A lattice Maxwell system with discrete space–time symmetry and local energy–momentum conservation

A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space–time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete group symmetries for the lattice Maxwell system. As a result, the lattice Maxwell system is shown to admit a discrete local energy–momentum conservation law corresponding to the discrete space–time symmetry. A lattice model that respects all local conservation laws and geometric structures is as good as and probably more preferable than standard models on continuous space–time. It can also be viewed as an effective algorithm for the governing differential equations on continuous space–time.     

Discrete spherical means of directional derivatives and Veronese maps

We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension, we present a general construction for obtaining discrete spherical means of directional derivatives. The construction is based on using Minkowski’s existence theorem and Veronese maps. Approximating the directional derivatives by appropriate finite differences allows one to obtain finite difference operators with good rotation invariance properties. In particular, we use discrete circular and spherical means to derive discrete approximations of various linear and nonlinear first- and second-order differential operators, including discrete Laplacians. A practical potential of our approach is demonstrated by considering applications to nonlinear filtering of digital images and surface curvature estimation.     

Discrete ordinates interpolation method for radiative heat transfer problems in three-dimensional enclosures filled with non-gray or scattering medium

The discrete ordinates interpolation method (DOIM) is applied to three groups of problems of radiative heat transfer in three-dimensional rectangular enclosures containing non-gray or scattering medium. The original DOIM is first extended to a gray gas model using a new geometric interpolation scheme. It is applied to participating media for different scattering phase functions and optical thicknesses. For the non-gray gas model, the DOIM coupled with the narrow band-based weighted-sum-of-gray-gases (WSGG) model is developed. A few test problems with real gases such as pure H₂O and a mixture of CO₂, H₂O and N₂ are taken. The wall heat flux is calculated and compared with the exact solutions or reference values. All results of test problems are found to be reliable in this study. The DOIM closely reproduces the Monte Carlo reference solutions for different scattering phase functions and optical thicknesses. The non-gray gas results are compared with reference calculations based on the statistical narrow band model and they also show good agreements. The DOIM shows a remarkable merit in the computation time and the grid compatibility, to prove its usefulness for engineering applications.     

Small-grid analysis of discrete model for evacuation from a hall

 In this paper, small-grid analysis of discrete model is described, and simulation that some walkers leave a hall is carried out to check the effects of different desired walk velocities with the same walk time at a time step, and different numbers of small grid at a time step with the same desired walk velocity, on the evacuation time. The simulation results show that small-grid analysis have reproduced some typical phenomena of evacuation, including jam, block and faster-is-slower, etc. as good as the continuum model, i.e., the social force model, but with high simulation efficiency. In addition, the power-law distribution of evacuation flow duration and block duration with the different desired walk velocities is found. The block duration with different numbers of small grid at a time step also takes on power-law characteristics, only their intercepts in log–log coordinates are different.     

A fast iterative model for discrete velocity calculations on triangular grids

A fast synthetic type iterative model is proposed to speed up the slow convergence of discrete velocity algorithms for solving linear kinetic equations on triangular lattices. The efficiency of the scheme is verified both theoretically by a discrete Fourier stability analysis and computationally by solving a rarefied gas flow problem. The stability analysis of the discrete kinetic equations yields the spectral radius of the typical and the proposed iterative algorithms and reveal the drastically improved performance of the latter one for any grid resolution. This is the first time that stability analysis of the full discrete kinetic equations related to rarefied gas theory is formulated, providing the detailed dependency of the iteration scheme on the discretization parameters in the phase space. The corresponding characteristics of the model deduced by solving numerically the rarefied gas flow through a duct with triangular cross section are in complete agreement with the theoretical findings. The proposed approach may open a way for fast computation of rarefied gas flows on complex geometries in the whole range of gas rarefaction including the hydrodynamic regime.     

复杂区域上的一种结构网格生成方法

讨论复杂区域上的一种结构网格生成方法,其主要思想是:以变分形式的Winslow网格生成方法为基础,通过引入网格解扭机制和网格面积均匀化技术,构造出一种新的离散泛函,进而采用一类优化算法求解这一离散泛函的极小化问题,得到所希望的网格.通过分析及大量数值实验表明,这一方法比较健壮,针对二维复杂区域通常能够生成几何品质较优的网格,它在保持Winslow方法优点的同时,克服了它的一些缺点.     

九点格式中网格边上切向流的计算——节点自适应加权格式

针对网格扭曲的不同情形,直接考虑网格边上切向流的离散.基于扩散方程法向流连续的条件,给出离散法向流的构造,导出扭曲网格上九点计算格式中网格边上离散切向流的表达式,从而推导出加权系数的计算公式,适应于各种扭曲的网格.数值结果表明,与九点格式中节点量简单加权的方法相比,基于网格边离散切向流的节点自适应加权九点格式的精度有明显改进,迭代求解次数减少,计算效率明显提高.     

FDTD结合DFT分析宽频高功率微波大气传播

联立麦克斯韦方程与电子流体方程,用时域有限差分法(FDTD)模拟高斯型和阻尼正弦型等宽频高功率微波(HPM)的大气传播.在每个时间网格上,根据窄带脉冲的电子速度,通过离散傅立叶变换(DFT)方法求解出宽频脉冲的等效电场,将等效电场和压强代入电离参数公式,使电离参数随空间网格不断更新,提高计算准确性.结果表明,宽频HPM脉冲幅值、脉宽以及海拔高度等参数对大气击穿有明显的影响;大气击穿导致尾蚀效应;随着传播距离的增加,宽频HPM脉冲的尾部衰减加剧,脉宽缩短,引起宽频脉冲的频谱出现展宽、分裂及中心频率移动等现象.     

用Sin-DVR方法求解在绝热表象下锥形交叉分子振动本征态

在波恩-奥本海默近似中,分子中原子核的运动通常采用绝热表象的基态势能面来描述,一般情况下这样是比较好的近似. 然而当势能面上存在锥形交叉时,即使体系的能量远远低于锥形交叉点,绝热基态势能面近似将不再有效. 锥形交叉的出现,使得绝热表象下描述核运动的哈密顿中出现了两个额外的附加项：对角波恩－奥本海默近似校正(DBOC)项和几何相位(GP)项. 尤其GP项,使得基态绝热势能面近似失效. 这两项在锥形交叉点处的数值是发散的,因此在绝热表象中来严格描述核运动,会使量子动力学的计算存在数值收敛的困难. 在量子分子动力学计算中,最常用的数值方法是分离变量表象方法(DVR). 本文通过在绝热表象和透热表象下求解涉及两个电子态且包含锥形交叉的二维的薛定谔方程来验证Sinc-DVR的数值收敛性. 计算结果显示,在绝热表象中采用通常格点密度分布的Sinc-DVR方法,即使在没有特别的处理DBOC和GP项时,也可以得到比较可靠的结果. 此时的数值不确定性并没有比引入任意的向量势来纠正GP效应的不确定性更差. 需要特别注意的是,纠正GP效应的任意向量势的精确形式,通常是不易得到其精确形式的.     

Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein–Gordon equation and numerical comparisons

We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of solutions to the discrete nonlinear Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein–Gordon equation.     

基于非结构变形网格的间断装配法原理

在激波捕捉法计算得到的流场基础上采用辨识算法得到初始间断位置, 从ALE方程出发, 考虑离散几何守恒律, 采用变形网格和网格重构技术解决计算过程中间断运动和变形, 新旧网格之间流场采用高精度信息传递方法保持时间精度, 建立了基于非结构动网格技术的间断装配方法.通过激波管问题的二维模拟, 模拟了初始间断分解为激波和接触间断激波遇到固壁反射后与接触间断相交的非定常流动过程, 对这种新方法的基本原理进行了介绍.      

离散小波变换耦合静电场理论的图像快速伪造检测算法

为了解决当前图像伪造检测算法主要是在图像空域中定位伪造区域,难以降低图像维数,使其复杂度大;且不能有效检测几何变换篡改形式的伪造区域,导致其鲁棒性不佳的不足,本文提出了离散小波变换耦合静电场理论的图像伪造检测算法。首先,引入离散小波变换,提取伪造图像的低频子带,降低图像空间;再基于静电场理论,将提取子带映射到虚拟电场中,提取鲁棒性较强的特征,利用Radix排序算法对特征完成重组,形成特征矩阵;最后,定义相同仿射变换,并用其处理排序矩阵,完成伪造区域检测。实验测试结果显示：与当前的移动复制伪造检测技术相比,本文算法具有更高的定位效率与检测精度;同时拥有较强的鲁棒性,有效抗击几何变换篡改。     

Discrete ordinates interpolation method incorporated into a flow and energy solver for solution of combined heat transfer problems

Combined conduction-radiation and natural convection-radiation in two-dimensional enclosures containing gray absorbing/emitting medium are numerically investigated. The discrete ordinates interpolation method (DOIM) is used to solve the radiative transfer equation (RTE). It is incorporated into a commercial software (FLUENT^®) by using user-defined function (UDF) to be used in a finite volume-based code for fluid flow computation. Two issues are critically examined: accuracy and versatility. Cases of combined conduction-radiation are considered first and the results are compared with other benchmark solutions to validate the accuracy. Additional problems are also tested to verify the capability of handling unstructured grid system and irregular geometry. Combined natural convection-radiation problem is then examined varying the optical thickness. The radiation effect is investigated through the profiles of velocity, temperature distributions and streamlines. The results are compared with discrete ordinates (DO) solutions, Rosseland solutions and P1 solutions which are offered by FLUENT^® package. The accuracy and other numerical characteristics of DOIM are scrutinized. The DOIM shows very successful results from the viewpoint of accuracy and grid compatibility. It is proved to be a reliable future numerical tool for combined heat transfer problems in engineering applications.     

在局域子空间中计算给定范围内的能量本征值

通过能量算符δ函数作用于完全随机格点波函数,构造了可用于直接计算给定范围[Emin,Emax]内能量本征值和本征函数的局域子空间.在非正交局域基下详细推导了交迭积分和哈密顿算符在分立位置表象中的表示,讨论了广义本征值问题的解法.以Morse势和Henon-Heiles势的多个能量范围为例检验了算法     

TDI线扫相机光学通道建模与仿真

卫星相机建模与仿真研究不论在民用还是军事领域都具有重要的理论研究和实际应用价值。根据TDI线扫相机的工作原理建立了一个TDI线扫相机光学通道的数学模型,该模型包括从景物到TDI CCD离散图像的几何投影关系和能量传递关系两部分,对于确定的成像系统,给定景物参数和光学系统参数,就可以确定对应图像传感器上的离散图像。为了验证模型,对一幅卫星图像进行了计算机仿真。建立的模型可以用来研究当成像条件改变时对图像的影响,进一步还可以用来发展虚拟卫星相机系统。     

On a discretization of asymptotic nets

We discretize some notions of the theory of asymptotic nets and of the theory of transformations of asymptotic nets. These are the Lelieuvre formulas, the Moutard equation, the Moutard transformation, the Weingarten congruences and the Jonas formulas. It allows us to extend the theory of reductions of the discrete version of the Darboux system, applied primarily to multidimensional quadrilateral lattices, on the theory of discrete asymptotic nets which in turn is helpful in a discretization of some classical differential nonlinear integrable systems of physical interest, e.g. the Ernst equation and the stationary modified Nizhnik–Veselov–Novikov system (in form which we call the Fubini–Ragazzi system).     

On the validity of the variational approximation in discrete nonlinear Schrödinger equations

The variational approximation is a well known tool to approximate localized states in nonlinear systems. In the context of a discrete nonlinear Schrödinger equation with a small coupling constant, we prove error estimates for the variational approximations of site-symmetric, bond-symmetric, and twisted discrete solitons. This is shown for various trial configurations, which become increasingly more accurate as more parameters are taken. It is also shown that the variational approximation yields the correct spectral stability result and controls the oscillatory dynamics of stable discrete solitons for long but finite time intervals.     

Optical orthogonal frequency division multiplexed transmission using all‐optical discrete Fourier transform

Orthogonal frequency division multiplexing (OFDM) can provide spectrally efficient communication channels because it can utilize carrier orthogonality and various impairment mitigation methods. An optical OFDM signal can be generated electronically to multiplex lower‐rate carriers. In recent advancements, OFDM signals are also shown to be generated and demultiplexed by all‐optical discrete Fourier transform (DFT), overcoming the speed limit of electronics for >Tbps capacity. High‐performance DFT devices, such as arrayed waveguide grating (AWG) or planar lightwave circuit (PLC), are critically required to obtain strong orthogonality for scalable all‐optical OFDM (AO‐OFDM) system implementations. Advanced techniques such as coherent modulation and detection with digital impairment mitigation are also important for long‐reach AO‐OFDM transmissions. More recently, optical superchannel schemes have been introduced utilizing coherent detection for multi‐Tbps AO‐OFDM transmissions. This paper reviews the device and system aspects for the AO‐OFDM technology, including a generalized theoretical model to provide an indepth understanding.     

离散余弦变换域抗二次打印-扫描鲁棒零水印算法

由于现有的抵抗打印-扫描攻击的鲁棒数字水印算法缺乏抵抗二次打印-扫描的能力.本文利用子块的离散余弦变换域直流系数与所有子块直流系数的均值之间的大小关系稳定性,提出一种抗二次打印-扫描鲁棒零水印算法.通过对图像进行分块离散余弦变换,计算所有子块直流系数的均值;通过比较各个子块的直流系数与所有子块直流系数的均值之间的大小关...     

Single-electron tunneling and Coulomb blockade in carbon-based quantum dots

Single-electron tunneling (SET) and Coulomb blockade (CB) phenomena have been widely observed in nanoscaled electronics and have received intense attention around the world. In the past few years, we have studied SET in carbon nanotube fragments and fullerenes by applying the so-called “Orthodox” theory [28]. As outlined in this review article, we investigated the single-electron charging and discharging process via current-voltage characteristics, gate effect, and electronic structure-related factors. Because the investigated geometric structures are three-dimensionally confined, resulting in a discrete spectrum of energy levels resembling the property of quantum dots, we evidenced the CB and Coulomb staircases in these structures. These nanostructures are sufficiently small that introducing even a single electron is sufficient to dramatically change the transport properties as a result of the charging energy associated with this extra electron. We found that the Coulomb staircases occur in the I–V characteristics only when the width of the left barrier junction is smaller than that of the right barrier junction. In this case, the transmission coefficient of the emitter junction is larger than that of the collector junction; also, occupied levels enter the bias window, thereby enhancing the tunneling extensively.