Modelica建模软件形成的高指标微分代数方程系统指标约简算法研究

随着产品设计的复杂化，应用领域中的数学建模和仿真越来越重要，传统建模方法基于赋值语句，主要考虑单一系统，工程人员需要对程序设计语言和算法求解有相当程度的熟悉，这导致了传统建模方法很难满足复杂产品设计的需要。欧洲仿真界的学者在总结现有建模方法的基础上于1997年推出了一种面向对象的、陈述式的基于方程的语言——Modelica，Modelica语言支持多领域建模，Modelica语言得到了仿真领域众多厂商的支持，成为统一建模领域的事实标准，实现Modelica仿真环境具有重大意义。 编译器是Modelica仿真环境中的核心组件，Modelica编译器会产生高指标DAE系统，除了部分特殊结构的高指标DAE，现有求解器一般不能对通用高指标DAE直接求解，现在一般做法是先对高指标DAE进行指标约简，将其转换成等价的低指标DAE，然后进行求解。这就要求Modelica编译器具有指标约简的功能，以便利用现有求解器进行求解。 本文介绍了几种现有的指标约简算法，给出了各个算法指标约简原理和约简步骤，并对这些算法进行了分析和比较，得出各自的优缺点。最后，本文设计并实现了一个指标约简系统，采用三个Modelica模型产生的方程对系统进行了测试，并验证了实验结果的正确性。

Modelica软件中微分代数方程指标约简算法分析

Modelica建模软件会产生高指标的微分代数方程(DAE),因为现有数值求解器一般不能直接对高指标DAE进行求解,所以Modelica建模软件必须对高指标DAE进行指标约简。为提高Modelica建模软件性能,针对现有指标约简算法,展开了理论分析和实验比较,着重对负权二部图算法进行了详细分析,并给出了负权二部图算法的时间复杂度。理论分析和实验结果表明,负权二部图算法相对Pantelides算法有较好的性能,因此可以考虑在Modelica建模软件中使用负权二部图算法来提高性能。

指标约简中Gear算法的实现

基于组件的建模有时会产生高指标的微分代数方程(DAE),不能直接求解,需要进行指标约简。Gear方法是一个经典的指标约简方法,对Gear方法从理论上进行了说明和分析。对于一类具有特殊结构的DAE,提出了Gear方法实现中的优化策略,以降低指标约简后得到的方程规模。把优化后的实现与未优化的实现进行了比对,实验结果表明,优化过的实现方法针对这类特殊的问题确实达到了更好的约简效果。

Study of drag reduction by gas injection for power-law fluid flow in horizontal stratified and slug flow regimes

In this work, the drag reduction by gas injection for power-law fluid flow in stratified and slug flow regimes has been studied. Experimentswere conducted to measure the pressure gradient within air/CMC solutions in a horizontal Plexiglas pipe that had a diameter of 50mm and a length of 30 m. The drag reduction ratio in stratified flow regime was predicted using the two-fluid model. The results showed that the drag reduction should occur over the large range of the liquid holdup when the flow behaviour index remained at the low value. Furthermore, for turbulent gas-laminar liquid stratified flow, the drag reduction by gas injection for Newtonian fluid was more effective than that for shear-shinning fluid, when the dimensionless liquid height remained in the area of high value. The pressure gradient model for a gas/Newtonian liquid slug flow was extended to liquids possessing the Ostwald–de Waele power law model. The proposed model was validated against 340 experimental data point over a wide range of operating conditions, fluid characteristics and pipe diameters. The dimensionless pressure drop predicted was well inside the 20% deviation region for most of the experimental data. These results substantiated the general validity of the model presented for gas/non-Newtonian two-phase slug flows.

Research on improved methods of reduction of bend loss of silicon-on-insulator waveguides

Improved methods of reduction of bend loss of silicon-on-insulator waveguides were simulated and analyzed by means of effective index method (EIM) and two dimensional beam propagation method (2D-BPM). The simulation results indicate that two different methods, one of which are introducing an offset at the junction of two waveguides and the other is etching groove at the outside of bend waveguide, can decrease bend loss. And the later one is more effective. Meanwhile, experiments validate them. By etching groove, the insertion loss of bend waveguide of R = 16mm, transverse displacement 70mum was decreased 5dB. And its bend loss was almost eliminated.

Reduction Approaches for Vibration Control of Repetitive Structures

The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.

Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n - 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n - r)-dimensional DFV.

Refractive index and thickness analysis of natural silicon dioxide film growing on silicon with variable-angle spectroscopic ellipsometry

The refractive index and thickness of SiO2 thin films naturally grown on Si substrates were determined simultaneously within the wavelength range of 220-1100 nm with variable-angle spectroscopic ellipsometry. Different angles of incidence and wavelength ranges were chosen to enhance the analysis sensitivity for more accurate results. Several optical models describing the practical SiO2-Si system were investigated, and best results were obtained with the optical model, including an interface layer between SiO2 and Si, which proved the existence of the interface layer in this work as described in other publications.

The vector fields admitting one-parameter spatial symmetry group and their reduction

For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.

Experimental Demonstration Of A New Concept Of Drag Reduction And Thermal Protection For Hypersonic Vehicles

A new idea of drag reduction and thermal protection for hypersonic vehicles is proposed based on the combination of a physical spike and lateral jets for shock-reconstruction. The spike recasts the bow shock in front of a blunt body into a conical shock, and the lateral jets work to protect the spike tip from overheating and to push the conical shock away from the blunt body when a pitching angle exists during flight. Experiments are conducted in a hypersonic wind tunnel at a nominal Mach number of 6. It is demonstrated that the shock/shock interaction on the blunt body is avoided due to injection and the peak pressure at the reattachment point is reduced by 70% under a 4A degrees attack angle.

Negative refractive index in a four-level atomic system

We propose a scheme for realizing negative refractive index in a four-level atomic system. It is shown that such a system can simultaneously exhibit negative permittivity and negative permeability in an optical frequency range. Furthermore, by analysing the dispersion property of the left-handed material, we find that the probe beam can be controlled from superluminal to subluminal or vice versa via choosing appropriate parameters.

Phase control of switching from positive to negative index material in a four-level atomic system

Electric and magnetic responses of the medium to the probe field are analysed in a four-level loop atomic system by taking into account the relative phase of the applied fields. An interesting phenomenon is found: under suitable conditions, a change of the refractive index from positive to negative can occur by modulating the relative phase of the applied fields. Then the medium can be switched from a positive index material to a negative index material in our scheme. In addition, a negative index material can be realized in different frequency regions by adjusting the relative phase. It may give us a convenient way to obtain the desired material with positive or negative index.

Electromagnetically induced negative refractive index in a V-type four-level atomic system

We propose a scheme for realizing negative refractive index in a V-type four-level atomic system. It is shown that the negative refractive index can be achieved in a wide frequency band based on the effect of quantum coherence. It is also found that the frequency band of negative refractive index and the absorption property of left-handed material are manipulated by the pump and control fields. Furthermore, left-handed material with reduced absorption is possible by choosing appropriate parameters. (c) 2006 Elsevier B.V. All rights reserved.

Characteristics of recording and thermal fixing in lithium niobate

We present a theoretical model in which the band-transport equations and the coupled-wave equations are considered to study the two thermal-fixing methods (simultaneous fixing and postfixing) in Fe:LiNbO3. We found that, in simultaneous fixing, the existing ionic-grating affects the writing of the electronic grating by reduction of the coupling gain, and the grating envelope of the fixed-index grating is quite uniform inside the photorefractive crystal in comparison with the method of postfixing. The resulting diffraction efficiency of the fixed-volume grating is dependent mainly on the initial intensity modulation of the two writing beams. A set of experiments is also presented. (C) 1998 Optical Society of America.