This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically...This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions are obtained by two powerful methods Toeplitz Matrix Method (TMM) and Product Nystr?m Methods (PNM). The given numerical examples showed the efficiency and accuracy of the introduced methods.展开更多
Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic...Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.展开更多
In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of an...In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of analytic solutions for this type of equations,and then analyze the convergence orders of the collocation solutions and give corresponding error estimates.The numerical results verify our theoretical analysis.展开更多
Amorphous carbon materials play a vital role in adsorbed natural gas(ANG) storage. One of the key issues in the more prevalent use of ANG is the limited adsorption capacity, which is primarily determined by the porosi...Amorphous carbon materials play a vital role in adsorbed natural gas(ANG) storage. One of the key issues in the more prevalent use of ANG is the limited adsorption capacity, which is primarily determined by the porosity and surface characteristics of porous materials. To identify suitable adsorbents, we need a reliable computational tool for pore characterization and, subsequently, quantitative prediction of the adsorption behavior. Within the framework of adsorption integral equation(AIE), the pore-size distribution(PSD) is sensitive to the adopted theoretical models and numerical algorithms through isotherm fitting. In recent years, the classical density functional theory(DFT) has emerged as a common choice to describe adsorption isotherms for AIE kernel construction. However,rarely considered is the accuracy of the mean-field approximation(MFA) commonly used in commercial software. In this work, we calibrate four versions of DFT methods with grand canonical Monte Carlo(GCMC) molecular simulation for the adsorption of CH_4 and CO_2 gas in slit pores at 298 K with the pore width varying from 0.65 to 5.00 nm and pressure from 0.2 to 2.0 MPa. It is found that a weighted-density approximation proposed by Yu(WDA-Yu) is more accurate than MFA and other non-local DFT methods. In combination with the trapezoid discretization of AIE, the WDA-Yu method provides a faithful representation of experimental data, with the accuracy and stability improved by 90.0% and 91.2%, respectively, in comparison with the corresponding results from MFA for fitting CO_2 isotherms. In particular, those distributions in the feature pore width range(FPWR)are proved more representative for the pore-size analysis. The new theoretical procedure for pore characterization has also been tested with the methane adsorption capacity in seven activated carbon samples.展开更多
In characterizing the semistable law, Shimizu reduced the problem to solving the equationH(x)=integral from n=1 to∞(H(x+y)d(μ-ν)(y), x≥0) where μ andτ are given positive measures on [0,∞). In thisnote, we obtai...In characterizing the semistable law, Shimizu reduced the problem to solving the equationH(x)=integral from n=1 to∞(H(x+y)d(μ-ν)(y), x≥0) where μ andτ are given positive measures on [0,∞). In thisnote, we obtain a simple proof and show that some of his conditions can be weakened.展开更多
文摘This work proposes a new definition of the functional Fredholm integral equation in 2D of the second kind with discontinuous kernels (FT-DFIE). Furthermore, the work is concerned to study this new equation numerically. The existence of a unique solution of the equation is proved. In addition, the approximate solutions are obtained by two powerful methods Toeplitz Matrix Method (TMM) and Product Nystr?m Methods (PNM). The given numerical examples showed the efficiency and accuracy of the introduced methods.
基金This project is supported by National Natural Science Foundation of China(No.50175031).
文摘Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.
基金The first author is partially supported by forefront of science and interdisciplinary innovation projects of Jilin University and NNSF(No.11071102 of China).
文摘In this paper,we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays(VIFEMPDs).We shall present the existence,uniqueness and regularity properties of analytic solutions for this type of equations,and then analyze the convergence orders of the collocation solutions and give corresponding error estimates.The numerical results verify our theoretical analysis.
基金Supported by the National Sci-Tech Support Plan(2015BAD21B05)China Scholarship Council(201408320127)
文摘Amorphous carbon materials play a vital role in adsorbed natural gas(ANG) storage. One of the key issues in the more prevalent use of ANG is the limited adsorption capacity, which is primarily determined by the porosity and surface characteristics of porous materials. To identify suitable adsorbents, we need a reliable computational tool for pore characterization and, subsequently, quantitative prediction of the adsorption behavior. Within the framework of adsorption integral equation(AIE), the pore-size distribution(PSD) is sensitive to the adopted theoretical models and numerical algorithms through isotherm fitting. In recent years, the classical density functional theory(DFT) has emerged as a common choice to describe adsorption isotherms for AIE kernel construction. However,rarely considered is the accuracy of the mean-field approximation(MFA) commonly used in commercial software. In this work, we calibrate four versions of DFT methods with grand canonical Monte Carlo(GCMC) molecular simulation for the adsorption of CH_4 and CO_2 gas in slit pores at 298 K with the pore width varying from 0.65 to 5.00 nm and pressure from 0.2 to 2.0 MPa. It is found that a weighted-density approximation proposed by Yu(WDA-Yu) is more accurate than MFA and other non-local DFT methods. In combination with the trapezoid discretization of AIE, the WDA-Yu method provides a faithful representation of experimental data, with the accuracy and stability improved by 90.0% and 91.2%, respectively, in comparison with the corresponding results from MFA for fitting CO_2 isotherms. In particular, those distributions in the feature pore width range(FPWR)are proved more representative for the pore-size analysis. The new theoretical procedure for pore characterization has also been tested with the methane adsorption capacity in seven activated carbon samples.
文摘In characterizing the semistable law, Shimizu reduced the problem to solving the equationH(x)=integral from n=1 to∞(H(x+y)d(μ-ν)(y), x≥0) where μ andτ are given positive measures on [0,∞). In thisnote, we obtain a simple proof and show that some of his conditions can be weakened.
