Su-Schrieffer-Heeger model under open boundary conditions. Beyond our general theory, there exist infernal points in 1D non-Hermitian systems, where the energy spectra under open boundary conditions converge on some discrete energy values. We study two 1D non-Hermitian models with the existence of infernal points. We generalize the infernal points to the infernal knots in four-dimensional non-Hermitian systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-hermitian" title="non-hermitian">non-hermitian</a>, <a href="https://publications.waset.org/abstracts/search?q=degeneracy" title=" degeneracy"> degeneracy</a>, <a href="https://publications.waset.org/abstracts/search?q=defectiveness" title=" defectiveness"> defectiveness</a>, <a href="https://publications.waset.org/abstracts/search?q=exceptional%20points" title=" exceptional points"> exceptional points</a>, <a href="https://publications.waset.org/abstracts/search?q=infernal%20points" title=" infernal points"> infernal points</a> </p> <a href="https://publications.waset.org/abstracts/149871/degeneracy-and-defectiveness-in-non-hermitian-systems-with-open-boundary" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/149871.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">130</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10628</span> Divergence Regularization Method for Solving Ill-Posed Cauchy Problem for the Helmholtz Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benedict%20Barnes">Benedict Barnes</a>, <a href="https://publications.waset.org/abstracts/search?q=Anthony%20Y.%20Aidoo"> Anthony Y. Aidoo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=divergence%20regularization%20method" title="divergence regularization method">divergence regularization method</a>, <a href="https://publications.waset.org/abstracts/search?q=Helmholtz%20equation" title=" Helmholtz equation"> Helmholtz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20inhomogeneous%20Cauchy%20boundary%20conditions" title=" ill-posed inhomogeneous Cauchy boundary conditions"> ill-posed inhomogeneous Cauchy boundary conditions</a> </p> <a href="https://publications.waset.org/abstracts/137727/divergence-regularization-method-for-solving-ill-posed-cauchy-problem-for-the-helmholtz-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137727.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">189</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10627</span> Combined Effect of Moving and Open Boundary Conditions in the Simulation of Inland Inundation Due to Far Field Tsunami</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Ashaque%20Meah">M. Ashaque Meah</a>, <a href="https://publications.waset.org/abstracts/search?q=Md.%20Fazlul%20Karim"> Md. Fazlul Karim</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Shah%20Noor"> M. Shah Noor</a>, <a href="https://publications.waset.org/abstracts/search?q=Nazmun%20Nahar%20Papri"> Nazmun Nahar Papri</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Khalid%20Hossen"> M. Khalid Hossen</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Ismoen"> M. Ismoen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Tsunami and inundation modelling due to far field tsunami propagation in a limited area is a very challenging numerical task because it involves many aspects such as the formation of various types of waves and the irregularities of coastal boundaries. To compute the effect of far field tsunami and extent of inland inundation due to far field tsunami along the coastal belts of west coast of Malaysia and Southern Thailand, a formulated boundary condition and a moving boundary condition are simultaneously used. In this study, a boundary fitted curvilinear grid system is used in order to incorporate the coastal and island boundaries accurately as the boundaries of the model domain are curvilinear in nature and the bending is high. The tsunami response of the event 26 December 2004 along the west open boundary of the model domain is computed to simulate the effect of far field tsunami. Based on the data of the tsunami source at the west open boundary of the model domain, a boundary condition is formulated and applied to simulate the tsunami response along the coastal and island boundaries. During the simulation process, a moving boundary condition is initiated instead of fixed vertical seaside wall. The extent of inland inundation and tsunami propagation pattern are computed. Some comparisons are carried out to test the validation of the simultaneous use of the two boundary conditions. All simulations show excellent agreement with the data of observation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=open%20boundary%20condition" title="open boundary condition">open boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=moving%20boundary%20condition" title=" moving boundary condition"> moving boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary-fitted%20curvilinear%20grids" title=" boundary-fitted curvilinear grids"> boundary-fitted curvilinear grids</a>, <a href="https://publications.waset.org/abstracts/search?q=far-field%20tsunami" title=" far-field tsunami"> far-field tsunami</a>, <a href="https://publications.waset.org/abstracts/search?q=shallow%20water%20equations" title=" shallow water equations"> shallow water equations</a>, <a href="https://publications.waset.org/abstracts/search?q=tsunami%20source" title=" tsunami source"> tsunami source</a>, <a href="https://publications.waset.org/abstracts/search?q=Indonesian%20tsunami%20of%202004" title=" Indonesian tsunami of 2004"> Indonesian tsunami of 2004</a> </p> <a href="https://publications.waset.org/abstracts/38523/combined-effect-of-moving-and-open-boundary-conditions-in-the-simulation-of-inland-inundation-due-to-far-field-tsunami" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38523.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">446</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10626</span> Implementation of Free-Field Boundary Condition for 2D Site Response Analysis in OpenSees</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Eskandarighadi">M. Eskandarighadi</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20R.%20McGann"> C. R. McGann</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is observed from past experiences of earthquakes that local site conditions can significantly affect the strong ground motion characteristics experience at the site. One-dimensional seismic site response analysis is the most common approach for investigating site response. This approach assumes that soil is homogeneous and infinitely extended in the horizontal direction. Therefore, tying side boundaries together is one way to model this behavior, as the wave passage is assumed to be only vertical. However, 1D analysis cannot capture the 2D nature of wave propagation, soil heterogeneity, and 2D soil profile with features such as inclined layer boundaries. In contrast, 2D seismic site response modeling can consider all of the mentioned factors to better understand local site effects on strong ground motions. 2D wave propagation and considering that the soil profile on the two sides of the model may not be identical clarifies the importance of a boundary condition on each side that can minimize the unwanted reflections from the edges of the model and input appropriate loading conditions. Ideally, the model size should be sufficiently large to minimize the wave reflection, however, due to computational limitations, increasing the model size is impractical in some cases. Another approach is to employ free-field boundary conditions that take into account the free-field motion that would exist far from the model domain and apply this to the sides of the model. This research focuses on implementing free-field boundary conditions in OpenSees for 2D site response analysisComparisons are made between 1D models and 2D models with various boundary conditions, and details and limitations of the developed free-field boundary modeling approach are discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20condition" title="boundary condition">boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=free-field" title=" free-field"> free-field</a>, <a href="https://publications.waset.org/abstracts/search?q=opensees" title=" opensees"> opensees</a>, <a href="https://publications.waset.org/abstracts/search?q=site%20response%20analysis" title=" site response analysis"> site response analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20propagation" title=" wave propagation"> wave propagation</a> </p> <a href="https://publications.waset.org/abstracts/158087/implementation-of-free-field-boundary-condition-for-2d-site-response-analysis-in-opensees" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/158087.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">158</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10625</span> Inverse Mode Shape Problem of Hand-Arm Vibration (Humerus Bone) for Bio-Dynamic Response Using Varying Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ajay%20R">Ajay R</a>, <a href="https://publications.waset.org/abstracts/search?q=Rammohan%20B"> Rammohan B</a>, <a href="https://publications.waset.org/abstracts/search?q=Sridhar%20K%20S%20S"> Sridhar K S S</a>, <a href="https://publications.waset.org/abstracts/search?q=Gurusharan%20%20N"> Gurusharan N</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The objective of the work is to develop a numerical method to solve the inverse mode shape problem by determining the cross-sectional area of a structure for the desired mode shape via the vibration response study of the humerus bone, which is in the form of a cantilever beam with anisotropic material properties. The humerus bone is the long bone in the arm that connects the shoulder to the elbow. The mode shape is assumed to be a higher-order polynomial satisfying a prescribed set of boundary conditions to converge the numerical algorithm. The natural frequency and the mode shapes are calculated for different boundary conditions to find the cross-sectional area of humerus bone from Eigenmode shape with the aid of the inverse mode shape algorithm. The cross-sectional area of humerus bone validates the mode shapes of specific boundary conditions. The numerical method to solve the inverse mode shape problem is validated in the biomedical application by finding the cross-sectional area of a humerus bone in the human arm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cross-sectional%20area" title="Cross-sectional area">Cross-sectional area</a>, <a href="https://publications.waset.org/abstracts/search?q=Humerus%20bone" title=" Humerus bone"> Humerus bone</a>, <a href="https://publications.waset.org/abstracts/search?q=Inverse%20mode%20shape%20problem" title=" Inverse mode shape problem"> Inverse mode shape problem</a>, <a href="https://publications.waset.org/abstracts/search?q=Mode%20shape" title=" Mode shape"> Mode shape</a> </p> <a href="https://publications.waset.org/abstracts/125654/inverse-mode-shape-problem-of-hand-arm-vibration-humerus-bone-for-bio-dynamic-response-using-varying-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125654.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">126</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10624</span> Introduction to Two Artificial Boundary Conditions for Transient Seepage Problems and Their Application in Geotechnical Engineering</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shuang%20Luo">Shuang Luo</a>, <a href="https://publications.waset.org/abstracts/search?q=Er-Xiang%20Song"> Er-Xiang Song</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many problems in geotechnical engineering, such as foundation deformation, groundwater seepage, seismic wave propagation and geothermal transfer problems, may involve analysis in the ground which can be seen as extending to infinity. To that end, consideration has to be given regarding how to deal with the unbounded domain to be analyzed by using numerical methods, such as finite element method (FEM), finite difference method (FDM) or finite volume method (FVM). A simple artificial boundary approach derived from the analytical solutions for transient radial seepage problems, is introduced. It should be noted, however, that the analytical solutions used to derive the artificial boundary are particular solutions under certain boundary conditions, such as constant hydraulic head at the origin or constant pumping rate of the well. When dealing with unbounded domains with unsteady boundary conditions, a more sophisticated artificial boundary approach to deal with the infinity of the domain is presented. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global artificial boundary conditions (ABCs) are simplified to local ones so that the computational efficiency is enhanced significantly. The introduced two local ABCs are implemented in a finite element computer program so that various seepage problems can be calculated. The two approaches are first verified by the computation of a one-dimensional radial flow problem, and then tentatively applied to more general two-dimensional cylindrical problems and plane problems. Numerical calculations show that the local ABCs can not only give good results for one-dimensional axisymmetric transient flow, but also applicable for more general problems, such as axisymmetric two-dimensional cylindrical problems, and even more general planar two-dimensional flow problems for well doublet and well groups. An important advantage of the latter local boundary is its applicability for seepage under rapidly changing unsteady boundary conditions, and even the computational results on the truncated boundary are usually quite satisfactory. In this aspect, it is superior over the former local boundary. Simulation of relatively long operational time demonstrates to certain extents the numerical stability of the local boundary. The solutions of the two local ABCs are compared with each other and with those obtained by using large element mesh, which proves the satisfactory performance and obvious superiority over the large mesh model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=transient%20seepage" title="transient seepage">transient seepage</a>, <a href="https://publications.waset.org/abstracts/search?q=unbounded%20domain" title=" unbounded domain"> unbounded domain</a>, <a href="https://publications.waset.org/abstracts/search?q=artificial%20boundary%20condition" title=" artificial boundary condition"> artificial boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a> </p> <a href="https://publications.waset.org/abstracts/66266/introduction-to-two-artificial-boundary-conditions-for-transient-seepage-problems-and-their-application-in-geotechnical-engineering" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66266.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">294</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10623</span> Wave Transmitting Boundary in Dynamic Analysis for an Elastoplastic Medium Using the Material Point Method </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chinh%20Phuong%20Do">Chinh Phuong Do</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Dynamic analysis of slope under seismic condition requires the elimination of spurious reflection at the bounded domain. This paper studies the performances of wave transmitting boundaries, including the standard viscous boundary and the viscoelastic boundary to the material point method (MPM) framework. First, analytical derivations of these non-reflecting conditions particularly to the implicit MPM are presented. Then, a number of benchmark and geotechnical examples will be shown. Overall, the results agree well with analytical solutions, indicating the ability to accurately simulate the radiation at the bounded domain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20analysis" title="dynamic analysis">dynamic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=implicit" title=" implicit"> implicit</a>, <a href="https://publications.waset.org/abstracts/search?q=MPM" title=" MPM"> MPM</a>, <a href="https://publications.waset.org/abstracts/search?q=non-reflecting%20boundary" title=" non-reflecting boundary"> non-reflecting boundary</a> </p> <a href="https://publications.waset.org/abstracts/137872/wave-transmitting-boundary-in-dynamic-analysis-for-an-elastoplastic-medium-using-the-material-point-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137872.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">204</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10622</span> Critical Buckling Load of Carbon Nanotube with Non-Local Timoshenko Beam Using the Differential Transform Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tayeb%20Bensattalah">Tayeb Bensattalah</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Zidour"> Mohamed Zidour</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Ait%20Amar%20Meziane"> Mohamed Ait Amar Meziane</a>, <a href="https://publications.waset.org/abstracts/search?q=Tahar%20Hassaine%20Daouadji"> Tahar Hassaine Daouadji</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdelouahed%20Tounsi"> Abdelouahed Tounsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. In铿倁ence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20conditions" title="boundary conditions">boundary conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=buckling" title=" buckling"> buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=non-local" title=" non-local"> non-local</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20transform%20method" title=" differential transform method"> differential transform method</a> </p> <a href="https://publications.waset.org/abstracts/81382/critical-buckling-load-of-carbon-nanotube-with-non-local-timoshenko-beam-using-the-differential-transform-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/81382.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">301</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10621</span> Existence Solutions for Three Point Boundary Value Problem for Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Houas">Mohamed Houas</a>, <a href="https://publications.waset.org/abstracts/search?q=Maamar%20Benbachir"> Maamar Benbachir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii's fixed point theorem. At the end, some illustrative examples are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=caputo%20derivative" title="caputo derivative">caputo derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20problem" title=" boundary value problem"> boundary value problem</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point%20theorem" title=" fixed point theorem"> fixed point theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=local%20conditions" title=" local conditions"> local conditions</a> </p> <a href="https://publications.waset.org/abstracts/13970/existence-solutions-for-three-point-boundary-value-problem-for-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13970.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">428</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10620</span> Numerical Computation of Sturm-Liouville Problem with Robin Boundary Condition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Theddeus%20T.%20Akano">Theddeus T. Akano</a>, <a href="https://publications.waset.org/abstracts/search?q=Omotayo%20A.%20Fakinlede"> Omotayo A. Fakinlede</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The modelling of physical phenomena, such as the earth鈥檚 free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm-Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solutions of classical Sturm鈥揕iouville problems are presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sturm-Liouville%20problem" title="Sturm-Liouville problem">Sturm-Liouville problem</a>, <a href="https://publications.waset.org/abstracts/search?q=Robin%20boundary%20condition" title=" Robin boundary condition"> Robin boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title=" finite element method"> finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=eigenvalue%20problems" title=" eigenvalue problems"> eigenvalue problems</a> </p> <a href="https://publications.waset.org/abstracts/37320/numerical-computation-of-sturm-liouville-problem-with-robin-boundary-condition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37320.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">362</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10619</span> Comparison of the Boundary Element Method and the Method of Fundamental Solutions for Analysis of Potential and Elasticity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Zenhari">S. Zenhari</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Hematiyan"> M. R. Hematiyan</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Khosravifard"> A. Khosravifard</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Feizi"> M. R. Feizi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The boundary element method (BEM) and the method of fundamental solutions (MFS) are well-known fundamental solution-based methods for solving a variety of problems. Both methods are boundary-type techniques and can provide accurate results. In comparison to the finite element method (FEM), which is a domain-type method, the BEM and the MFS need less manual effort to solve a problem. The aim of this study is to compare the accuracy and reliability of the BEM and the MFS. This comparison is made for 2D potential and elasticity problems with different boundary and loading conditions. In the comparisons, both convex and concave domains are considered. Both linear and quadratic elements are employed for boundary element analysis of the examples. The discretization of the problem domain in the BEM, i.e., converting the boundary of the problem into boundary elements, is relatively simple; however, in the MFS, obtaining appropriate locations of collocation and source points needs more attention to obtain reliable solutions. The results obtained from the presented examples show that both methods lead to accurate solutions for convex domains, whereas the BEM is more suitable than the MFS for concave domains. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20element%20method" title="boundary element method">boundary element method</a>, <a href="https://publications.waset.org/abstracts/search?q=method%20of%20fundamental%20solutions" title=" method of fundamental solutions"> method of fundamental solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=elasticity" title=" elasticity"> elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=potential%20problem" title=" potential problem"> potential problem</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20domain" title=" convex domain"> convex domain</a>, <a href="https://publications.waset.org/abstracts/search?q=concave%20domain" title=" concave domain"> concave domain</a> </p> <a href="https://publications.waset.org/abstracts/163380/comparison-of-the-boundary-element-method-and-the-method-of-fundamental-solutions-for-analysis-of-potential-and-elasticity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163380.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">90</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10618</span> Exact Vibration Analysis of a Rectangular Nano-Plate Using Nonlocal Modified Sinusoidal Shear Deformation Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Korosh%20Khorshidi">Korosh Khorshidi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Khodadadi"> Mohammad Khodadadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, exact close form solution for out of plate free flexural vibration of moderately thick rectangular nanoplates are presented based on nonlocal modified trigonometric shear deformation theory, with assumptions of the Levy's type boundary conditions, for the first time. The aim of this study is to evaluate the effect of small-scale parameters on the frequency parameters of the moderately thick rectangular nano-plates. To describe the effects of small-scale parameters on vibrations of rectangular nanoplates, the Eringen theory is used. The Levy's type boundary conditions are combination of six different boundary conditions; specifically, two opposite edges are simply supported and any of the other two edges can be simply supported, clamped or free. Governing equations of motion and boundary conditions of the plate are derived by using the Hamilton鈥檚 principle. The present analytical solution can be obtained with any required accuracy and can be used as benchmark. Numerical results are presented to illustrate the effectiveness of the proposed method compared to other methods reported in the literature. Finally, the effect of boundary conditions, aspect ratios, small scale parameter and thickness ratios on nondimensional natural frequency parameters and frequency ratios are examined and discussed in detail. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=exact%20solution" title="exact solution">exact solution</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20modified%20sinusoidal%20shear%20deformation%20theory" title=" nonlocal modified sinusoidal shear deformation theory"> nonlocal modified sinusoidal shear deformation theory</a>, <a href="https://publications.waset.org/abstracts/search?q=out%20of%20plane%20vibration" title=" out of plane vibration"> out of plane vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=moderately%20thick%20rectangular%20plate" title=" moderately thick rectangular plate"> moderately thick rectangular plate</a> </p> <a href="https://publications.waset.org/abstracts/36318/exact-vibration-analysis-of-a-rectangular-nano-plate-using-nonlocal-modified-sinusoidal-shear-deformation-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36318.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">387</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10617</span> Thermal Buckling Analysis of Functionally Graded Beams with Various Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gholamreza%20Koochaki">Gholamreza Koochaki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=buckling" title="buckling">buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=functionally%20graded%20beams" title=" functionally graded beams"> functionally graded beams</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%27s%20principle" title=" Hamilton's principle"> Hamilton's principle</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler-Bernoulli%20beam" title=" Euler-Bernoulli beam"> Euler-Bernoulli beam</a> </p> <a href="https://publications.waset.org/abstracts/30892/thermal-buckling-analysis-of-functionally-graded-beams-with-various-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30892.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">392</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10616</span> Human Intraocular Thermal Field in Action with Different Boundary Conditions Considering Aqueous Humor and Vitreous Humor Fluid Flow</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dara%20Singh">Dara Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Keikhosrow%20Firouzbakhsh"> Keikhosrow Firouzbakhsh</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Taghi%20Ahmadian"> Mohammad Taghi Ahmadian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, a validated 3D finite volume model of human eye is developed to study the fluid flow and heat transfer in the human eye at steady state conditions. For this purpose, discretized bio-heat transfer equation coupled with Boussinesq equation is analyzed with different anatomical, environmental, and physiological conditions. It is demonstrated that the fluid circulation is formed as a result of thermal gradients in various regions of eye. It is also shown that posterior region of the human eye is less affected by the ambient conditions compared to the anterior segment which is sensitive to the ambient conditions and also to the way the gravitational field is defined compared to the geometry of the eye making the circulations and the thermal field complicated in transient states. The effect of variation in material and boundary conditions guides us to the conclusion that thermal field of a healthy and non-healthy eye can be distinguished via computer simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bio-heat" title="bio-heat">bio-heat</a>, <a href="https://publications.waset.org/abstracts/search?q=boussinesq" title=" boussinesq"> boussinesq</a>, <a href="https://publications.waset.org/abstracts/search?q=conduction" title=" conduction"> conduction</a>, <a href="https://publications.waset.org/abstracts/search?q=convection" title=" convection"> convection</a>, <a href="https://publications.waset.org/abstracts/search?q=eye" title=" eye"> eye</a> </p> <a href="https://publications.waset.org/abstracts/60991/human-intraocular-thermal-field-in-action-with-different-boundary-conditions-considering-aqueous-humor-and-vitreous-humor-fluid-flow" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/60991.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">345</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10615</span> A Continuous Boundary Value Method of Order 8 for Solving the General Second Order Multipoint Boundary Value Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20A.%20Biala">T. A. Biala</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the numerical integration of the general second order multipoint boundary value problems. This has been achieved by the development of a continuous linear multistep method (LMM). The continuous LMM is used to construct a main discrete method to be used with some initial and final methods (also obtained from the continuous LMM) so that they form a discrete analogue of the continuous second order boundary value problems. These methods are used as boundary value methods and adapted to cope with the integration of the general second order multipoint boundary value problems. The convergence, the use and the region of absolute stability of the methods are discussed. Several numerical examples are implemented to elucidate our solution process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20multistep%20methods" title="linear multistep methods">linear multistep methods</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20methods" title=" boundary value methods"> boundary value methods</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20order%20multipoint%20boundary%20value%20problems" title=" second order multipoint boundary value problems"> second order multipoint boundary value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence" title=" convergence"> convergence</a> </p> <a href="https://publications.waset.org/abstracts/50749/a-continuous-boundary-value-method-of-order-8-for-solving-the-general-second-order-multipoint-boundary-value-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50749.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">377</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10614</span> Finite Time Blow-Up and Global Solutions for a Semilinear Parabolic Equation with Linear Dynamical Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xu%20Runzhang">Xu Runzhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Yang%20Yanbing"> Yang Yanbing</a>, <a href="https://publications.waset.org/abstracts/search?q=Niu%20Yi"> Niu Yi</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhang%20Mingyou"> Zhang Mingyou</a>, <a href="https://publications.waset.org/abstracts/search?q=Liu%20Yu"> Liu Yu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(惟). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=high%20energy%20level" title="high energy level">high energy level</a>, <a href="https://publications.waset.org/abstracts/search?q=critical%20energy%20level" title=" critical energy level"> critical energy level</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20dynamical%20boundary%20condition" title=" linear dynamical boundary condition"> linear dynamical boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=semilinear%20parabolic%20equation" title=" semilinear parabolic equation"> semilinear parabolic equation</a> </p> <a href="https://publications.waset.org/abstracts/24012/finite-time-blow-up-and-global-solutions-for-a-semilinear-parabolic-equation-with-linear-dynamical-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24012.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">436</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10613</span> Inverse Heat Conduction Analysis of Cooling on Run-Out Tables</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20S.%20Gadala">M. S. Gadala</a>, <a href="https://publications.waset.org/abstracts/search?q=Khaled%20Ahmed"> Khaled Ahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=Elasadig%20Mahdi"> Elasadig Mahdi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%20analysis" title="inverse analysis">inverse analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=function%20specification" title=" function specification"> function specification</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20net%20works" title=" neural net works"> neural net works</a>, <a href="https://publications.waset.org/abstracts/search?q=particle%20swarm" title=" particle swarm"> particle swarm</a>, <a href="https://publications.waset.org/abstracts/search?q=run-out%20table" title=" run-out table"> run-out table</a> </p> <a href="https://publications.waset.org/abstracts/15665/inverse-heat-conduction-analysis-of-cooling-on-run-out-tables" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15665.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">240</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10612</span> Image Transform Based on Integral Equation-Wavelet Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang">Yuan Yan Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Lina%20Yang"> Lina Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Hong%20Li"> Hong Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20model" title="harmonic model">harmonic model</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation%20%28PDE%29" title=" partial differential equation (PDE)"> partial differential equation (PDE)</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equation" title=" integral equation"> integral equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20representation" title=" integral representation"> integral representation</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20measure%20formula" title=" boundary measure formula"> boundary measure formula</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20collocation" title=" wavelet collocation"> wavelet collocation</a> </p> <a href="https://publications.waset.org/abstracts/3920/image-transform-based-on-integral-equation-wavelet-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3920.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">558</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10611</span> Numerical Investigation of the Boundary Conditions at Liquid-Liquid Interfaces in the Presence of Surfactants</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bamikole%20J.%20Adeyemi">Bamikole J. Adeyemi</a>, <a href="https://publications.waset.org/abstracts/search?q=Prashant%20Jadhawar"> Prashant Jadhawar</a>, <a href="https://publications.waset.org/abstracts/search?q=Lateef%20Akanji"> Lateef Akanji</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Liquid-liquid interfacial flow is an important process that has applications across many spheres. One such applications are residual oil mobilization, where crude oil and low salinity water are emulsified due to lowered interfacial tension under the condition of low shear rates. The amphiphilic components (asphaltenes and resins) in crude oil are considered to assemble at the interface between the two immiscible liquids. To justify emulsification, drag and snap-off suppression as the main effects of low salinity water, mobilization of residual oil is visualized as thickening and slip of the wetting phase at the brine/crude oil interface which results in the squeezing and drag of the non-wetting phase to the pressure sinks. Meanwhile, defining the boundary conditions for such a system can be very challenging since the interfacial dynamics do not only depend on interfacial tension but also the flow rate. Hence, understanding the flow boundary condition at the brine/crude oil interface is an important step towards defining the influence of low salinity water composition on residual oil mobilization. This work presents a numerical evaluation of three slip boundary conditions that may apply at liquid-liquid interfaces. A mathematical model was developed to describe the evolution of a viscoelastic interfacial thin liquid film. The base model is developed by the asymptotic expansion of the full Navier-Stokes equations for fluid motion due to gradients of surface tension. This model was upscaled to describe the dynamics of the film surface deformation. Subsequently, Jeffrey鈥檚 model was integrated into the formulations to account for viscoelastic stress within a long wave approximation of the Navier-Stokes equations. To study the fluid response to a prescribed disturbance, a linear stability analysis (LSA) was performed. The dispersion relation and the corresponding characteristic equation for the growth rate were obtained. Three slip (slip, 1; locking, -1; and no-slip, 0) boundary conditions were examined using the resulted characteristic equation. Also, the dynamics of the evolved interfacial thin liquid film were numerically evaluated by considering the influence of the boundary conditions. The linear stability analysis shows that the boundary conditions of such systems are greatly impacted by the presence of amphiphilic molecules when three different values of interfacial tension were tested. The results for slip and locking conditions are consistent with the fundamental solution representation of the diffusion equation where there is film decay. The interfacial films at both boundary conditions respond to exposure time in a similar manner with increasing growth rate which resulted in the formation of more droplets with time. Contrarily, no-slip boundary condition yielded an unbounded growth and it is not affected by interfacial tension. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20conditions" title="boundary conditions">boundary conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=liquid-liquid%20interfaces" title=" liquid-liquid interfaces"> liquid-liquid interfaces</a>, <a href="https://publications.waset.org/abstracts/search?q=low%20salinity%20water" title=" low salinity water"> low salinity water</a>, <a href="https://publications.waset.org/abstracts/search?q=residual%20oil%20mobilization" title=" residual oil mobilization"> residual oil mobilization</a> </p> <a href="https://publications.waset.org/abstracts/114002/numerical-investigation-of-the-boundary-conditions-at-liquid-liquid-interfaces-in-the-presence-of-surfactants" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/114002.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">129</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">10610</span> Second-Order Slip Flow and Heat Transfer in a Long Isothermal Microchannel</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Huei%20Chu%20Weng">Huei Chu Weng</a>, <a href="https://publications.waset.org/abstracts/search?q=Chien-Hung%20Liu"> Chien-Hung Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a study on the effect of second-order slip and jump on forced convection through a long isothermally heated or cooled planar microchannel. The fully developed solutions of thermal flow fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and Smoluchowski jump boundary conditions. Results reveal that the second-order term in the Karniadakis slip boundary condition is found to contribute a negative velocity slip and then to lead to a higher pressure drop as well as a higher fluid temperature for the heated-wall case or to a lower fluid temperature for the cooled-wall case. These findings are contrary to predictions made by the Deissler model. In addition, the role of second-order slip becomes more significant when the Knudsen number increases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=microfluidics" title="microfluidics">microfluidics</a>, <a href="https://publications.waset.org/abstracts/search?q=forced%20convection" title=" forced convection"> forced convection</a>, <a href="https://publications.waset.org/abstracts/search?q=gas%20rarefaction" title=" gas rarefaction"> gas rarefaction</a>, <a href="https://publications.waset.org/abstracts/search?q=second-order%20boundary%20conditions" title=" second-order boundary conditions"> second-order boundary conditions</a> </p> <a href="https://publications.waset.org/abstracts/26201/second-order-slip-flow-and-heat-transfer-in-a-long-isothermal-microchannel" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/26201.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> 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