Optimal vibration control of flexible spacecraft during a minimum-time maneuver

This paper is concerned with the simultaneous maneuver and vibration control of a flexible spacecraft. The problem is solved by means of a perturbation approach whereby the slewing of the spacecraft regarded as rigid represents the zero-order problem and the control of vibration, as well as of perturbations from the rigid-body maneuver, represents the first-order problem. The zero-order control is to be carried out in minimum time, which implies bang-bang control. On the other hand, the first-order control is a time-dependent linear quadratic regulator including integral feedback and prescribed convergence rate.This research was sponsored by USAF/ASD and AFOSR Research Grant F33615-86-C-3233 monitored by Drs. A. K. Amos and V. B. Venkayya, whose support is greatly appreciated.     

连续平均场Ising模型的显式差分格式

将离散的平均场Ｉｓｉｎｇ模型转换为连续的模型，给出了显式差分格式。利用有界延拓法，证明了差分解的收敛性与稳定性。最后通过数值例子说明了此格式的可信性。     

Radon activity and exhalation rates measurements in fly ash from a thermal power plant

Radon exhalation rate from fly ash samples and from the homogeneous mixture of fly ash of different proportions additive in soil and cement samples to study the effect of the addition was measured by cup dosimeter using SSNTDs. Radon activities were found to vary from (1018±38) to ( whereas the radon exhalation rate varied from (366±14) to . A gradual increase has been observed in samples having fly ash as an additive in cement samples whereas a gradual decrease was observed in soil samples after the addition of fly ash. ²³⁸U in fly ash was measured by a low-level NaI (Tl)-based gamma ray spectrometer. The results show enhancement in U concentration in fly ash as compared to coal samples, whereas radon exhalation rate is less in fly ash samples.     

Multiscale methods for elliptic homogenization problems

In this article we study two families of multiscale methods for numerically solving elliptic homogenization problems. The recently developed multiscale finite element method [Hou and Wu, J Comp Phys 134 (1997), 169–189] captures the effect of microscales on macroscales through modification of finite element basis functions. Here we reformulate this method that captures the same effect through modification of bilinear forms in the finite element formulation. This new formulation is a general approach that can handle a large variety of differential problems and numerical methods. It can be easily extended to nonlinear problems and mixed finite element methods, for example. The latter extension is carried out in this article. The recently introduced heterogeneous multiscale method [Engquist and Engquist, Comm Math Sci 1 (2003), 87–132] is designed for efficient numerical solution of problems with multiscales and multiphysics. In the second part of this article, we study this method in mixed form (we call it the mixed heterogeneous multiscale method). We present a detailed analysis for stability and convergence of this new method. Estimates are obtained for the error between the homogenized and numerical multiscale solutions. Strategies for retrieving the microstructural information from the numerical solution are provided and analyzed. Relationship between the multiscale finite element and heterogeneous multiscale methods is discussed. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian Systems

We suggest sufficient conditions for the existence of weak limits of solutions of the Liouville equation as time increases indefinitely. The presence of the weak limit of the probability distribution density leads to a new interpretation of the second law of thermodynamics for entropy increase.     

Some variant of Newton’s method with third-order convergence

We present a new modification of the Newton’s method which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given, and the best efficiency, in term of function evaluations, of two of this new methods is provided.     

Entry of Material into an Arc Discharge in the Case of a Diffusion Mechanism of Impurity Exit to the Surface of a Small-Weight Sample

The process of formation of a radiating discharge cloud in the case of a diffusion mechanism of impurity exit to the surface of a molten small-weight sample is considered. An analytical expression describing the behavior of the relative rate of impurity entry into a discharge is obtained.     

Structural properties of Markov chains with weak and strong interactions

Markov chains have been frequently used to characterize uncertainty in many real-world problems. Quite often, these Markov chains can be decomposed into a vector consisting of fast and slow components; these components are coupled through weak and strong interactions. The main goal of this work is to study the structural properties of such Markov chains. Under mild conditions, it is proved that the underlying Markov chain can be approximated in the weak topology of L² by an aggregated process. Moreover, the aggregated process is shown to converge in distribution to a Markov chain as the rate of fast transitions tends to infinity. Under an additional Lipschitz condition, error bounds of the approximation sequences are obtained.     

随机规划中的一些逼近结果

主要讨论了一类随机规划的目标函数分别在概率测度序列分布收敛、函数序列上图收敛以及随机变量序列均方可积收敛等收敛意义下目标函数序列的收敛情况。基于上述收敛情况给出了一些逼近思想，这些思想可应用于求解这类随机规划问题。     

岩心表面润湿性与化学选堵剂对油水的封堵能力

选择阳离子聚丙烯酰胺类选堵剂,进行岩心模拟实验,研究不同岩心表面润湿性与化学选堵剂封堵能力之间的关系.表面润湿性强烈影响对水的堵塞率,水润湿性越强,对水的堵塞率越高,典型的亲水表面和亲油表面对水的堵塞率相差20%左右;使用水基凝胶,水驱后的残余阻力系数(RRF)大于油驱后的RRF,水基凝胶使水相渗透率的降低比油相渗透率的降低多.对于润湿性相同,渗透率不同的天然岩心,选堵剂的堵水率大于85%,堵油率在20%左右,表现出良好的选择性.