Time-dependent modelling and asymptotic analysis of electrochemical cells

A (time-dependent) model for an electrochemical cell, comprising a dilute binary electrolytic solution between two flat electrodes, is formulated. The method of matched asymptotic expansions (taking the ratio of the Debye length to the cell width as the small asymptotic parameter) is used to derive simplified models of the cell in two distinguished limits and to systematically derive the Butler–Volmer boundary conditions. The first limit corresponds to a diffusion-limited reaction and the second to a capacitance-limited reaction. Additionally, for sufficiently small current flow/large diffusion, a simplified (lumped-parameter) model is derived which describes the long-time behaviour of the cell as the electrolyte is depleted. The limitations of the dilute model are identified, namely that for sufficiently large half-electrode potentials it predicts unfeasibly large concentrations of the ion species in the immediate vicinity of the electrodes. This motivates the formulation of a second model, for a concentrated electrolyte. Matched asymptotic analyses of this new model are conducted, in distinguished limits corresponding to a diffusion-limited reaction and a capacitance-limited reaction. These lead to simplified models in both of which a system of PDEs, in the outer region (the bulk of the electrolyte), matches to systems of ODEs, in inner regions about the electrodes. Example (steady-state) numerical solutions of the inner equations are presented.     

Nodally exact Ritz discretizations of 1D diffusion–absorption and Helmholtz equations by variational FIC and modified equation methods

This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework. FIC provides a steplength parametrization of mesh dimensions, which is used to modify the shape functions. This approach is applied to the FEM discretization of the steady-state, one-dimensional, diffusion–absorption and Helmholtz equations. Parametrized linear shape functions are directly inserted into a FIC functional. The resulting Ritz-FIC equations are symmetric and carry a element-level free parameter coming from the function modification process. Both constant- and variable-coefficient cases are studied. It is shown that the parameter can be used to produce nodally exact solutions for the constant coefficient case. The optimal value is found by matching the finite-order modified differential equation (FOMoDE) of the Ritz-FIC equations with the original field equation. The inclusion of the Ritz-FIC models in the context of templates is examined. This inclusion shows that there is an infinite number of nodally exact models for the constant coefficient case. The ingredients of these methods (FIC, Ritz, MoDE and templates) can be extended to multiple dimensions     

Ergodicity of filtering process by vanishing discount approach

A new approach to study ergodicity of filtering processes is presented. It is based on the vanishing discount approach to discounted functional of filtering process. We show that limit superior of the Cesaro averages of the functionals is the same for all initial conditions from which the uniqueness of invariant measures of filtering processes follows. The approach is based on certain assumption for which we provide a sufficient condition using concavity arguments. In addition we show the existence of solutions to the Poisson equation corresponding to filtering process with concave functional. The assumptions are then extended to the controlled case and using similar concave arguments we obtain the existence of solutions to the Bellman equation corresponding to partially observed average cost per unit time problem.     

Effect of 3D lip deformations on elastohydrodynamic lip seals behaviour

The numerical simulation of comparative elastohydrodynamic lubrication between axisymmetrical and 3D elastic approaches on the radial lip seals is presented in order to determine the 3D effect of the elastic aspect of the seal lip. Indeed, the consideration of 3D model in other words the circumferential variation of the lip elastic deformation indicated a difference in the deformation distribution of the lip compared to the axisymmetrical approach. Consequently, the results show that the presence of the circumferential variation of the seal lip deformation has a significant effect on the pumping rate values.     

Density of 1,1-dichloro-1-fluoroethane (HCFC 141b) as a function of temperature and pressure

The density of HCFC 141b has been measured at several temperatures between 260 and 320 K, Mid pressures up to 20 MPa, with a mechanical oscillator densimeter. The densimeter was calibrated with 2,2,4-trimethylpentane, whose density was obtained from a correlating cyuation with 0.3% uncertainty. The density data obtained for HCFC 14H) hits a reproducibility of 0.05% and an uncertainty of 0.3%. The data obtained were fitted to a Tait-type equation. which reproduced the experimental densities within 0.11 % and were compared with the data obtained in other works.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

耦合模模型的峰峰值与有效值

介绍了峰峰值和有效值的偶合模方程,给出了峰峰值P矩阵和有效值P矩阵的表达式。利用峰峰值P矩阵和有效值P矩阵模拟了纵向耦合谐振结构以及阻抗元结构的声表面波滤波器的频响。对比两种P矩阵的模拟结果,说明了峰峰值耦合模方程和有效值耦合模方程分析频响的等效性。     

THE ANALYSIS OF THE SEPARATED LAYERS ALGORITHM BY DOMAIN DECOMPOSITION METHOD

From the principle of of the Domain Decomposition Method (DDM), we analyse the 2nd-order linear elliptic partial differential problems and link the Separated-Layers Algorithm (SLA) with DDM. The mathematical properties of SLA and numerical example are presented to obtain satisfactory computation results. For general linear differential ones, also are the structure of SLA and its characteristics discussed.     

岩石液压致裂中几个问题的研究

论证了流体压力变化与岩石强度变化之间的关系，阐述了流体保持与释放的应力条件和构造环境，总结了两种围岩下的液压致裂模型及其流量方程。     

非线性光孤子传输方程的研究

本文在从描述光孤子在单模光纤中的非线性传输方程（ＮＬＳ，即非线性薛定谔方程）出发，利用Ｍａｘｗｅｌｌ方程和慢变包络近似性，导出ｐｓ量级光孤子高阶修正的非线性薛定谔方程（ＨＭＮＬＳ）可进一步研究色散，损耗等高价效应对孤子传输造成的影响。     

基于波动方程的聚焦点控制照明叠前深度偏移

 基于波动方程的聚焦点控制照明叠前深度偏移技术借助于差分计算，把速度、密度等介质参数的影响体现在差分计算的矩阵方程中，能够自动适应速度场的任意变化，快速傅里叶变换的使用也加速了波场延拓的计算速度。因此此法兼具有限差分偏移方法和傅里叶偏移方法的优点，既可适应速度场的剧烈变化，又可保证对陡倾地层的成像效果，是目前针对复杂构造最有效的成像方法之一。对于单个聚焦点及其周围的成像步骤为：①采用矩形网格情况下绕射走时的有限差分计算方法生成合成算子；②应用合成算子来合成面炮震源和面波记录；③对合成的面炮震源和面波记录做傅里叶有限差分法波动方程叠前深度偏移，得到该聚焦点及其附近区域的成像结果。按照上述成像步骤，将震源波场和炮集记录依据相应的外推公式进行延拓，最终应用成像条件求取成像值。在地质目标处选取多个聚焦点，可以得到面向目标的控制照明偏移成像，在多个层位上选取多个聚焦点进行控制照明叠前深度偏移，可以得到整块区域的成像。通过对Marmousi模型的试算，取得了较好的效果。