Fokker—Planck方程在快波加热中的应用

快波加热算法，一般都是假定托卡马克中粒子为麦克斯韦分布．其实由于准线性扩散效应，共振粒子的平行温度与垂直温度不相等，这样必然产生一定的计算误差．针对这种情况，本文引入ＦｏｋｋｅｒＰｌａｎｃｋ方程，采用叠代算法较好地解决了这一问题     

电子束能量沉积的相对论Fokker-Planck方程的计算方法

针对相对论电子束在高密度等离子体中的能量沉积过程,建立三维动量空间中快电子能量沉积的相对论Fokker-Planck方程的可计算物理模型,构造数值算法并研制数值模拟程序.通过与解析模型和蒙特卡罗模拟相比较,验证数值方法和程序的可靠性.在二维动量空间的模拟基础上,通过计算能量区间为0.5 MeV~3.5 MeV的快电子在背景密度为300 g·cm^-3的氘氚等离子体中的能量沉积过程,发现由于碰撞效应使平均散射角趋近平衡,三维动量空间计算快电子连续射程和穿透深度与二维结果基本一致.     

毛细作用的变分法理论

以圆柱形毛细管内壁、毛细管内的液体和气体为研究对象.设毛细管液体的表面为旋转面,写出了系统的自由能(表面能及重力势能)的泛函.使自由能泛函取极值的欧拉方程就是关于附加压强的拉普拉斯公式.泛函取极值时在可动边界(毛细管内壁)上的边界条件就可导出关于接触角的杨氏方程.此二方程是自由能取极值的密不可分的两个必要条件.     

用量子力学方法计算H+H2碰撞的反应几率

利用量子力学耦合通道扭曲波近似法(CCDWA)和三种势能面计算了H+H2碰撞的反应几率,结果发现在相同的势能面下利用CCDWA方法计算的反应几率和公认较好的计算结果符合很好,不同势能面共线势垒高度的差别将引起反应几率的不同.     

从流体、电场到几率波、连续性方程的对比

 量子力学是反映微观粒子运动规律的理论,它的诞生是对经典物理的突破。正因如此,建立在统计和测不准关系上的量子力学概念和原理具有很高的抽象性,对于习惯于经典理论的初学者,理解和接受这些概念和原理有相当的困难。如果我们能在经典理论中找到量子力学中对应的概念和原理,将二者进行比较,实现认识上的由实到虚,无疑将大大降低对其理解的难度。作为一个实例,本文简略地对比了从流体、电场到几率波的连续性方程,以显示这种对比法在帮助理解量子力学的概念和原理中所起的作用。     

重离子裂变反应中的能级密厦参数和裂变几率

本工作从Ｎｉｌｓｓｏｎ单粒子能级入手,计算了形变核１８６Ｏｓ、１８７Ｉｒ、１８９Ｏｓ和１９３Ａｕ作为激发函数的固有能级密度参数ａｉｎｔ和有效能级密度参数（包括核集体运动效应）ａｅｆｆ．由这样能量相关的能级密度参数计算的裂变几率Ｐｆ（Ｕ）与本工作的裂变几率符合很好． Based on the single-particle levels given by Nilsson,the intrinsic and effective(with collective effects)level density parameters as a function of theexcitation energy for the 186Os, 187Ir, 189Os and 193Au deformation nuclei have been calculatedin the range of the excitation energy up to 150MeV. The calculated fission probabilities Pf(U) are consistent satisfactorily with the experimental data when a nonadiabtic estimation ofthe collective effects was used to calculate the nuclear level density parameters.     

裂变过程的动力学和统计自洽描述及不同方法之间的分析与比较

简要介绍了裂变过程动力学和统计自洽描述的研究概况、意义及应用前景.重点描述了考虑扩散动力学过程的裂变道理论以及P.Frobrich等人依据Strutinsky方法给出的Kramers-modified Bohr-Wheeler公式,并以n+²³⁸U,激发能至80MeV为例对上述两种模型进行了较详细的分析与比较.     

用松弛法解薛定谔方程

求解定态薛定谔方程常常会涉及到常微分方程的本征值问题.目前解常微分方程本征值用的比较多的方法是以龙格-库塔方法为基础的打靶方法.打靶方法常用,但是计算时间长.当边界条件比较复杂或比较敏感的时候,用松弛法会有更好的效果.本文用松弛法解薛定谔方程,并和理论解进行比较.发现松弛法得到的数值解和理论解符合度很高,而且使用松弛法...     

Numerical Method for the Time Fractional Fokker-Planck Equation

In this paper, a new numerical algorithm for solving the time fractional Fokker-Planck equation is proposed. The analysis of local truncation error and the stability of this method are investigated. Theoretical analysis and numerical experiments show that the proposed method has higher order of accuracy for solving the time fractional Fokker-Planck equation.     

等离子体中Fokker-Planck方程的有限元模拟

利用有限元方法设计了一套相对简单明了的求解Fokker-Planck方程的方案.这个方案不必严格限制计算格点的步长和时间步长,就可以确保分布函数的非负性和粒子数的守恒.通过一维程序模拟,进一步证实了这个方案的可靠性.对于多维问题的分析和一维问题完全一样,所以非常容易将其推广到多维问题.     

Fokker-Planck Equation of a Stochastic System Driven by Spatially-Related Noises

In this paper we study a general stochastic system driven by the spatially-related Gaussian white noises. The corresponding Fokker-Planck equation is calculated; and some typical cases are analyzed. Finally, by the Fokker-Planck equation derived in the paper we study a single bistable kinetic process with spatially-related noise. The results obtained in the paper provide a correct foundation for the.treatment of the stochastic systems driven by spatially-related noises.     

耗散子运动方程与福克-普朗克量子主方程

发展非线性耦合环境下精确、非微扰的量子耗散方法仍然是一个巨大的挑战.本文针对线性和二次耦合热浴模型,介绍了两种刻画系统与环境耦合动力学的有效方法.一个是耗散子运动方程（DEOM）理论,最近已被扩展到处理非线性耦合环境.另一个是推广的福克-普朗克量子主方程（FP-QME）方法,将在这项工作中基于DEOM推导给出.本文对这两种方法进行了详细的比较,并重点介绍了所涉及的准粒子图像、物理含义以及实现方案.     

裂变扩散方程的协变性

研究了描述原子核裂变过程的Langevin方程和Fokker-Planck方程的协变性,给出了动力学参数的坐标交换规律.     

Quasiclassical Describing of the Bloch Oscillation in a Superlattice by Fokker-Planck Equation

A theoretical study of Bloch electron transport in a superlattice miniband driven by an electric field parallel to the growth axis is carried out, by Fokker-Planck equation (FPE) in momentum space with the averaged momentum relaxation time (γ) approximation. Steadystate drift-velocity/field characteristics exhibit the expected maximum followed by negative differential conductivity (NDC), and then followed by drift-velocity oscillation when γ or electric field is large. The oscillation frequency is an increasing function of γ, and when γ → ∞, the limit of the oscillation frequency is the Bloch frequency as expected.     

Variation of Parameters Method for Solving System of Nonlinear Volterra Integro-Differential Equation

It is well known that nonlinear integro-differential equations play vital role in modeling of many physical processes, such as nano-hydrodynamics, drop wise condensation, oceanography, earthquake and wind ripple in desert. Inspired and motivated by these facts, we use the variation of parameters method for solving system of nonlinear Volterra integro-differential equations. The proposed technique is applied without any discretization, perturbation, transformation, restrictive assumptions and is free from Adomian's polynomials. Several examples are given to verify the reliability and efficiency of the proposed technique.     

On New Invariant Solutions of Generalized Fokker-Planck Equation

The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported.     

Potential Symmetries and Associated Conservation Laws to Fokker-Planck and Burgers Equation

Kara and Mahomed have derived an identity, which does not rely on use of a Lagrangian as needed to obtain conservation laws by Noethers theorem. By using the identity and symbolic computation, conservation laws arising from nonlocal symmetries are obtained for Fokker-Planck equation and burgers equation.