Probability of boundary conditions in quantum cosmology

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler–DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler–DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.     

Quantization Conditions in Curved Spacetime and Uncertainty-Driven Inflation

An alternative inflationary model is proposed predicated upon a considerationof the form of the uncertainty principle in a curved background spacetime. Anargument is presented suggesting a possible curvature dependence in the correctcommutator relations for a quantum field in a classical background which cannotbe deduced simply by extrapolation from the flat spacetime theory. To assess thepossible consequences of this dependence, we apply the idea to a scalar field ina closed Friedmann-Robertson-Walker background, using a simple model forthe curvature dependence (along the way, a previous erroneous result obtainedby Bunch for the adiabatically expanded wave function is corrected). The resultis a time-dependent cosmological constant, producing a vast amount of inflationthat is independent of either the mass of the matter field or its effectivepotential.Furthermore, it is seen that the field modes are initially zero for allwavelengthsand come into being as the universe evolves. In this sense, the universe createsits contents out of its own expansion. At the end of the process, the matterfieldis far from equilibrium and essentially reproduces the initial conditions forthe New Inflationary Model.     

Data extrapolation method for boundary element method-based near-field acoustical holography

A new data extrapolation method for boundary element method (BEM)-based near-field acoustical holography (NAH) is proposed to reduce an error of the reconstructed result obtained from the pressure measured on an aperture small compared with the structure. The finiteness of the measurement aperture is a serious impediment to actual large-scale implementation of NAH, because NAH requires the measurement of the pressure field over a complete surface of structure. To eliminate the requirement, the wave number-space data extrapolation method for fast Fourier transform (FFT)-based NAH has been proposed. In this paper, the extension of this data extrapolation method to BEM-based NAH is presented. The effectiveness of this method is demonstrated by experiments. The experiment results confirm that the reconstruction error is sufficiently suppressed by the proposed method.     

矩形单元声场波函数构造及其应用

在波叠加法中,结构外部声场是在离散边界上对Green函数进行积分并叠加得到,但数值积分的计算效率较低。而等效源法虽然提高了计算效率,但其面源简化为点源的过程中存在较大的积分近似误差。针对上述两种方法的缺陷,构造了一种波函数以替代离散单元关于Green函数积分的声场。首先,利用球坐标系下Helmholtz方程的解,推导了替代矩形单元积分的一般形式波函数及效率更高的内推波函数。其次,当离散单元为正方形时,将其近似成圆形域,进一步简化了内推波函数的表达式。最后,将所构造的波函数应用于声场计算。数值结果表明,在计算单个矩形单元外部辐射声场时,构造的波函数不仅保证了计算精度,而且相比于直接积分大幅度提高了计算效率。其中,矩形域一般形式和内推形式的波函数计算效率是直接积分的5～6倍,圆形域内推波函数计算效率达到了直接积分的12～13倍。在简支板声源和立方箱体辐射声源数值算例中,圆形域内推波函数在整个计算频段的声场计算精度均高于等效源法。     

Dirac operator zero-modes on a torus

We study Dirac operator zero-modes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In suitable torus coordinates the zero-mode wave functions can be related to holomorphic functions of the complex torus coordinates. Half of the twisted boundary conditions for the holomorphic part of the zero-mode wave function can be made periodic or anti-periodic. The remaining half is until coordinate dependent but diagonal. We completely solve the twisted boundary conditions and construct the zero-mode wave functions. The chirality and the degeneracy of the zero-modes are uniquely determined by the gauge background and are consistent with the index theorem.     

Inverse Lax-Wendroff procedure for numerical boundary conditions of conservation laws

We develop a high order finite difference numerical boundary condition for solving hyperbolic conservation laws on a Cartesian mesh. The challenge results from the wide stencil of the interior high order scheme and the fact that the boundary intersects the grids in an arbitrary fashion. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions. We repeatedly use the partial differential equation to write the normal derivatives to the inflow boundary in terms of the time derivatives and the tangential derivatives. With these normal derivatives, we can then impose accurate values of ghost points near the boundary by a Taylor expansion. At outflow boundaries, we use Lagrange extrapolation or least squares extrapolation if the solution is smooth, or a weighted essentially non-oscillatory (WENO) type extrapolation if a shock is close to the boundary. Extensive numerical examples are provided to illustrate that our method is high order accurate and has good performance when applied to one and two-dimensional scalar or system cases with the physical boundary not aligned with the grids and with various boundary conditions including the solid wall boundary condition. Additional numerical cost due to our boundary treatment is discussed in some of the examples.     

格子Boltzmann守恒型非平衡态的外推边界

针对非平衡态外推边界处理方法在某些条件下发生质量泄漏的问题,结合质量守恒定律对其进行修正,建立一种新的质量守恒型的边界处理格式.其基本思想是在边界处定义一个虚拟密度来修正平衡态分布函数,使得系统质量守恒.以重力作用下的密度场及磁流体模拟问题为例,利用该格式进行分析,讨论质量泄露问题的本质及各种因素的影响.通过对三种典型的流动:二维Poiseuille流、Couette流、Womersley流的模拟,验证该边界格式的计算精度和稳定性.     

Interaction of an obliquely incident electromagnetic wave with collisional plasma half space

Penetration and reflection of an electromagnetic wave incident obliquely on a semi-infinite collisional plasma is studied. The linearized Boltzmann equation is used for the perturbed plasma. Using Fourier transform technique, specular boundary condition and simple collisional model the solution of coupled Maxwell-Boltzmann equations is presented. The field solutions consist of both longitudinal and transverse parts into the plasma region. The reflection coefficient is also obtained.     

一种基于傅里叶变换的分析载波条纹的新方法

针对传统傅里叶变换法处理光载波干涉条纹图时会有边缘效应产生的问题,提出了一种基于傅里叶变换法的外推延拓方法,并从理论上进行了数学推导。为了验证这种方法的正确性,分别对一维数字信号和二维空间载波条纹图进行了数值模拟,进一步分析了误差产生的原因,并与传统的傅里叶变换法对比。结果表明该法可以有效抑制传统傅里叶变换法处理光载波干涉条纹图时边缘效应所造成的较大误差,在基于空间域相位调制技术的波面干涉测量中,对空间载波条纹图进行处理,可以使相位的计算精度达到3.3 mrad。     

激波与层流/湍流边界层相互作用实验研究

在超声速风洞中,分别对层流和湍流来流条件下的边界层和斜激波(激波强度足以引起流动分离)相互干扰进行了实验研究,利用纳米粒子示踪平面激光散射(NPLS)技术获得了两种条件下流场的精细结构图像;利用粒子图像测速(PIV)技术获得了两种条件下流场的速度场和涡量场;综合运用NPLS结果和PIV结果对比分析了两种流动的瞬时流动结构和时间相关性,实验结果表明:层流边界层内的分离区呈现出狭长的条状,而湍流边界层内分离区呈现出较规则的椭圆;在入射激波上游距入射点较远的位置,层流边界层外围拟序结构会诱导出一系列压缩波系,进而汇聚成空间位置不稳定的诱导激波,而湍流边界层则是在入射激波上游较近的地方直接形成较强且稳定的诱导激波;在入射激波下游,层流边界层内的膨胀区域较小且急促,膨胀后产生的再附激波很弱,而湍流边界层内的膨胀区域较大,膨胀后产生的激波较强。     

Boundary condition model for diffractive elastic scattering

Diffractive elastic scattering is studied by a boundary condition model that does not utilize a potential model.S-matrix elements are calculated and compared to those found from an optical potential model calculation. The unitarity of the model is related to the boundary condition imposed. A radially ingoing boundary condition is imposed on the wave function at one angle only, at a scattering angle of 180 °. This condition is required to hold in the vicinity of the nuclear radius, but not for all radii. Elastic scattering peaks at forward and backward angles are reproduced and discussed. The model is applied to composite particle scattering above the Coulomb barrier.     

DISCRETE HUYGENS' MODELLING APPROACH TO WAVE PROPAGATIONS IN A HOMOGENEOUS ELASTIC FIELD

The application of the discrete Huygens' modelling has been discussed for acoustic wave propagation problems, in which the scalar wave field problems have been focused. The present paper extends the application of the modelling to the elastic wave propagation in a homogeneous elastic medium in which two types of waves, the longitudinal wave and the shear wave, are independent except at the boundary. Each wave can be treated like a scalar wave until the two waves reach the boundary where they couple so as to satisfy the displacement or stress boundary condition. We propose the approach confining ourselves to the two-dimensional field. Some examples are demonstrated, whose solutions are compared with the vectorial wave modelling and finite difference modelling solutions whenever they are available.     

Mechanism for the streamer propagation toward the anode and cathode due to background electron multiplication

A simple mechanism for the propagation of an ionization wave in a dense gas due to the multiplication of background electrons in a nonuniform electric field is proposed. The mechanism does not depend on the sign of the field projection onto the streamer propagation direction. The streamer propagation is caused by the enhancement of the electric field at the streamer head. It is shown that, in a prebreakdown field, the intense multiplication of electrons takes place in both electropositive and electronegative gases. The prebreakdown multiplication can provide a fairly high density of background electrons; this allows one to treat the background as a continuous medium when considering streamer propagation as a multiplication wave. The initial ionization is enabled by the natural background of ionizing radiation and cosmic rays. An analytical expression for the velocity of the ionization front is obtained based on a simple equation for the multiplication of background electrons. This expression is in good agreement with numerical simulations performed within both a simple model of background electron multiplication and a more comprehensive drift-diffusion model. In particular, the drift-diffusion model predicts the propagation of the ionization front from a small-radius anode to the cathode due to the multiplication of background electrons. The velocity of the ionization wave front is calculated as a function of the electric field at the streamer head for helium, xenon, nitrogen, and sulfur hexafluoride. It is shown that some features of streamer propagation (e.g., its jerky motion) can be related to the recently found nonmonotonic dependence of ionization frequency on the electric field.     

平面光波导器件时域有限差分束传输法分析中边界和初始条件的处理

从慢变包络（SVEA）时域光传输方程出发,对比了综合道格拉斯（GD）和传统的中心差分（CN）两种离散化格式,指出GD法比CN法精度有了很大提高.重点讨论了GD法的TD-BPM边界处理问题,给出了吸收边界和透明边界离散的显式和隐式表达式,分析并确定了交替方向隐式法（ADIM）的边界处理方式;同时,对激励源加入的连接边界进行了仔细讨论.结果表明对于隐式GD-TD-BPM法边界处理应采用隐式,中间激励更能反映光波导反射场的情况.     

Numerical observation of the rescattering wave packet in laser-atom interactions

We present a full-quantum nonperturbative method to study the electron rescattering process in the intense laser-atom interactions. We separate the ionized wave function from the background by solving the time-integral equation. Imposing the incoming boundary condition on the wave function, we reproduce the motion of the rescattering wave packet predicted by the rescattering theory. Our calculated rescattering energies differ significantly from the semiclassical ones. The difference would be substantial for the evaluation of the rescattering induced dynamics such as the molecular dissociation.     

计算波导加载谐振腔谐振频率的新方法

基于边界元法,提出了一种新的简单有效的计算速调管输出系统波导加载腔的谐振频率、场分布的方法。计算了一种矩形波导加载矩形谐振腔的常见结构。利用主模TE10波激励,在波导的端口处采用推导出的Robin-type边界条件,通过扫频的方式,观测选定场点的值,极值对应系统的谐振频率。数值结果表明:波导加载谐振腔的谐振频率要低于同尺寸谐振腔的频率,谐振腔内的电场分布也受到耦合孔的影响。利用边界元法计算波导加载腔这样的半开放系统,具有实现简单、计算精确度高、数据输入少、计算时间短等优点。     

等离子体电子压强的Hartree-Fock-Slater自洽场计算

在对传统平均原子模型(AAM1)作动态自由电子判据改进的基础上，在中心场近似下使用了带边界条件的正能态波函数，提高电子压强的计算精度，使得电子压强满足常态物理条件.作为算例，计算了Fe，Ni，Pb，Am的电子压强. 关键词： 自治场原子结构 电子压强     

旋转体时域有限差分法的另一推导方法和单向波方程吸收边界条件

提出了旋转体时域有限差分法的另一推导方法.基于这一方法,推导了旋转体电磁波的波动方程,进一步得出了旋转体时域有限差分法的单向波方程吸收边界条件.数值实验证实了该吸收边界条件的正确性.