Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation

The process of electrodeposition can be described in terms of a reaction-diffusion partial differential equation (PDE) system that models the dynamics of the morphology profile and the chemical composition. Here we fit such a model to the different patterns present in a range of electrodeposited and electrochemically modified alloys using PDE constrained optimization. Experiments with simulated data show how the parameter space of the model can be divided into zones corresponding to the different physical patterns by examining the structure of an appropriate cost function. We then use real data to demonstrate how numerical optimization of the cost function can allow the model to fit the rich variety of patterns arising in experiments. The computational technique developed provides a potential tool for tuning experimental parameters to produce desired patterns.     

An Implementation of Bouchouev's Method for a Short Time Calibration of Option Pricing Models

We analyse the Bouchouev integral equation for the deterministic volatility function in the Black–Scholes option pricing model. We areable to reduce Bouchouev's original triple integral equation to a single integral equation and describe its numerical solution. Moreover we show empirically that the most complex term in the equation may often be safely ignored for the purposes of numerical calculations. We present a selection of numerical examples indicating the range of time values for which we would expect the equation to be valid.     

基于NURBS的PDE曲面构造法研究及应用

由非均匀有理Ｂ样条曲线曲面给定边界条件，用偏微分方程来构造曲面，以参数“ａ”控制其整体形状，本文分析其思路原理及过程，并列举了在ＣＡＤ上的应用，最后分析了优缺点。     

变形体温度场和位移场的计算

本文用热源法对简单热传导问题进行了解析解的计算，并应用PDE工具箱求解热传导偏微分方程得到数值解。通过两种温度场的计算结果求出相应的位移场结果，比较可知MATLAB中PDE工具箱对难以用解析法求解的热传导问题有一定的指导作用。     

非对映选择性合成他达那非

以D-色氨酸为起始原料经酯化、Pictect-Spengler反应、酰化和氨解-环合四步制备新的磷酸二酯酶5抑制剂他达那非,总收率为66.8%。在Pictect-Spengler反应中采用非对映控制方法高选择性地合成cis-β-咔啉关键中间体,避免了trans-异构体的分离。     

Averaged control

We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter.First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition, in the spirit of the classical rank condition for linear control systems, but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action.We also describe some open problems and directions of possible research, in particular on the average controllability of evolution partial differential equations. In this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system.     

基于偏微分方程的条码预处理

由于受到条码采集设备的限制,图像中经常混有很多噪声,导致出现误码．引入了基于偏微分方程（PDE）的Perona—Malik模型,并对Perona-Malik模型的缺点进行了算法改进,给出了一种针对条码图像去噪的方法．通过合理地设计和选择参数,得到了比较令人满意的结果．     

基于偏微分方程的图像修复技术

介绍了图像修复技术的概念和原理,并在修复方法的理论与技术基础上,深入研究了偏微分方程修复模型中几种具有代表性的BSCB模型、曲率驱动扩散(CDD)模型、TV模型等图像修复模型.最后对上述模型进行了分析比较.     

严寒地区村镇给水管道周围土壤温度场的数值模拟

开展埋地管道周围土壤温度场变化的研究,对于解决地处严寒地区的东北广大农村给水冬季经常发生给水管道冻胀现象具有重要意义.本文在建立浅理外加保温层给水管道与周围土壤非稳态传热,以及土壤自身导热的物理模型基础上,利用Matlab-PDE工具箱进行求解,分析浅埋保温给水管道运行情况及周围土壤温度场随时间变化情况.结果表明,这种浅埋外加保温层的给水管道防冻胀技术,可以基本解决给水管道在冬季运行时发生的冻胀现象.     

Optimal boundary control of coupled parabolic PDE–ODE systems using infinite-dimensional representation

The optimal boundary control problem is studied for coupled parabolic PDE–ODE systems. The linear quadratic method is used and exploits an infinite-dimensional state-space representation of the coupled PDE–ODE system. Linearization of the nonlinear system is established around a steady-state profile. Using appropriate state transformations, the linearized system has been formulated as a well-posed infinite-dimensional system with bounded input and output operators. It has been shown that the resulting system is a Riesz spectral system. The linear quadratic control problem has been solved using the corresponding Riccati equation and the solution of the corresponding eigenvalue problem. The results were applied to the case study of a catalytic cracking reactor with catalyst deactivation. Numerical simulations are performed to illustrate the performance of the proposed controller.