Formal iteration scheme for scalar fields in some spherically symmetric spaces

The characteristic initial-value problem for the scalar wave equation in some spherically symmetrical geometries, including Reissner-Nordström exterior geometry, is considered. A modified Picard iteration making explicit use of the (known) static solutions yields a formula for the fields. The formulas extend in to the outer horizon, and from them are obtained useful expressions for the reflection and transmission amplitudes in terms of the static solutions.     

Solving the 3D MHD equilibrium equations in toroidal geometry by Newton’s method

We describe a novel form of Newton’s method for computing 3D MHD equilibria. The method has been implemented as an extension to the hybrid spectral/finite-difference Princeton Iterative Equilibrium Solver (PIES) which normally uses Picard iteration on the full nonlinear MHD equilibrium equations. Computing the Newton functional derivative numerically is not feasible in a code of this type but we are able to do the calculation analytically in magnetic coordinates by considering the response of the plasma’s Pfirsch–Schlüter currents to small changes in the magnetic field. Results demonstrate a significant advantage over Picard iteration in many cases, including simple finite-β stellarator equilibria. The method shows promise in cases that are difficult for Picard iteration, although it is sensitive to resolution and imperfections in the magnetic coordinates, and further work is required to adapt it to the presence of magnetic islands and stochastic regions.     

间断有限元方法求解一维非平衡辐射扩散方程

研究一维非平衡辐射扩散方程的数值方法.通过求解间断系数热传导方程的广义黎曼问题,得到一种带加权数值流量,基于该数值流量构造了一类新型的间断有限元方法.在时间离散上采用向后Euler方法,形成的非线性方程组采用Picard迭代求解.数值试验表明该方法具有捕捉大梯度的能力,而且能适应扩散系数间断的情形.     

Global Existence and Decay Rates of the Solutions Near Maxwellian for Non-linear Fokker–Planck Equations

In this paper, we study the global existence and decay rates of the solutions near Maxwellian for non-linear Fokker–Planck equations in the whole space. The global existence is proved by combining uniform-in-time energy estimates with local solution constructed by Picard type iteration sequence. The decay rates of the nonlinear model is obtained by using the precise spectral analysis of the linearized Fokker–Planck operator as well as the energy method. The nonlinearity in the model brings new difficulty to the energy estimates, which is resolved by additional tailored weighted-in-v energy estimates suitable for Fokker–Planck operators.     

Implementation of the Jacobian-free Newton–Krylov method for solving the first-order ice sheet momentum balance

We have implemented the Jacobian-free Newton–Krylov (JFNK) method for solving the first-order ice sheet momentum equation in order to improve the numerical performance of the Glimmer-Community Ice Sheet Model (Glimmer-CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on significant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in Glimmer-CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.8–3.6 times more efficient than the standard Picard solver in Glimmer-CISM. Importantly, this computational gain of JFNK over the Picard solver increases when refining the grid. Global convergence of the JFNK solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.     

JMCT与子通道程序耦合方法研究及验证

蒙特卡罗与热工水力的耦合计算是目前反应堆数值模拟的重要研究方向,在蒙特卡罗方法连续能量点截面的基础上结合热工程序的温度反馈,反应堆中子计算的准确性得到大幅提高。为了提高计算精度,堆芯模型分辨率也需进一步提高,相比于组件均匀化模型,pin-by-pin的建模方式能够获得更好的结果。利用蒙特卡罗程序JMCT与子通道程序COBRA-EN实现了蒙特卡罗-热工的内耦合,内耦合方式通过内存进行数据传递,其计算效率及安全性均优于外耦合方法。随后利用NURISP项目迷你堆的pin-by-pin模型对耦合程序进行验证。计算结果与同类耦合程序相似,验证了程序的准确性。同时,对耦合过程的收敛性问题进行了初步分析。     

Super elliptic curves

A detailed study is made of super elliptic curves, namely super Riemann surfaces of genus one considered as algebraic varieties, particularly their relation with their Picard groups. This is the simplest setting in which to study the geometric consequences of the fact that certain cohomology groups of super Riemann surfaces with odd spin structure are not freely generated modules. The divisor theory of Rosly, Schwarz, and Voronov gives a map from a supertorus to its Picard group Pic, but this map is a projection, not an isomorphism as it is for ordinaty tori. The geometric realization of the addition law on Pic via intersections of the supertorus with superlines in projective space is described. The isomorphisms of Pic with the Jacobian and the divisor class group are verified. All possible isogenies, or surjective holomorphic maps between supertori, are determined and shown to induce homomorphisms of the Picard groups. Finally, the solutions to the new super Kadomtsev-Petviashvili hierarchy of Mulase-Rabin which arise from super elliptic curves via the Krichever construction are exhibited.     

红外光谱辐射计探测器高阶非线性响应校正方法

针对傅里叶变换红外光谱辐射计辐射定标需要黑体辐射面充满仪器视场的技术特点,分析了由于入射光子流较高导致红外探测器产生非线性响应误差的机理.通过仿真包含非线性误差的黑体辐射数据,研究了非线性误差对光谱产生的影响,并根据卷积和交叉迭代两种校正方法,提出了适合校正高阶非线性响应误差的迭代方法—梯度下降法.利用傅里叶变换红外光谱辐射计进行辐射定标实验,对比卷积、交叉迭代和梯度下降法三种校正方法的效果,结果显示三种校正方法均可有效减小非线性误差,分别使拟合优度提高了0.15%,0.29%和0.39%,梯度下降法校正后的光谱数据更为准确.     

Phase iteration and spacing iteration algorithms for speckle fringe pattern processing

Speckle fringe pattern is characterized by speckle noise because the speckle is the information carrier. Phase iteration and Spacing iteration are algorithms that are able to extract the information as well as suppress noise. Phase iteration is a loop of smoothing, phase calculation, and pattern reconstruction. Spacing Iteration is a repetition of correlation, phase calculation, and least-squares fit. The two algorithms are reviewed and compared in this paper. The modern computer provides the capability to explore all sorts of convergent methods by simply ‘do it again’. Phase iteration and Spacing iteration are two of the convergent methods in processing optical metrology fringe pattern.     

ADS瞬态分析中的概率论-确定论耦合方法

针对加速器驱动次临界系统(ADS)瞬态问题,采用预估校正改进准静态方法(PCQS)处理时空中子动力学方程中的时间自变量,采用蒙特卡罗方法处理相应的空间-角度-能量自变量,重点解决了低次临界度下模拟计算不稳定的问题,验证了TWGIL-Seed-Blanket动力学基准问题和小型模拟ADS问题,得到瞬态过程的功率变化结果,与基于其他方法的程序比较,经初步验证取得了较好结果,证明了该耦合方法可行。     

X光图像中缺陷的自动提取方法研究

针对炭素制品X光图像的特点,对其缺陷的提取技术进行了研究,提出了基于迭代的阈值构造方法和基于数学形态学的边缘提取算法。为快速准确地提取缺陷,设计了目标边界提取算法和基于小波变换的图像增强算法,实现了原始图像中目标区域的增强及其背景的去除。在此基础上,为排除噪声干扰的影响,采用数学形态学和迭代阈值分割相结合的方法从目标区域中提取出缺陷区域,并在迭代阈值分割的基础上,利用基于数学形态学的边缘提取算法提取了缺陷的边缘。实验结果表明,该法很好地实现了缺陷区域及其边缘的自动提取,且受噪声影响很小,为进一步的缺陷特征参量的提取与选择奠定了良好的基础。     

Classification of Invariant Star Products up to Equivariant Morita Equivalence on Symplectic Manifolds

In this paper we investigate equivariant Morita theory for algebras with momentum maps and compute the equivariant Picard groupoid in terms of the Picard groupoid explicitly. We consider three types of Morita theory: ring-theoretic equivalence, *-equivalence, and strong equivalence. Then we apply these general considerations to star product algebras over symplectic manifolds with a Lie algebra symmetry. We obtain the full classification up to equivariant Morita equivalence.     

Iterative solutions of the Lotka-Volterra equations

Summary Lotka-Volterra equations for two-species predator-prey system are solved by an iteration method. The first iteration step reproduces elliptical trajectories known from the linearization treatment. The second iteration step leads to analytical expressions describing large-amplitude motions and lying beyong the elliptical approximation. The range of validity of the method is discussed. It is shown that deviations from the exact trajectories increase if the initial state is far from the centre of motion. For illustration some trajectories are calculated showing a good agreement with trajectories obtained by numerical methods.     

求解流动和传热问题的一种新的全隐算法-CLEAR(下)

本文上篇阐述了CLEAR算法的推导过程和计算步骤,本文下篇通过五个二维不可压缩流动和传热的算例,对CLEAR算法和SIMPLER算法进行了比较,比较的内容为,在相同的收敛条件下, CLEAR算法和SIMPLER算法收敛所需的迭代次数的比值和对应的CPU时间的比值,以及这两个比值和时步倍率的关系,从而进一步研究了CLEAR算法的健壮性。计算结果表明,CLEAR算法可以在很大程度上加速迭代收敛,就所比较的算例而言,其可以节省迭代次数31％-85％,节省CPU时间17％-78％,而且该算法的健壮性可以通过引入第二松弛因子而得以提高。     

解粒子输运问题的半随机模拟数值方法

分析了解粒子输运问题的随机模拟方法和确定性方法的优缺点,提出了零方差迭代格式和半随机模拟方法——把MC方法和确定性方法有机结合起来,达到扬长避短的目的。扼要地介绍了近年来在这方面的工作。     

He's variational iteration method applied to the solution of the prey and predator problem with variable coefficients

In this Letter, a mathematical model of the problem of prey and predator is presented and He's variational iteration method is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The results are compared with the results obtained by Adomian decomposition method and homotopy perturbation method. Comparison of the methods show that He's variational iteration method is a powerful method for obtaining approximate solutions to nonlinear equations and their systems.     

Pair approximation for polarization interaction and adiabatic nuclear and electronic sampling method for fluids with dipole polarizability

The adiabatic nuclear and electronic sampling method (ANES), originally formulated as an efficient Monte Carlo algorithm for systems with fluctuating charges, is applied to the simulation of a polarizable water model with induced dipole moments. Structural, thermodynamic and dipolar properties obtained by ANES and a newer algorithm, the pair approximation for polarization interaction (PAPI), are compared with full iteration. With the best parameters, the inaccuracy of both approximate methods was found to be comparable with the uncertainty of the full iteration. The PAPI method with iteration radius equal to the second minimum of the oxygen—oxygen correlation function is, depending on the convergence tolerance, 10–15 times faster than the full iteration for 256 molecules, and yields very accurate structure and thermodynamics with deviation about 0.3%. When the iteration radius is increased to the cutoff distance, exact results are recovered at the cost of decreased efficiency. The ANES method with small nuclear displacements proved to inefficiently sample the configurational space. Simulations at low electronic temperatures with large nuclear displacements are inaccurate for up to 100 electronic moves, and increasing this number would make the simulations as slow as the full iteration. The most accurate and efficient adiabatic ANES simulations are those with infinite electronic temperature, large nuclear displacements and 1–10 electronic moves. The extra freedom of induced dipoles in the ANES method at high electronic temperatures modifies the observed dipolar properties; however, the question of whether the dielectric constant is also modified needs further consideration.     

分数量子Hall体系的电荷分布

对1/3 Landau填充因子的二维电子气体系,用迭代自洽的计算方法得到了局域电中性背景下的电荷密度分布。我们发现电荷密度分布与基态能量的尖角有密切的联系。 关键词：     

The use of iteration factors in the solution of the NLTE line transfer problem—II. Multilevel atom

The iteration factors method (IFM) developed in Paper I [1] (Atanackovi?-Vukmanovi? and Simonneau, 1994) to solve the NLTE line transfer problem for a two-level atom model, is extended here to deal with a multilevel atom case. At the beginning of each iteration step, for each line transition, angle and frequency averaged depth-dependent iteration factors are computed from the formal solution of radiative transfer (RT) equation and used to close the system of the RT equation moments, non-linearly coupled with the statistical equilibrium (SE) equations. Non-linear coupling of the atomic level populations and the corresponding line radiation field intensities is tackled in two ways. One is based on the linearization of the equations with respect to the relevant variables, and the other on the use of the old (known from the previous iteration) level populations in the line-opacity-like terms of the SE equations. In both cases the use of quasi-invariant iteration factors provided very fast and accurate solution. The properties of the proposed procedures are investigated in detail by applying them to the solution of the prototype multilevel RT problem of Avrett and Loeser [2], and compared with the properties of some other methods.