基于Hopf-Cole变换的Burgers方程初边值问题的Sinc-Galerkin法

利用Sinc-Galerkin法数值求解Burgers方程的初边值问题。首先,用Hopf-Cole变换将二阶非线性的Burgers方程变换为二阶线性方程,同时把第一类边界条件变为第二类边界条件。时间上的导数采用θ加权格式离散,空间导数采用Sinc-Galerkin法离散,端点处分别引入权函数处理变换后的第二类边界条件。最后,通过数值算例验证了Sinc-Galerkin法的指数收敛性,与精确解相比,本文构造的数值格式精度高,能够有效捕捉激波等物理现象。     

Self-similar vortex reconnection

As shown by Crow in 1970, the evolution of two almost parallel vortex filaments with opposite circulation exhibits a long-wave instability. Ultimately, the symmetric mode increases its amplitude reconnecting both filaments and ending into the formation of an almost periodic structure of vortex rings. This is a universal process, which appears in a wide range of scales: from the vortex trails behind an airplane to a microscopic scale of superfluids and Bose–Einstein condensates. In this paper, I will focus on the vortex reconnection for the latter case by employing Gross–Pitaevskii theory. Essentially, I focus on the well-known laws of interaction and motion of vortex filaments. By means of numerical simulations, as well as theoretically, I show that a self-similar finite-time dynamics manifests near the reconnection time. A self-similar profile is selected showing excellent agreement with numerical simulations.     

Data assimilation and pollution forecasting in Burgers' equation with model error function

This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence.     

Symmetry classification of quasi-linear PDE’s containing arbitrary functions

We consider the problem of performing the preliminary “symmetry classification” of a class of quasi-linear PDE’s containing one or more arbitrary functions: we provide an easy condition involving these functions in order that nontrivial Lie point symmetries be admitted, and a “geometrical” characterization of the relevant system of equations determining these symmetries. Two detailed examples will elucidate the idea and the procedure: the first one concerns a nonlinear Laplace-type equation, the second a generalization of an equation (the Grad–Schlüter–Shafranov equation) which is used in magnetohydrodynamics.     

乙醇-环己烷体系中NaI活度系数的测定与计算

由于非水溶剂的应用日趋广泛,促使物理化学工作者对于溶剂和溶液性质进行研究,同时开展了有关物理化学数据的测定和积累工作,以利于指导实践[1]。目前文献报道含水混合溶剂中的电解质活度系数较多,但非水混合溶剂中电解质活度系数报道较少。电解质浓溶液活度系数的计算方法目前应用较广的是Pitzer半经验算法[2]。Pitzer的算法中具体物系的β(0)、β(1)等系数需从实测活度系数数据拟合求得。孙仁义等通过测定汽液平衡盐效应的方法研究了盐在混合溶剂中的活度系数[3-4]。最近孙仁义等[5]提出了双液比固定条件下含盐体系汽液平衡数据热力学一…     

整数环上一类三阶矩阵方程有解的充要条件

给出了整数环上一类三阶矩阵方程有解的充要条件.     

2-乙酰氨基-3-苯基-N-苯基-丙烯酰胺衍生物的电子轰击质谱研究

本文报道了6种新的丙烯酰胺衍生物的EI谱。在精确质量测量和B/E,B~2/E联动扫描亚稳离子测定的基础上,着重讨论了该类化合物的共同质谱特征:如分子离子失去H_2O的成环反应;产物离子的开环反应;分子内的氢重排反应等。同时,利用Hammett方程讨论了化合物中N-苯基端苯环上不同取代基对特定碎片离子强度的影响     

Experimental study on high-pressure adsorption of hydrogen on activated carbon

A systematic measurement of H2 adsorption on activated carbon over a wide scope of conditions was completed for the first time using a novel cryostat developed by the present authors. The equilibrium temperatures covered 77-298 K with the space of about 20 K, and the equilibrium pressures increased from 0 to about 7MPa. A set of adsorption/desorption isotherms was obtained by a standard volumetric method. This set of experimental data was fitted to all the well-known models of type-I isotherms, and Dubinin-Astakhov (D-A) equation was found to be the best-fit one On the basis of D-A model one can predict adsorption with relative error of ±4%. A 3-dimensional adsorption surface was also constructed, and the isosteric heat of adsorption was analytically determined. Except in the low pressure area, the calculated values agreed well with the experimental ones. Finally, the troubles encountered in applying D-A equation to supercritical adsorption is discussed.