Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

Effects of Polymer Bridging and Electrostatics on the Rheological Behavior of Aqueous Colloidal Dispersions†

Effects of a low molecular weight physically adsorbed polyethylene oxide (PEO) and the range of the electrostatic repulsion on the rheological behavior of silica dispersions (as a model system) has been investigated. Particular attention is given to the evolution of the rheological behavior with increasing the polymer concentration in the system and also effectiveness of the polymer as a dispersant under extreme conditions (high ionic strength). Results indicate that at small separation distances and low polymer coverage, the polymer chains are long enough to adsorb on the surface of two particles simultaneously causing bridging flocculation in the system and hence increasing the viscosity and linear viscoelastic functions of the dispersion. A significant increase was observed in the viscosity of the dispersion at salt concentrations high enough to eliminate electrostatics between the particles. Under these conditions,the viscosity of the system increased significantly when PEO was added to the dispersion showing that at high electrolyte concentrations, a neutral polymer such as PEO is not able to stabilize the system.     

Viscosity solution theory of a class of nonlinear degenerate parabolic equations II. Lipschitz continuity of free boundary

In [1] we construct a unique bounded Hölder continuous viscosity solution for the nonlinear PDEs with the evolutionp-Laplacian equation and its anisotropic version as typical examples. In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however, this result does not include the anisotropic case.This research is supported by the National Natural Sciences Foundation of China.     

人工神经网络在SARS疫情分析与预测中的应用

讨论人工神经网络在 SARS疫情分析与预测中的应用 .采用三层结构的反向传播网络 ( Backpropagation network,简称 BP网络 ) ,对 SARS在中国的传播与流行趋势及控制策略建立了网络模型 .并利用实际数据拟合参数 ,针对北京、山西的疫情进行了计算仿真 .结果表明 ,该网络模型算法收敛速度较快 ,预测精度很高     

HIGH ACCURACY NUMERICAL METHOD OF THIN-FILM PROBLEMS IN MICROMAGNETICS

In this paper, a new high accuracy numerical method for the thin-film problems of micron and submicron size ferromagnetic elements is proposed. For the computation of stray field, we use the finite element method(FEM) by introducing a semi-discrete artificial boundary condition [1, 2]. In our numerical experiments about the domain patterns and their movement, we can see that the results are accordant to that of experiments and other numerical methods. Our method are very convenient to deal with arbitrary shape of thin films such as a polygon with high accuracy.     

微纳米加工技术在纳米物理与器件研究中的应用

物质在纳米尺度下可能呈现出与体材料不同的物理特件，这正是纳米科技发展的基础之一。要想探索在纳米尺度下材料物埋性质的变化规律及可能的应用领域，离不开相应的技术手段，微纳米加工技术作为当今高技术发展的重要技术领域之一，是实现功能人工纳米结构与器件微纳米化的基础。本文根据几个不同的应用领域，介绍了微纳米加工技术在纳米物理与器件研究领域的应用。     

HKD-1型航空润滑油的粘温特性

利用SYP1003型运动粘度测量器测量了HKD-1型航空润滑油在不同温度时的运动粘度，提出了粘度与温度之间的新关系式，并与Walther粘温模型进行了比较。结果表明：HKD-1型航空润滑油的粘度随温度升高而减小，其在低温时粘温特性较差，适合于20℃以上时使用。新的粘温模型比Walther模型预测精度高，适用的温度范围宽，尤其低温时的计算精度远远高于Walther模型。     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

Polygermoxanes suitable for biochemical purposes. Part I. Digermoxanes (low-viscosity oils)

In order to replace silicones in some of their biomedical applications, e.g. syringe lubrication, implants ets., a series of digermoxanes (R¹R²R³Ge)₂O (R = n–alkyl, aryl) were synthesized. These compounds are thermally stable oils; their viscosities, depending on the nature of substituents, lie in the range 1–72 cPo (mPa s) at 20°C.     

黏度在炼铁生产中的作用分析

黏度是流体的一个重要物理量。炼铁高炉内炉料，最终产生两个液相：铁水扣炉渣。炉渣黏度对炼铁生产有重大实际意义。通过分析炉渣黏度对高炉冶炼的作用，提出了调控炉渣黏度的有效措施。