On the Solution of Discontinuous IVPs by Adaptive Runge–Kutta Codes

In this paper an automatic technique for handling discontinuous IVPs when they are solved by means of adaptive Runge–Kutta codes is proposed. This technique detects, accurately locates and passes the discontinuities in the solution of IVPs by using the information generated by the code along the numerical integration together with a continuous interpolant of the discrete solution. A remarkable feature is that it does not require additional information on the location of the discontinuities. Some numerical experiments are presented to illustrate the reliability and efficiency of the proposed algorithms.     

An existence result for a quadrature surface free boundary problem

The aim of this paper is to present two different approachs in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.     

Shape Hessian for generalized Oseen flow by differentiability of a minimax: A Lagrangian approach

The goal of this paper is to compute the shape Hessian for a generalized Oseen problem with nonhomogeneous Dirichlet boundary condition by the velocity method. The incompressibility will be treated by penalty approach. The structure of the shape gradient and shape Hessian with respect to the shape of the variable domain for a given cost functional are established by an application of the Lagrangian method with function space embedding technique. This work was supported by the National Natural Science Fund of China (No. 10371096) for ZM Gao and YC Ma.     

一种模拟沸石分子筛扩散反应的Monte Carlo方法

在考虑了沸石分子筛中吸附、脱附、扩散和反应的特点的基础上，发展了一种模拟沸石分子筛中扩菜反应的ＭｏｎｔｅＣａｒｌｏ方法。用Ｌａｎｇｍｕｉｒ吸附等温式验证了该方法的合理性，并证明了轰击频率λ代表了反应物气相压力，而吸附、脱附几率之比即为吸附平衡常数。同时，通过改变轰击频率λ和反应几率Ｐｔ，得到了吸附等温线和有效因子随Ｔｈｉｅｌｅ模数变化的曲线。     

Diffusion in organic solvents: Interdiffusion coefficient of 1,1,2,2-tetrabromoethane

Interdiffusion coefficient have been measured for 1,1,2,2-tetrabromoethane in 21 organic solvents in order to ascertain the influence of shape, size, viscosity, nature and degree of branching, of the solvent molecules on transport properties. None of the existing correlations for diffusion in binary liquid systems appear to fit all the experimental data. Steric effects due to the solvent molecules are shown to be very important in the interpretation of the diffusion process.     

载铂铝交联蒙脱土的烷烃芳构化特性──Ⅰ．载铂铝交联蒙脱土对烷烃的择形芳构化作用

对比考察了Ｐｔ／ＫＬ沸石，Ｐｔ／Ａｌ２Ｏ３和载铂铝交联蒙脱土（Ｐｔ／Ａｌ－ＣＬＭ）催化剂对不同碳原子数烷烃的芳构化特性．脉冲微反的评价结果表明：Ｐｔ／Ａｌ－ＣＬＭ比Ｐｔ／Ａｌ２Ｏ３和Ｐｔ／ＫＬ具有较高的转化ｎ－Ｃ８，ｎ－Ｃ９为其对应芳烃的选择性，在转化ｎ－Ｃ８时，产物中的间、对位二甲苯收率很高，而转化ｎ－Ｃ９时有高的正丙苯收率．采用１２９Ｘｅ－ＮＭＲ、ＸＲＤ和孔分布测定考察了Ｐｔ／Ａｌ－ＣＬＭ和Ｐｔ／ＫＬ、Ｐｔ／Ａｌ２Ｏ３之间孔结构的差异．结果表明：由于ｎ－Ｃ８，ｎ－Ｃ９在反应过程中其过渡态的极限尺寸与Ｐｔ／Ａｌ－ＣＬＭ０．９ｎｍ左右的层间域相匹配，因而它对ｎ－Ｃ８，ｎ－Ｃ９具有择形芳构化作用．     

Molecular shape effects and quantum theory

Certain features of the chemist's molecular structure model, viz. size and shape, are retrieved even in the best non-adiabatic variational calculations thus far carried out for ground states of H ₂ ⁺ and H₂. Those features do not conflict with the full symmetry of exact molecular eigenstates, once they are properly understood as correlation effects.