基于空间基函数优化组合的微波加热温度分布数值求解

针对微波加热是一个多物理场各自演变及相互耦合的过程,无法直接求得媒质温度分布偏微分方程(PDE)解析解的问题,本文提出一种快速及准确求解微波加热温度分布的新方法.首先,本文在无限维PDE降维到有限维ODE温度模型的基础上,分析了ODE温度模型阶次选择与温度分布求解精度量化关系.其次,通过自适应变异粒子群算法(AMPSO)优化误差函数近似得到最优的空间基函数转换矩阵,利用该矩阵将空间基函数进行线性优化组合,进一步降低ODE模型阶数,进而使得在一定误差范围内可以更快速的求解微波加热过程中媒质的温度分布.再次,通过数值仿真实验证明,温度分布求解误差主要产生于模型阶次的选择,且优化后的低维ODE模型的温度分布精度相对误差控制在1.64%以内,求解速度提升72.2%.最后,使用多物理场耦合有限元方法求解微波加热PDE温度模型,进一步验证了优化后的低维ODE温度模型的准确性,充分验证了本文方法的有效性.     

(RbCl)108离子簇固液相变的分子动力学研究

通过分子动力学模拟,考察并分析了(RbCl)108离子簇的结构、能量和相变的动力学行为.观察到的(RbCl)108离子簇的熔点约为910K.当完全熔融的(RbCl)108离子簇以2.5×1011K/s的速率冷却时,在约625K时观察到成核和晶体生长.在快速冷却时,熔融的(RbCl)108离子簇自发地由液相变为立方面心相.在450K、500K、550K和600K的成核速率大于1035m-3s-1.由成核速率得到的固液界面自由能约为70mJ/m2.     

二维带分数阶Laplacian算子的对流扩散方程的格子Boltzmann模型研究

带有分数阶Laplacian算子的对流扩散方程常被用来刻画自然界与社会系统中的反常扩散现象.本文提出了一种新的格子Boltzmann模型,用于求解二维带分数阶Laplacian算子的对流扩散方程.首先,基于分数阶Laplacian算子的Fourier变换和Gauss型求积公式,得到控制方程的近似方程.然后,将速度空间、时间和空间进行离散,并构造合适的平衡态分布函数和离散作用力,建立有效的格子Boltzmann-BGK模型.通过Chapman-Enskog分析,可由建立的格子Boltzmann-BGK模型恢复出宏观方程,从而证明了模型的有效性.最后,将模型应用于求解带有解析解的数值算例和Allen-Cahn方程,数值结果进一步验证了模型的正确性和有效性.     

（RbCl）108离子簇均相成核的分子动力学研究

分子动力学模拟测得熔融（RbCl)108离子簇在300K至600K温度时凝固的成核速率大于10^35m^-3s^-1,用均相成核的经典理论加以分析,估算得氯化铷离子簇的固液界面自由能σalT^1.4,用Grunasy提出的扩散界面理论加以分析,估算得扩展界面厚度约为0．195nm,σalT^0.97,2个理论在实验温度范围内没有明显判别,且均能较好地分子动力学模型的结果,但预测的较高温度下的成核速率有比较显著区别,因此进一步地研究将有助于鉴别它们。     

(RbCl)_(108)离子簇固液相变的分子动力学研究

通过分子动力学模拟 ,考察并分析了 (RbCl) 1 0 8离子簇的结构、能量和相变的动力学行为。观察到的(RbCl) 1 0 8离子簇的熔点约为 91 0K。当完全熔融的 (RbCl) 1 0 8离子簇以 2 5× 1 0 1 1 K/s的速率冷却时 ,在约 62 5K时观察到成核和晶体生长。在快速冷却时 ,熔融的 (RbCl) 1 0 8离子簇自发地由液相变为立方面心相。在 450K、 50 0K、550K和 60 0K的成核速率大于 1 0 35m- 3s- 1 。由成核速率得到的固液界面自由能约为 70mJ/m2 。     

面向人工重力技术的绳系自旋航天器动力学建模与分析

面向人工重力技术,对哑铃型绳系自旋航天器系统进行了动力学建模、近似解析分析和数值仿真.首先,基于凯恩方法建立了二维平面上系统动力学方程组.然后,适当选取空间和时间标尺,将系统方程去量纲化.引入系绳长度与空间标尺之比作为小参数,利用小参数摄动方法,对无量纲系统方程作了合理简化.基于椭圆积分和椭圆函数理论,对绳系系统自旋周期进行了近似解析估算.给出乘员舱内人工重力和科氏力的计算公式.数值仿真表明,合理选择系绳长度和自旋角速度,可以在乘员舱内产生适合航天员居住的人工重力,其波动幅值甚微,波动频率远离人体敏感频带,且科氏力与人工重力相比其值甚微.     

求解二维对流扩散方程的格子Boltzmann方法

针对二维对流扩散方程,基于D2Q4格子速度,用Chapman-Enskog多尺度分析技术,将时间尺度取为二阶,空间尺度取为一阶,推导了各个速度方向上的平衡态分布函数所满足的条件,给出了简单且对称的平衡态分布函数表达式,所得到的平衡态分布函数能正确地恢复出二维对流扩散方程,从而构建了一种新的求解二维对流扩散方程的D2Q4格子Boltzmann（LB）模型。用所给LB模型对扩散方程和两个不同初边界条件的对流扩散方程进行了数值求解,数值实验结果表明数值解与精确解吻合较好,与相关文献结果比较边界误差要小得多,验证了模型的有效性。     

图像处理技术在单晶硅生产监测中的应用研究

以半导体材料单晶生长为背景,利用图像处理与分析技术对单晶生产过程进行监测研究.晶体生长是具有相变与移动边界的复杂分布参数系统,但是单晶炉所采用的监测控制手段仍然是相当基本的,以至阻碍了高纯度、高均匀性、高完整性和大直径半导体单晶材料的生产.在对现场摄取的单晶生长图像序列进行边缘检测和二值化等预处理的基础上,优化设计了自动阈值分割算法,有效地提取了几何特征量,直观给出了单晶生长固体--液体界面的图像信息.对计算机视觉检测和分析应用于单晶生产作了有益的探索.     

暖通空调节能系统的测温数值模拟仿真研究

由于传统测温数值模拟方法与实测值存在偏差且模拟值波动范围较大的问题。因此,提出暖通空调节能系统测温数值模拟仿真方法。计算系统密闭空间冷负荷,当冷负荷监测达到稳定值时,将系统空间测温过程,看作气体湍流的流动过程,构建温度场数学模型,网格划分三维立体空间,对温度场模型进行边界约束,改变边界条件参数设定,获得系统测温的多个变化因素,迭代运算后,导出三维网格空间温度分布。将暖通空调节能系统安装在驾驶室内,进行对比实验,结果表明：提出的设计方法降低了温度模拟值与实测温度的差值,缩短了数值模拟仿真时间,减小了模拟值波动范围。     

图像的扩散界面无监督聚类算法

图像的无监督聚类就是基于图像数据,在无任何先验信息的情况下将整个图像集合划分成若干子集的过程。由于图像的本征维度很高,在图像处理中会遇到“维数灾难”问题。针对图像无监督聚类的特点,提出了一种图像的扩散界面无监督聚类算法,将图像编码成高维观测空间中的点,再通过投影变换映射到低维特征空间,在低维特征空间中构建扩散界面无监督聚类模型,并在模型中引入维度约简算子,采用循环迭代算法优化扩散界面模型的能量函数。基于最优的扩散界面,将整个图像集合聚类成不同的子集。实验结果表明,扩散界面无监督聚类算法优于传统聚类算法中的K-means算法、DBSCAN算法和Spectral Clustering算法,能够更好地实现图像的无监督聚类,在相同条件下具有更高的准确度。     

Optimal control of convection–diffusion process with time-varying spatial domain: Czochralski crystal growth

This paper considers the optimal control of convection–diffusion systems modeled by parabolic partial differential equations (PDEs) with time-dependent spatial domains for application to the crystal temperature regulation problem in the Czochralski (CZ) crystal growth process. The parabolic PDE model describing the temperature dynamics in the crystal region arising from the first principles continuum mechanics is defined on the time-varying spatial domain. The dynamics of the domain boundary evolution, which is determined by the mechanical subsystem pulling the crystal from the melt, are described by an ordinary differential equation for rigid body mechanics and unidirectionally coupled to the convection–diffusion process described by the PDE system. The representation of the PDE as an evolution system on an appropriate infinite-dimensional space is developed and the analytic expression and properties of the associated two-parameter semigroup generated by the nonautonomous operator are provided. The LQR control synthesis in terms of the two-parameter semigroup is considered. The optimal control problem setup for the PDE coupled with the finite-dimensional subsystem is presented and numerical results demonstrate the regulation of the two-dimensional crystal temperature distribution in the time-varying spatial domain.     

A galerkin/neural-network-based design of guaranteed cost control for nonlinear distributed parameter systems.

This paper presents a Galerkin/neural-network- based guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities. A parabolic PDE system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this, in the proposed control scheme, Galerkin method is initially applied to the PDE system to derive an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently parameterized by a multilayer neural network (MNN) with one-hidden layer and zero bias terms. Then, based on the neural model and a Lure-type Lyapunov function, a linear modal feedback controller is developed to stabilize the closed-loop PDE system and provide an upper bound for the quadratic cost function associated with the finite-dimensional slow system for all admissible approximation errors of the network. The outcome of the GCC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.     

Delay compensated control of the Stefan problem and robustness to delay mismatch

This paper presents a control design for the one‐phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid‐solid phase change phenomenon which describes the time evolution of a material's temperature profile and the interface position. The actuator delay is modeled by a first‐order hyperbolic partial differential equation (PDE), resulting in a cascaded transport‐diffusion PDE system defined on a time‐varying spatial domain described by an ordinary differential equation (ODE). Two nonlinear backstepping transformations are utilized for the control design. The setpoint restriction is given to guarantee a physical constraint on the proposed controller for the melting process. This constraint ensures the exponential convergence of the moving interface to a setpoint and the exponential stability of the temperature equilibrium profile and the delayed controller in the norm. Furthermore, robustness analysis with respect to the delay mismatch between the plant and the controller is studied, which provides analogous results to the exact compensation by restricting the control gain.     

Two- and three-dimensional transient melt-flow simulation in vapour-pressure-controlled Czochralski crystal growth

Flow and thermal properties associated with semiconductor melt flow in an axisymmetric crucible container are studied numerically. Axisymmetric and three-dimensional computational solutions are obtained using a standard-Galerkin, finite-element solver. The crucible and crystal are optionally rotated, and the influence of gravity (through buoyancy) is accounted for via a Boussinesq approximation in the controlling Navier–Stokes equations. The results indicate a strong dependence of the flow on both rotation and buoyancy. Results for axisymmetric flows, computed with both flat and curved geometries, are presented first, and strongly suggest that rotation of crystal and crucible in the same direction (iso-rotation) is most favourable for producing a desired convexity for the crystal/melt interface. Three-dimensional results are then presented for higher Reynolds numbers, and, in particular, reveal that for iso-rotation under moderate buoyancy, the flow undergoes a switch from a steady 2D state to an unsteady 3D state, and that the temperature becomes non-trivially advected by the flow beneath the crystal. Further evidence reveals however, that on a time scale more appropriate to the crystal growth process, the (time-averaged) flow has a weaker three-dimensionality, in relation to the mean axisymmetric part, and there is only slight distortion to the temperature field beneath the crystal. A detailed examination of the instability properties is also made, revealing the underlying nonlinear mode interaction and associated frequency responses around the bifurcation point.     

Finite-element methods for analysis of the dynamics and control of Czochralski crystal growth

Numerical methods are presented for solution of the complex moving-boundary problem described by a thermal-capillary model for Czochralski crystal growth, which accounts for conduction through melt, crystal, and crucible and radiation between diffuse-gray body surfaces. Transients are included that are caused by energy transport, by changes in the shapes of the melt-crystal, melt-ambient phase boundaries and the moving crystal, and by the batchwise decrease of the melt volume in the crucible. Finite-element discretizations are used to approximate the moving boundaries and the energy equation in each phase. A two-level, implicit integration algorithm is presented for transient calculations. The temperature fields and moving boundaries are advanced in time by a trapezoid rule approximation with modified Newton's iterations to solve algebraic systems for effective ambient temperatures computed with diffuse-gray radiation. The implicit coupling between radiative exchange, interface shapes, and the temperature field is necessary for preserving the second-order accuracy of the integration method and is achieved by successive iterations between the radiation calculation and solution of the thermal capillary model. Analysis of a quasi-steady-state model (QSSM) demonstrates the inherent stability of the CZ process. Including either diffuse-gray radiation among crystal, melt, and crucible or a simple controller for maintaining constant radius can lead to oscillations in the crystal radius. The effects of these oscillations on batchwise crystal growth are addressed.     

Image analysis of solid-liquid interface morphology in freezing solutions

This paper describes a system which analyzes a sequence of images of the mobile solid-liquid interface during the process of solidification in freezing solutions. The specific objective is to measure the two-dimensional morphology of the varying interface. The three stages that typify the temporal evolution of this boundary through varying temperature conditions are planar, cellular and dendritic. Image analysis techniques were developed for identifying these solid-liquid interfaces and extracting the corresponding boundaries. Statistical measures of shape were utilized in distinguishing between various patterns of growth in the solid phase. Performance of the system is depicted in several illustrative examples.     

Isogeometric Analysis for Topology Optimization with a Phase Field Model

We consider a phase field model for the formulation and solution of topology optimization problems in the minimum compliance case. In this model, the optimal topology is obtained as the steady state of the phase transition described by the generalized Cahn?CHilliard equation which naturally embeds the volume constraint on the amount of material available for distribution in the design domain. We reformulate the model as a coupled system and we highlight the dependency of the optimal topologies on dimensionless parameters. We consider Isogeometric Analysis for the spatial approximation which facilitates encapsulating the exactness of the representation of the design domain in the topology optimization and is particularly suitable for the analysis of phase field problems. We demonstrate the validity of the approach and numerical approximation by solving two and three-dimensional topology optimization problems.     

Distributed Proportional-spatial Derivative control of nonlinear parabolic systems via fuzzy PDE modeling approach

In this paper, a distributed fuzzy control design based on Proportional-spatial Derivative (P-sD) is proposed for the exponential stabilization of a class of nonlinear spatially distributed systems described by parabolic partial differential equations (PDEs). Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to accurately represent the nonlinear parabolic PDE system. Then, based on the T-S fuzzy PDE model, a novel distributed fuzzy P-sD state feedback controller is developed by combining the PDE theory and the Lyapunov technique, such that the closed-loop PDE system is exponentially stable with a given decay rate. The sufficient condition on the existence of an exponentially stabilizing fuzzy controller is given in terms of a set of spatial differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is also provided to solve these SDLMIs. Finally, the developed design methodology is successfully applied to the feedback control of the Fitz-Hugh-Nagumo equation.