Galerkin domain decomposition procedures for parabolic equations on rectangular domain

Galerkin domain decomposition procedures for parabolic equations with three cases of boundary conditions on rectangular domain are discussed. These procedures are non‐iterative and non‐overlapping ones. They rely on implicit Galerkin method in the sub‐domains and integral mean method on the inter‐domain boundaries to present explicit flux calculation. Thus, the parallelism can be achieved by the use of these procedures. Two kinds of approximating schemes are presented. Because of the explicit nature of the flux calculation, a less severe time‐step constraint is derived to preserve stability. To bound L²‐norm error estimates, new elliptic projections are established and analyzed. Numerical experiments are provided to confirm theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.     

广义近似空间的拓扑结构

在本文中,我们引入了论域X上的自反关系θ的传递化表示θs的概念,研究了拓扑空间(X,тθ)的基本性质,得到了一些有较大价值的结果,这不仅有助于理解粗糙集理论中的一些基本概念及其性质,而且对拓扑学本身都有理论和实际意义.     

Roughness-induced effects on the thermomicropolar fluid flow through a thin domain

In this paper, we study the asymptotic behavior of the thermomicropolar fluid flow through a thin channel with rough boundary. The flow is governed by the prescribed pressure drop between the channel's ends and the heat exchange through the rough wall is allowed. Depending on the limit of the ratio between channel's thickness and the wavelength of the roughness, we rigorously derive different asymptotic models clearly showing the roughness-induced effects on the average velocity and microrotation. To accomplish that, we employ the adaptation of the unfolding method to a thin-domain setting.     

Tb0.3Dy0.7Fe2合金的本构参数辨识方法研究

建立了一种简便的、适用于磁畴模型应用的Tb0.3Dy0.7Fe2合金本构参数辨识方法.针对Tb0.3Dy0.7Fe2合金磁畴模型中本构参数不明确且直接实验测试困难的问题,提出了一种数值计算与实验测试相结合的参数辨识方法.采用坐标变换与绘制自由能等势曲线相结合的方法,简化了载荷作用下Tb0.3Dy0.7Fe2合金内磁畴角度偏转的数值计算,研究了合金磁畴角度偏转模型的参数依赖性.在此基础上,结合简单的实验测试,建立了Tb0.3Dy0.7Fe2合金各向异性常数K1和K2、能量分布因子ω、晶轴取向分布的辨识及修正方法.该方法能够简单、快速地完成Tb0.3Dy0.7Fe2合金磁畴模型中本构参数的辨识,对完善磁致伸缩材料磁畴偏转的数值计算模型非常有意义.理论分析可为类磁致伸缩材料磁机耦合模型的建立、完善,以及材料本构参数的辨识、获取提供参考.     

Sobolev spaces on bounded symmetric domains

We obtain a formula for the Sobolev inner product in standard weighted Bergman spaces of holomorphic functions on a bounded symmetric domain in terms of the Peter–Weyl components in the Hua–Schmidt decomposition, and use it to clarify the relationship between the analytic continuation of these standard weighted Bergman spaces and the Sobolev spaces on bounded symmetric domains.     

稳健宽带波束形成器设计的低阶统计量法*

由于传声器阵列通常对阵元失配误差较为敏感,因此稳健波束形成器的设计已成为传声器阵列处理领域的研究热点之一。概率密度法是目前传声器阵列稳健波束形成器设计中的一类重要方法,但该方法所需的阵元失配误差的概率密度信息在实际中较难获取。针对这一问题,本文研究了基于阵元失配误差低阶统计量的稳健波束形成器设计方法,该方法仅利用在实际中较易获取的阵元失配误差的一阶和二阶统计量信息。本文分别研究了基于阵元失配误差低阶统计量的固定权和变加权最小二乘波束形成器设计,给出了两种波束形成器的相关设计理论。理论和仿真分析表明,在小误差条件下,低阶统计量法所设计的波束形成器仍保持与概率密度法相当的性能。     

Extensions and traces of functions of bounded variation on metric spaces

In the setting of a metric space equipped with a doubling measure and supporting a Poincaré inequality, and based on results by Björn and Shanmugalingam (2007) [7], we show that functions of bounded variation can be extended from any bounded uniform domain to the whole space. Closely related to extensions is the concept of boundary traces, which have previously been studied by Hakkarainen et al. (2014) [17]. On spaces that satisfy a suitable locality condition for sets of finite perimeter, we establish some basic results for the traces of functions of bounded variation. Our analysis of traces also produces novel pointwise results on the behavior of functions of bounded variation in their jump sets.     

雪崩倍增GaAs光电导太赫兹辐射源研究进展

在飞秒激光激励下用GaAs光电导开关作为太赫兹(THz)辐射天线, 已经广泛用于太赫兹时域光谱系统, 但目前国际上都是使用GaAs光电导开关的线性工作模式, 而GaAs光电导开关的雪崩倍增工作模式所输出的超快电脉冲功率容量远大于其线性工作模式, 迄今为止, 还没有人提出用雪崩倍增机理的GaAs 光电导开关作为辐射源产生THz电磁辐射. 本文探讨了用 雪崩倍增工作模式的GaAs光电导开关作为光电导天线产生THz电磁波的可能性及研究进展. 通过理论分析及实验研究, 在实验上实现了: 1) 利用nJ量级飞秒激光触发GaAs光电导天线, 可以进入雪崩倍增工作模式; 2) 利用光激发电荷畴的猝灭模式, 可以使GaAs光电导天线载流子雪崩倍增模式的延续时间(lock-on 时间)变短. 这为利用具有雪崩倍增机理的GaAs光电导天线产生强THz辐射奠定了基础.     

Viscoelastic swirling flow with free surface in cylindrical chambers

The flow of a viscoelastic liquid driven by the steadily rotating bottom cover of a cylindrical cup is investigated. The flow field and the shape of the free surface are determined at the lowest significant orders of the regular domain perturbation in terms of the angular velocity of the bottom cap. The meridional field superposed on a primary azimuthal field shows a structure of multiple cells. The velocity field and the shape of the free surface are strongly effected by the cylinder aspect ratio and the elasticity of the liquid. The use of this flow configuration as a free surface rheometer to determine the first two Rivlin-Ericksen constants is shown to be promising.Nomenclature R, ,Z Coordinates in the physical domain D - , , Coordinates in the rest stateD ₀ - r, ,z Dimensionless coordinates in the rest stateD ₀ - Angular velocity - Zero shear viscosity - Surface tension coefficient - Density - Dimensionless surface tension parameter - ₁, ₂ The first two Rivlin-Ericksen constants - Stream function - Dimensionless second order meridional stream function - ^* Dimensionless second normal stress function - 2 Dimensionless sum of the first and second normal stress functions - N ₁,N ₂ The first and second normal stress functions - n Unit normal vector - D Stretching tensor - A _n nth order Rivlin-Ericksen tensor - S Extra-stress - u Velocity field - U Dimensionless second order meridional velocity field - V Dimensionless first order azimuthal velocity field - p Pressure - Modified pressure field - P Dimensionless second order pressure field - J Mean curvature - a Cylinder radius - d Liquid depth at rest - D Dimensionless liquid depth at rest - h Free surface height - H Dimensionless free surface height at the second order