双曲方程外问题的完全无反射人工边界条件

研究了数值求解双曲方程外问题的人工边界方法.在圆形的人工边界上,得到了三类等价的完全无反射的人工边界条件.给出的数值例子验证了方法的有效性.     

求解声辐射问题的微分求积法与微分求积单元法

基于无限域中的Helmholtz波动方程,将微分求积法与微分求积单元法应用于二维及三维声辐射问题的求解,对最外层节点施加不同阶数的人工边界条件,区域内使用均匀及非均匀的节点分布方式,分析了节点分布方式及人工边界条件对计算结果的影响,比较了两种数值方法的计算精度。研究结果表明:微分求积法与微分求积单元法,前者精度更高,而后者耗时更少,在频率较低时,具备较高的效费比。人工边界条件对计算结果的影响主要体现在低频段,而节点分布方式的影响主要体现在高频段。非均匀的节点分布方式在不同频段都具备更好的计算精度。      

孔隙介质与液体界面上波动方程数值模拟的改进 方案——MPML边界条件的应用*

由于波场数值模拟的计算区域是有限的,为了压制截断边界造成的人工边界反射,通常采用完全匹配层作为吸收边界条件。但是在含液-固界面的弹性介质中进行正演模拟时,完全匹配层边界条件容易造成稳定性方面的问题。因此,该文将多轴完全匹配层应用于该类介质的正演模拟,以改善完全匹配层边界条件引起的不稳定问题。通过在具有弹性海底的海洋环境模型以及充填液体的井孔模型中进行弹性波方程的正演模拟,分别采用传统的完全匹配层和多轴完全匹配层作为吸收边界条件,对比验证了多轴完全匹配层在含液-固界面弹性介质中数值模拟的有效性和稳定性。     

耗散粒子动力学中施加无滑移边界条件的新方法

在耗散粒子动力学(DPD)中施加无滑移边界条件是较困难的,本文提出了一种新的处理方法来实现无滑移边界条件.通过选取合适的壁面与流体粒子之间的保守力系数可以控制近壁面区的粒子数,从而可以使密度波动降低至极小值,实现无滑移边界条件.通过该方法模拟泊肃叶流动求得的流体性质与通过使用Lees-Edwards边界条件模拟剪切流动所求得的流体性质一致,证明了该方法的可靠性.     

非对称全同质点共线系统的振动

研究了直线型三个、四个全同质点体系在不对称的边界条件下的内部运动，发现一些新的振动模式。     

广义边界条件和概率流密度的连续性

以四参量族－广义边界条件代替有限深方势阱内粒子波函数的对数的一阶导数连续性条件，表明这种替换比用广义边界条件取代一盒子内自由粒子波函数在两壁处为零的边界条件显行更加合理些。我们发现，如对参量ρ和θ取任意值，则会导致概率流密度连续性被破坏。我们找到了约束ρ和θ取值的条件，并得到一组新的解析解。     

辐射边界条件应用于流体中的声波散射

本文提出一种新的求解流体中声波散射的数值方法。本文应用辐射边界条件将无限空间的声波散射限制在有限区域内,采用有限差分技术数值求解Helmholtz方程、散射体表面边界条件以及辐射边界条件,从而获得声散射体的表面场及近场分布。本文给出的球体及长椭球体的数值计算结果表明,这种方法可获得与本征函数级数解相当吻合的结果,优于OSRC方法的结果,说明这种方法可能成为一种对现有解析或数值方法的有效替代方法。     

矩形微槽蒸发薄液膜新边界条件的设定

采用了一种新的边界条件来求解微槽内蒸发薄液膜的控制方程。这种新的边界条件保证在毛细微槽中,本征弯液面区域的液面弯曲中心位于微槽的中心线上,从而消除了传统微槽薄液膜计算模型中产生的物理矛盾。计算结果显示随着过热度的增加,本征弯液面部分的曲率半径不是恒定的,而是逐渐增加的,这导致了本征区域毛细吸力的降低。计算结果同时表明在本征区域的较薄位置,存在一个狭窄的热流密度相当大的子区域。在数值研究中,如果将此子区域用恒定半径的区域来替代,从理论上来讲是不合理的。     

人工光源对地面目标表面温度的影响分析

研究人工光源对地面目标表面温度的影响对目标红外特性的研究以及红外特征的模拟有重要的意义.以自然环境下人工光源照射地面目标的物理模型为基础,通过建立导热微分方程和改变目标的外边界辐射能量,建立起人工光源照射目标时目标表面温度的计算模型,结合目标表面温度的计算与目标所处的地理环境与方位有关,本文以合肥某建筑物正东方位表面为例,对在不同时间段、不同光照参量时目标的表面温度进行了仿真计算与分析.结果表明:改变目标的外边界条件即给目标表面采用人工光源照射时,目标的表面温度将发生改变,改变的程度取决于光源的照射功率、照射距离以及光源的入射角,一般情况下,晚上照射时表面温度变化明显,白天照射变化不太明显.     

运动边界的电磁场边界条件

基于Einstein相对论,给出了运动边界的电磁场边界条件,指出了以往运动边界条件存在的问题 关键词： 电磁场边界条件 运动边界 Einstein相对论     

Binary scattering and breakup in the three-nucleon system

We present the further development of the three-particle formalism for differential Faddeev equations. The asymptotic boundary conditions in the hyperspherical adiabatic representation have been constructed. We prove that these conditions are asymptotically equivalent to the standard Merkuriev boundary conditions. With these boundary conditions we have formulated the boundary-value problem for Faddeev equations which has the property that the binary channel and the breakup channel are explicitly orthogonal. The effective numerical scheme for solving the formulated boundary-value problem is given.     

Boundary conditions for the bending of a piezoelectric beam

For beam bending in transversely isotropic piezoelectric media, the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all orders for the beam of general edge geometry and loadings. By generalizing the method developed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. The prescribed edge-data of the beam must satisfy these conditions in order that they could generate a decaying state within the beam. When stress and mixed conditions are imposed on the beam edge, these decaying state conditions for the case of bending deformation of piezoelectric beam are derived explicitly. They are then used for the correct formulation of boundary conditions for the beam theory solution (or the interior solution). Besides, an analytical solution of elastic beam is formulated to verify validity of our boundary conditions. For the stress data, our boundary conditions coincide with those obtained in conventional forms of beam theories. More importantly, the appropriate boundary conditions with two sets of mixed edge-data are obtained for the first time.     

一维波动方程的解的长期稳定性

对有限区间上的一维波动方程,在各种边界条件下建立了位移函数与初始条件之间的不等式,并由此推论出多种边界条件下的解的长期稳定性．     

Nonreflecting boundary conditions for discrete waves

We introduce a new class of nonreflecting boundary conditions for lattice models, which minimizes reflections at artificial boundaries. Exact integrodifferential boundary conditions for finite chains and half-spaces are obtained by means of Green’s functions for initial value problems. Truncating the resulting integrals in time, we obtain absorbing boundary conditions. Numerical tests illustrate the ability of these conditions to suppress reflections.     

Alternative boundary conditions for solving optical diffusion equations by a finite difference time domain analysis in three-dimensional scattering medium

Alternative boundary conditions for solving optical diffusion equations in three-dimensional (3-D) scattering medium by a finite difference time domain (FDTD) analysis formulated by the author are proposed. The previous boundary conditions were defined only by fluence rate, which, although essential, is only one factor needed to solve approximated diffusion equations for fluence rate. In this paper, alternative boundary conditions defined both by fluence rate and radiant flux have been proposed for use in the FDTD analysis, which is derived from the two coupled differential equations for fluence rate and radiant flux. It has been become clear that these boundary conditions are almost equivalent to the previous boundary conditions in the FDTD analysis for sufficiently fine grid spacing. For the analysis with coarser grid spacing, the proposed boundary conditions suppress analytical errors, especially in intensity of time-resolved reflectance and transmittance.     

Advanced boundary conditions for eigenmode expansion models

In order to realise the full potential of eigenmode expansion models, advanced boundary conditions are required that can absorb the radiation impinging on the walls of the discretisation volume. In this paper, we will discuss and compare a number of these boundary conditions, like perfectly matched layers (PMLs), open (leaky mode) boundary conditions and transparent boundary conditions (TBCs). We will also introduce the case of PMLs with infinite absorption and discuss its relation to leaky mode expansion, leading to a deeper insight into the physics of PML.     

Advanced boundary conditions for eigenmode expansion models

In order to realise the full potential of eigenmode expansion models, advanced boundary conditions are required that can absorb the radiation impinging on the walls of the discretisation volume. In this paper, we will discuss and compare a number of these boundary conditions, like perfectly matched layers (PMLs), open (leaky mode) boundary conditions and transparent boundary conditions (TBCs). We will also introduce the case of PMLs with infinite absorption and discuss its relation to leaky mode expansion, leading to a deeper insight into the physics of PML.     

Supersymmetric Boundary Conditions in \mathcal{N}=4 Super Yang-Mills Theory

We study boundary conditions in ${\mathcal{N}}=4$ super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some of the scalar fields to have a “pole” at the boundary. The obvious Neumann boundary conditions can be modified by coupling to additional fields supported at the boundary. The obvious boundary conditions associated with orientifolds can also be generalized. In preparation for a separate study of how electric-magnetic duality acts on these boundary conditions, we explore moduli spaces of solutions of Nahm’s equations that appear in the presence of a boundary. Though our main interest is in boundary conditions that are Lorentz-invariant (to the extent possible in the presence of a boundary), we also explore non-Lorentz-invariant but half-BPS deformations of Neumann boundary conditions. We make preliminary comments on the action of electric-magnetic duality, deferring a more serious study to a later paper.     

Exact one-point function of N=1 super-Liouville theory with boundary

In this paper, exact one-point functions of N=1 super-Liouville field theory in two-dimensional space–time with appropriate boundary conditions are presented. Exact results are derived both for the theory defined on a pseudosphere with discrete (NS) boundary conditions and for the theory with explicit boundary actions which preserves super conformal symmetries. We provide various consistency checks. We also show that these one-point functions can be related to a generalized Cardy conditions along with corresponding modular S-matrices. Using this result, we conjecture the dependence of the boundary two-point functions of the (NS) boundary operators on the boundary parameter.