基于最佳质量网格的薄板问题的非协调流形方法

对于大部分非协调板单元,使用规则网格能得到很好的效果。但是,当网格不规则时,非协调元的数值特性将变得很差,甚至收敛性得不到保证。为解决网格依赖性问题,许多专家学者提出了改造单元,如拟协调元法和广义协调元法,这些方法能解决收敛性问题,但是数值实践证明没有一种单元能在所有情况下都具有良好的数值特性。考虑到流形方法采用两套完全独立的覆盖系统,可以用规则的数学网格来作为数学覆盖进行插值,取得最佳的插值效果,单元收敛性便能得到保证。再结合适用于流形方法的变分提法,建立起流形方法处理非规则物理边界非协调板单元的一般格式。以ACM 薄板单元为例,与ANSYS、拟协调元法和广义协调元法进行了对比,证明本文方法在处理具有曲线边界的薄板弯曲问题时具有收敛快和精度高等优势。     

Integral transformations by the index of Lommel's function

In this paper we study a class of integral transformations with kernels consisting of Lommel's functions of a certain index. Boundedness properties, Parseval type formula, inversion theorem are proved in Lebesgue spaces of integrable functions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Residue integrals and Waring’s formulas for algebraic or even transcendental systems

The present article is focused on the study of a special class of systems of non-linear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of study of such systems we develop a method for computing residue integrals with integration over certain cycles. We describe conditions under which the mentioned residue integrals coincide with power sums of the inverses to the roots of a system of equations (i.e. multidimensional Waring’s formulas). Based on this, we develop an algorithm that computes such power sums without computing the roots. As an application of the suggested method, we consider a problem of finding sums of multi-variable number series.     

孔隙压力作用下圆形巷道围岩的蠕变分析

在原有的岩土流变理论基础上,与渗流力学原理相结合,考虑孔隙压力及孔隙度在岩石蠕变过程中对于岩体变形的影响,在弹性解答的基础上,通过Laplace变换(对应性原理)得出解析解．在一定的假设条件下,利用弹性力学基本方程、蠕变方程及有效应力原理(Terzaghi有效应力方程),采用H-K体模型作为本构方程,将孔隙压力引入到围岩蠕变方程中．给出在孔隙压力作用下的蠕变曲线,并与不考虑孔隙压力和定孔隙压力条件下蠕变曲线相比,其更接近于实际．     

Une méthode inverse d'ordre un pour les problèmes de complétion de données

An iterative resolution method for inverse Cauchy problems is presented. The successive iterations satisfy the equilibrium equations exactly. Numerical simulations prove the accuracy of the method and its ability to solve Cauchy problems when the domain boundary is not regular. To cite this article: A. Cimetière et al., C. R. Mecanique 333 (2005).     

Dynamic Release of Propranolol HCl from Cationic Ion–Exchanger–Loaded Calcium Alginate Beads

The dynamic release of drug propranolol HCl from the propranolol HCl–resin complex (PRC) loaded calcium alginate beads has been studied in the buffer media of pH 1.2 at the physiological temperature 37°C. The PRC encapsulated beads demonstrated nearly 58.04% release while naked PRC particles released 98.00% drug in 24 h in the gastric fluid. The amount of drug released was found to increase with and decrease in the amount of sodium alginate in the beads. Similarly, with the increase in the amount of entrapped PRC particles within the beads, the quantity of drug released was also observed to increase. The degree of crosslinking of beads also affected the release kinetics. Interestingly, the release from naked PRC particles followed ‘first‐order’ kinetics while PRC particles, entrapped in calcium–alginate beads, exhibited ‘diffusion controlled’ release behavior as indicated by liner nature of fractional release vs. √t plot.     

Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD

Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Flow Through Diffusion Cell Method: A Better Approach to Study Drug Release Behavior as Compared to Traditional Dissolution Test Method

Co‐polymeric hydrogels consisting of N‐vinyl‐2‐pyrrolidone (NVP) and acrylic acid (AAc) were synthesized and evaluated for release of a model drug, i.e., vitamin B₁₂. Release studies in simulated gastric fluid (pH 1.2) and intestinal fluid (pH 7.4), at 37°C, showed the hydrogels to be pH sensitive. An in vitro release study by ‘traditional dissolution test’ (TDT) showed that percent drug released from the hydrogel was nearly 8.6±2.1 and 83.2±4.8 in the media of pH 1.2 and 6.8, respectively. However, in order to incorporate in vivo GI conditions such as acidic pH and high water content in the stomach, low water content and the presence of a semi–solid mass in the large intestine, a new test model, called flow through diffusion cell (FTDC) was also used. The two approaches yielded almost different release profiles. The gels were characterized by thermogravimetric analysis and FTIR spectroscopy.     

二维轴对称图象高阶胡氏不变矩快速算法的改进

提出了基于二维轴对称性目标图象矩快速算法的实用化改进方案.算法实用化改进是通过两个命题的证明实现的.一是通过轴对称目标图象质心在对称轴上的命题证明,实现了将二维轴对称图象矩快速算法用于轴对称性图象中心矩的计算;二是通过目标图象以坐标系中任意两点为圆心,旋转相同角度,结果图象具有平移性的命题证明,实现了算法用于对旋转不同角度的对称目标图象的中心矩的计算改进.在此基础上,完成了二维轴对称目标图象高阶胡氏不变矩实用化快速算法的实现.实验证明,该算法具有较好的实时性能,且具有较小的引入误差.