Adsorption operation is of great importance for separation and purification of semi-synthetic cephalosporin compounds in pharmaceutical industry. The adsorption dynamics of Cefoselis hydrochloride(CFH) on XR 920 C ads...Adsorption operation is of great importance for separation and purification of semi-synthetic cephalosporin compounds in pharmaceutical industry. The adsorption dynamics of Cefoselis hydrochloride(CFH) on XR 920 C adsorbent in fixed bed was predicted by the model of modified film-pore diffusion(MFPD). The intraparticle diffusion equation and mass balance equation in fixed bed are discretized into two ordinary differential equations(ODEs) using the method of orthogonal collocation which largely improves the calculation accuracy. The MFPD model parameters including the pore diffusion coefficient(Dp), external mass-transfer coefficient(kf), and the axial dispersion(DL) were estimated. The kfvalue was calculated by the Carberry equation, in which the effective diffusion coefficient Dewas fitted based on Crank Model through experimental data. Moreover, three key operating parameters(i.e., initial adsorbate concentration; flow rate of import feed, and bed height of adsorbent) and the corresponded breakthrough curves were systematically studied and optimized. Therefore,this research not only provides valuable experimental data, but also a successfully mathematical model for designing the continuous chromatographic adsorption process of CFH.展开更多
Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject...Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.展开更多
The HIV infection model of CD4＋ T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein poly...The HIV infection model of CD4＋ T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials （OBPs）. By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton＇s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.展开更多
基金Supported by the National Natural Science Foundation of China(U1407122)the Innovation Project of Jiangsu Province(CXZZ13_0451)
文摘Adsorption operation is of great importance for separation and purification of semi-synthetic cephalosporin compounds in pharmaceutical industry. The adsorption dynamics of Cefoselis hydrochloride(CFH) on XR 920 C adsorbent in fixed bed was predicted by the model of modified film-pore diffusion(MFPD). The intraparticle diffusion equation and mass balance equation in fixed bed are discretized into two ordinary differential equations(ODEs) using the method of orthogonal collocation which largely improves the calculation accuracy. The MFPD model parameters including the pore diffusion coefficient(Dp), external mass-transfer coefficient(kf), and the axial dispersion(DL) were estimated. The kfvalue was calculated by the Carberry equation, in which the effective diffusion coefficient Dewas fitted based on Crank Model through experimental data. Moreover, three key operating parameters(i.e., initial adsorbate concentration; flow rate of import feed, and bed height of adsorbent) and the corresponded breakthrough curves were systematically studied and optimized. Therefore,this research not only provides valuable experimental data, but also a successfully mathematical model for designing the continuous chromatographic adsorption process of CFH.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10872017, 90816024 and 10876100)111 Project (Grant No. B07009)
文摘Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method.
文摘The HIV infection model of CD4＋ T-cells corresponds to a class of nonlinear ordinary differential equation systems. In this study, we provide the approximate solution of this model by using orthonormal Bernstein polynomials （OBPs）. By applying the proposed method, the nonlinear system of ordinary differential equations reduces to a nonlinear system of algebraic equations which can be solved by using a suitable numerical method such as Newton＇s method. We prove some useful theorems concerning the convergence and error estimate associated to the present method. Finally, we apply the proposed method to get the numerical solution of this model with the arbitrary initial conditions and values. Furthermore, the numerical results obtained by the suggested method are compared with the results achieved by other previous methods. These results indicate that this method agrees with other previous methods.
