共查询到20条相似文献,搜索用时 15 毫秒
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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. 相似文献
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A New Numerical Method for Asymmetrical Abel Inversion 总被引:1,自引:0,他引:1
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. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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Ruan Huailin Wan Baonian Wu Zhenwei Hu Liqun Luo Jingqing 《International Journal of Infrared and Millimeter Waves》2004,25(3):489-501
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. 相似文献
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Huailin Ruan Baonian Wan 《International Journal of Infrared and Millimeter Waves》2000,21(12):1973-1987
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. 相似文献
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CHENG Geng 《理论物理通讯》1991,15(2):219-228
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. 相似文献
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A. Alexandrou Himonas Gerard Misiołek Gustavo Ponce Yong Zhou 《Communications in Mathematical Physics》2007,271(2):511-522
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. 相似文献
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Mustafa Gü lsu Yalç ın Ö ztü rk & Ayşe Anapali 《advances in applied mathematics and mechanics.》2013,5(6):872-884
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. 相似文献
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求解对流扩散方程的紧致修正方法 总被引:1,自引:0,他引:1
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... 相似文献
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阿贝尔逆变换数据处理算法在电弧诊断中的应用 总被引:1,自引:0,他引:1
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。 相似文献
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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. 相似文献
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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. 相似文献
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The initial value problem for an integrable system, such as the Nonlinear Schrödinger equation, is solved by subjecting the linear eigenvalue problem arising from its Lax pair to inverse scattering, and, thus, transforming it to a matrix Riemann-Hilbert problem (RHP) in the spectral variable. In the semiclassical limit, the method of nonlinear steepest descent ([4,5]), supplemented by the g-function mechanism ([3]), is applied to this RHP to produce explicit asymptotic solution formulae for the integrable system. These formule are based on a hyperelliptic Riemann surface ${\mathcal {R} = \mathcal {R}(x,t)}The initial value problem for an integrable system, such as the Nonlinear Schr?dinger equation, is solved by subjecting the
linear eigenvalue problem arising from its Lax pair to inverse scattering, and, thus, transforming it to a matrix Riemann-Hilbert
problem (RHP) in the spectral variable. In the semiclassical limit, the method of nonlinear steepest descent ([4,5]), supplemented
by the g-function mechanism ([3]), is applied to this RHP to produce explicit asymptotic solution formulae for the integrable system.
These formule are based on a hyperelliptic Riemann surface R = R(x,t){\mathcal {R} = \mathcal {R}(x,t)} in the spectral variable, where the space-time variables (x, t) play the role of external parameters. The curves in the x, t plane, separating regions of different genuses of R(x,t){\mathcal {R}(x,t)}, are called breaking curves or nonlinear caustics. The genus of R(x,t){\mathcal {R}(x,t)} is related to the number of oscillatory phases in the asymptotic solution of the integrable system at the point x, t. The evolution theorem ([10]) guarantees continuous evolution of the asymptotic solution in the space-time away from the
breaking curves.
In the case of the analytic scattering data f(z; x, t) (in the NLS case, f is a normalized logarithm of the reflection coefficient with time evolution included), the primary role in the breaking mechanism
is played by a phase function á h(z;x,t){{\Im\,h(z;x,t)}}, which is closely related to the g function. Namely, a break can be caused ([10]) either through the change of topology of zero level curves of á h(z;x,t){\Im\,h(z;x,t)} (regular break), or through the interaction of zero level curves of á h(z;x,t){{\Im\,h(z;x,t)}} with singularities of f (singular break). Every time a breaking curve in the x, t plane is reached, one has to prove the validity of the nonlinear steepest descent asymptotics in the region across the curve. 相似文献