基于伴随方程法的材料热传导系数反演方法

建立利用材料内部温度场的测量结果反演材料热传导系数随时间和空间位置变化函数的伴随方程法,参考迭代正则化的思想在优化过程中给目标函数设置停止准则.对典型算例计算表明,方法在测量噪声较小情况下能得出较为合理的反演结果.但在有测量噪声的情况下,反演结果与真值在边界x=0和L处存在着一定偏差.当测量噪声较大时,反演结果与真值的偏差较为明显,且初值选取会对反演结果有相当大的影响.     

解FOKKER-PLANCK-LANDAU方程的谱方法

利用谱方法和FFT技术对等离子体中带电粒子输运Fokker-Planck-Landau方程进行数值求解,研究空间均匀条件下粒子相空间分布函数随时间的演化.数值计算表明,所用计算格式能够很好地满足粒子数、动量和能量守恒要求,FFT技术的采用也使得运算工作量大为降低.     

A New Numerical Method for Asymmetrical Abel Inversion

A new asymmetrical Abel inversion is presented for application in asymmetrical data which is obtained from plasma diagnostics (for instance, interferometry or spectroscopy) on the toroidal plasma system, and in which asymmetry exists normal to the direction of observation. In this new numerical method a weight function, which was obtained by separating the integrated quantity into odd and even parts, was used for determination of the asymmetrical local value. To demonstrate the usefulness of this new method, we set up a hypothetical data set, which resulted in a valid local value.     

A Regularization Homotopy Strategy for the Constrained Parameter Inversion of Partial Differential Equations

The main difficulty posed by the parameter inversion of partial differential equations lies in the presence of numerous local minima in the cost function. Inversion fails to converge to the global minimum point unless the initial estimate is close to the exact solution. Constraints can improve the convergence of the method, but ordinary iterative methods will still become trapped in local minima if the initial guess is far away from the exact solution. In order to overcome this drawback fully, this paper designs a homotopy strategy that makes natural use of constraints. Furthermore, due to the ill-posedness of inverse problem, the standard Tikhonov regularization is incorporated. The efficiency of the method is illustrated by solving the coefficient inversion of the saturation equation in the two-phase porous media.     

A Framework for Non-Equilibrium Statistical Ensemble Theory

Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the Gibbsian theory to
non-equilibrium phenomena domain, however the status of the theory of non-equilibrium phenomena can not be said as firm as well established as the
Gibbsian ensemble theory. In this work, we present a framework for the non-equilibrium statistical ensemble formalism based on a subdynamic kinetic
equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.     

三分量磁场延拓的递推算法

提出一种三分量磁场延拓的递推算法,主要目的是解决三分量磁场的向下延拓问题.应用微分学基本原理,将具有相同水平坐标,不同垂向坐标的点上的三分量磁场,通过磁场的垂向偏导数的积分联系起来.根据磁场向量散度和旋度的性质,将磁场的垂向偏导数与水平方向的偏导数联系起来.这样,在已知一个平面上的磁场时,可以通过递推的办法逐层求取该平面以下任意平面上的三分量磁场.应用实例证明方法的快速性和准确性.     

Exact Stationary Solution of Fokker-Planck Equation and Generalized Potential for Non-Equilibrium Systems Without Detailed Balance

An exact analogy is approached between systems in thermal equilibrium and those far from equilibrium which can be the cases without detailed balance. The analogy is based on the requirement that a given drift in the Fokker-Planck equation can be decomposed into two parts, one of which is divergence-free and the other can be derived from a potential which is invariant along the direction of the first part. If the conditions are fulfilled the Fokker-Planck equation changes in to a standard Poisson equation. The relations of this requirement to other conditions are diecussed. As a concrete example, the stationary Fokker-Planck equation for optical bistability is solved by using"this method.     

A New Improvement Method of Abel Inversion

A new improvement method of Abel inversion is presented for application in asymmetrical measured value that is obtained from plasma diagnostics on the toroidal plasma system. The local value is symmetry up and town circle section, and asymmetry from left to right. This new method is aimed at general measuring configuration, and need not assume integration chords to be parallel (for instance, pinhole configurations). The local value in the boundary of toroidal plasma is obtained by other methods. In the center part, the asymmetrical local value is expanded to Fourier-Bessel series, and Fourier terms include the information of asymmetry. The coefficients of the expansions are determined using least-square-fitting method. We finally obtain the distribution of the local value by using the synthesis of the value in the boundary and the value in center part.     

A New Method for Asymmetrical Abel Inversion Using Fourier-Bessel Expansions

A new asymmetrical Abel inversion is presented for application in asymmetrical data which is obtained from plasma diagnostics on the toroidal plasma system. Asymmetry in the system exists in the direction along chord distribution. This new method is aimed at general measuring configuration, and need not assume integration chords to be parallel (for instance, pinhole configurations). In this new method, the asymmetrical local value is expanded to Fourier-Bessel series, and Fourier terms include the information of asymmetry, The coefficients of the expansions are determined using least-square-fitting method.     

Bethe-Salpeter Equation with Self-Energy Graphs I-Generalized Fredholm Theory,Parameter Imbedding Method

In this paper the classical Fredholm theory is generalized. The conceptions of the generalized fredholm denominator (GFD) and generalized Fredholm numerator (GFN) are defined. A set of parameter imbedding equations for GFD and GFN is deduced. In this way, the eigenvalue problem of the BS equation in ladder approximation with self-energy graphs, and the eigenvalue problem of nonlinear parameter integral equation, are carried over into an initial-value problem of a set of ordinary differential equations.     

Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation

It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also decays exponentially at a later time. In particular, a strong solution of the Cauchy problem with compact initial profile can not be compactly supported at any later time unless it is the zero solution.     

Hartmann－Shack传感器结构参量的自基准标定

提出一种标定Hartmann Shack波前传感器结构参量的新方法,通过基于Zernike多项式的模式复原算法推导出公式,结合实验手段获得相应数据,处理后得到微透镜阵列到CCD之间的距离.该方法有效改善了以微透镜焦距代替实际参量计算斜率引入较大误差的状况,在降低传感器装配准确度要求的同时,提高了Hartmann Shack波前传感器的探测准确度.经实验验证该方法在一般实验条件下即可获得满意效果.     

求解对流扩散方程的紧致修正方法

提出了求解对流扩散方程的紧致修正方法,该方法是在低阶离散格式的源项中,引入紧致修正项,从而构造高阶紧致修正格式,并进行求解.采用紧致修正方法对典型的对流扩散方程进行计算.结果表明,紧致修正方法虽然与二阶经典差分方法建立在相同的结点数上,但紧致修正方法的精度与紧致方法的精度相同,均具有四阶精度.所以紧致修正方法可以在少网...     

A Collocation Method for Solving Fractional Riccati Differential Equation

In this article, we have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation. The fractional derivatives are described in the Caputo sense. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, the systems of nonlinear algebraic equation are derived. We further solve the system of nonlinear algebraic equation using Maple 13 and thus obtain the coefficients of the generalized Taylor expansion. Illustrative examples are presented to demonstrate the effectiveness of the proposed method.     

阿贝尔逆变换数据处理算法在电弧诊断中的应用

提出了一种由等离子体辐射投影值重建发射系数的阿贝尔逆变换数据处理算法。采用计算简单、变换精度高的Bockasten插值方法实现阿贝尔逆变换积分方程的离散化。在阿贝尔逆变换前,运用傅里叶变换频域低通滤波去除实验数据中的噪声,通过多项式插值弥补数据采样率过低、提高空间分辨力,并对投影数据进行对称化处理以消除数据偏离对称对结果的影响。运用此算法对实验数据进行处理,得到电流200 A、弧长5 mm电弧温度在阴极下方0.5 mm处最高,超过22000 K,与文献中结果一致。该算法能够有效地克服噪声对变换结果的影响,运算速度快、计算精度高、稳定性好,处理大量数据时具有明显的优势。     

基于多算法优化SVM的粗糙面参数反演

支持向量机（SVM）是粗糙面参数反演中常用的一种反演算法,SVM反演中的惩罚参数C和核函数参数G对反演结果精度的影响较大,若参数取值不当,会使模型产生"过学习"或者"欠学习"的现象,从而降低预测精度.给出几种SVM参数C和参数G的优化算法,如K折交叉验证（K-CV）、遗传算法（GA）和粒子群算法（PSO）,并在此基础上提出一种基于K-CV和GA改进的PSO算法（GA-CV-PSO）.利用矩量法（MoM）获得的粗糙面后向散射系数构造训练集和测试集,通过不同参数反演的仿真结果对比不同优化算法的反演精度和计算时间,表明GA-CV-PSO算法克服了单一优化算法的缺陷,具有更精确的反演精度和更强的泛化能力.     

爆炸过程相关参量的计算机图像测量方法

提出了一种基于计算机图像学的爆炸速度和爆炸作用时间的图像测量方法.分析了爆炸速度测量图像和爆炸作用时间测量图像的特点,用计算机自动从爆炸图像中提取出特征点,并自动完成爆炸时间、爆炸速度的测量、计算.实验结果表明,该方法可以准确地实现自动判读测量.     

Multi-Symplectic Method for the Zakharov-Kuznetsov Equation

A new scheme for the Zakharov-Kuznetsov (ZK) equation with the accuracy order of $\mathcal{O}(∆t^2+∆x+∆y^2)$ is proposed. The multi-symplectic conservation property of the new scheme is proved. The backward error analysis of the new multi-symplectic scheme is also implemented. The solitary wave evolution behaviors of the Zakharov-Kunetsov equation are investigated by the new multi-symplectic scheme. The accuracy of the scheme is analyzed.