N维氢原子的另外四类升降算子

从N维氢原子的径向Schrodinger方程出发,完全用因式分解方法,直接导出N(d≥2)维氢原子的另外第一类、第二类升降算子,并用这两类算子构造出新的第三类、第四类升降算子.当d=3和d=2时,得到三维与二维氢原子的升降算子和文献[5,7]中相同.     

�Գ����Է���ȱ���շ�������ƽ����ŵвǿ

根据第二类气球模理论,在托卡马克中诸如不稳定漂移波类的环形局部模将在径向呈现源于环形性的对称性自发破缺。以流体离子温度梯度模模型方程为例,解出在准环坐标系中由对称性自发破缺产生的二维局部模本征模式。在略去边带效应后,它成为具有径向位移修正的平板模式。由位移修正离子温度梯度模式导出了种子平行雷诺胁强,而它在传统的(无位移修正的)平板模式下被证明为零。     

对称性自发破缺所诱发的种子平行雷诺胁强

根据第二类气球模理论,在托卡马克中诸如不稳定漂移波类的环形局部模将在径向呈现源于环形性的对称性自发破缺。以流体离子温度梯度模模型方程为例,解出在准环坐标系中由对称性自发破缺产生的二维局部模本征模式。在略去边带效应后,它成为具有径向位移修正的平板模式。由位移修正离子温度梯度模式导出了种子平行雷诺胁强,而它在传统的(无位移修正的)平板模式下被证明为零。     

橡胶气球非线性特性的理论与实验研究

根据橡胶气球的热力学性能及门尼模型理论,推导出橡胶气球膜在充气与放气两个过程中受到的附加压强与气球半径的关系,并以此推导出不同半径气球内部的压强,以及两个相互连通的气球体积变化与内部压强的关系,理论结果与实验相吻合.将橡胶气球模型应用于简易气垫船研究,建立了气垫船运动模型,并利用实验结果对理论模型进行了修正.     

“A=2托卡马克堆芯等离子体基本特性研究”2006年进展

主要涉及两方面的研究内容：第一是托卡马克等离子体的磁流体气球模稳定性研究；第二是HL-2A装置电子回旋加热有关的基础理论问题。包括三方面研究成果：（1）简要报道了关于负剪切区电阻气球模不稳定性及本征函数特性，给出了增长率与等离子体参数的定标关系；（2）利用Solov’ev位形中严格的气球模方程，讨论了应用广泛的s，α平衡模型的正确性；（3）计算分析了由弱磁场侧垂直入射的电子回旋波寻常模在HL-2A等离子体中的功率沉积剖面。     

晶体球中非相位匹配二次谐波产生及最佳聚焦条件

晶体球法是近年来在国际上发展起来的一种测量非线性系数的新方法。根据聚焦高斯光束二次谐波产生的孔径方程理论,分析了晶体球中的第Ⅰ类非相位匹配二次谐波产生过程,讨论了晶体球中第Ⅰ类非相位匹配二次谐波最佳聚焦参数的选择。报道了LiNbO3晶体球中皮秒激光脉冲抽运的相位匹配二次谐波实验。所得结果与理论预计相符。     

自我质疑机制下公共物品博弈模型的相变特性

公共物品博弈是研究群体相互作用的经典模型,广泛用于解释自私个体间合作的涌现和保持.本文从理论分析和蒙特卡罗模拟两个方面研究了二维正方格子上一个有偿惩罚机制下随自我质疑更新规则演化的公共物品博弈模型的相变特性.理论分析方面,将公共物品博弈模型转化为一个外场不为零的铁磁Ising模型.通过有效能量发现:不存在惩罚时,个体间的耦合强度为零,体系只有外场作用;存在惩罚时,个体间包含最近邻、次近邻和第三近邻相互作用且外场不为零.蒙特卡罗模拟方面,首先验证了理论分析的正确性,然后对公共物品博弈模型相关的一级相变和二级相变进行了有限尺度标度分析.研究发现:1)蒙特卡罗模拟所得结果与类Ising模型分析结果完全吻合;2)相比二维Ising模型,公共物品博弈的二级相变临界指数发生了变化;3)公共物品博弈的一级相变与二维Ising模型相同.     

临近空间高空气球光学散射特性研究EI北大核心CSCD

基于应用光学中基本辐射理论,研究了临近空间高空气球的光散射特性。利用计算几何学的坐标转换以及网格划分建模思想,对高空气球球面进行网格面元划分。根据高空气球等透明类物体几何结构和物体光学特性,推导出透明类物体双向散射分布函数（BSDF）镜反射/折射、近镜反射/折射、漫反射/折射、理想漫反射/折射相结合的计算模型,最终得出高空气球散射背景辐射在地面产生辐射亮度的计算模型。利用MODTRAN软件在3～5μm和8～14μm波段仿真计算临近空间高空气球的背景辐射亮度,在0.24～2.4μm波段仿真计算气球自身亮度。仿真结果表明：利用BSDF模型计算得到高空气球亮度为2.28×10^-3W/（cm^2·μm·sr）,计算结果误差为10.6%,精度相对双向反射分布函数（BRDF）模型提高2%。在分析高空气球等类透明体散射特性时,可参考此模型来进行计算。     

小车运动二次加速现象的探究

在以气球喷气推动小车运动的物理实验设计教学的过程中,小车出现二次加速现象.经过研究.找到了产生二次加速现象的原因,此外又提出了"用2个相同气球充气后使其大小不同,将其用吸管连通"的实验,其实验结果和理论分析相符.     

单向耦合下两个不同Lorenz系统的广义同步

对单向耦合下两个不同的Lorenz系统的广义同步进行了研究,利用辅助系统方法,基于稳定性理论和响应系统的有界性,得到了它们达到广义同步时的充分条件,并根据响应系统的修正系统具有零渐近稳定平衡点、非零渐近稳定平衡点和轨道渐近稳定周期解的情况,将广义同步分为第一类、第二类和第三类;利用Routh-Hurwitz定理,对修正系统平衡点的稳定性进行了分析,给出了单向耦合下两个不同Lorenz系统具有第一类、第二类广义同步的充分条件.数值仿真表明了该方法的有效性与可行性.     

�п���˶�ά�ֲ�ģ�ĵ�������������

The ballooning theory of the third kind is constructed in parallel to the ballooning theory of the first and the second kind by making use of the 2-D ballooning representation. Compared to the ballooning theory of the first kind, the restriction to applicability due to solvability condition is found greatly relaxed to wider parameter domain; and compared to the ballooning theory of the second kind, the solution with higher growth rate is obtained because the destabilization from “bad curvature” is well included within the framework of the theory, which in turn, makes the numerical results more comparable with those from initial value simulations. The fluid model equation for ion temperature gradient mode in toroidal coordinate is adopted to calculate growth rate and eigen frequency as well for selected profile parameters. The results are presented graphically, compared and discussed with the two previous ballooning theories; also discussed is the implication with regard to improved confinement in tokamaks.     

TOKAMAK BALLOONING MODE STUDIES-(I)

In this paper, the first part deals with the structure of the second stability regime of the ideal MHD ballooning modes in circular tokamaks. It is shown that in high-beta regime,the poloidal magnetic field destabilizes strongly the plasma and can eventually lead to the appearance of a new instability regime at modest beta-value for a flat q-profile. In the second part, th a various kinetic effects on ballooning modes or high-beta tokamaks are calculated. Results show that a new weak ballooning mode branch can exist in the second MHD stability regime in addition to the MHD-like strony ballooning mode branch in the first instability regime with its growth rate decreased by kinetic stabilizations.     

BECOOL: Ballooning eigensolver with COOL finite elements

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equation to a special block pentadiagonal matrix equation that is solved using an inverse vector iteration method. A benchmark test of BECOOL (Ballooning Eigensolver using COOL finite elements) with second order Legendre polynomials recovers precisely the eigenvalues computed by the VVBAL shooting code. Timing runs reveal the need to determine an optimal lower order case. Eigenvalue convergence runs show that cubic Legendre polynomials construct the optimal ballooning mode equation for intensive computations.     

Tokamak resistive magnetohydrodynamic ballooning instability in the negative shear regime

Improved confinement of tokamak plasma with central negative shear is checked against the resistive ballooning mode. In the negative shear regime, the plasma is always unstable for purely growing resistive ballooning mode. For a simplest tokamak equilibrium model, the s--α model, characteristics of this kind of instability are fully clarified by numerically solving the high n resistive magnetohydrodynamic ballooning eigen-equation. Dependences of the growth rate on the resistivity, the absolute shear value, the pressure gradient are scanned in detail. It is found that the growth rate is a monotonically increasing function of α while it is not sensitive to the changes of the shear s, the initial phase \ta₀ and the resistivity parameter \va_R.     

新经典MHD效应与内扭曲模本征方程

本文从一简化的新经典ＭＨＤ方程组出发，利用气球模表示及多尺度近似等方法，在ｑ＝１磁面附近的过渡层内导出了包含新经典ＭＨＤ效应的内扭曲模本征方程。与从前相关工作的比较表明，新经典ＭＨＤ效应对通常采用的磁流体或电阻磁流体内扭曲模本征方程，均产生十分重要的修正。     

Filamentary plasma eruptions: Results using the non‐linear ballooning model

This paper provides an overview of recent results on two distinct studies exploiting the non‐linear model for ideal ballooning modes with potential applications to edge‐localized modes (ELMs). The non‐linear model for tokamak geometries was developed by Wilson and Cowley in 2004 and consists of two differential equations that characterize the temporal and spatial evolution of the plasma displacement. The variation of the radial displacement along the magnetic field line is described by the first equation, which is identical to the linear ballooning equation. The second differential equation is a two‐dimensional non‐linear ballooning‐like equation, which is often second order in time but can involve a fractional time derivative depending on the geometry. In the first study, the interaction of multiple filamentary eruptions is addressed in a magnetized plasma in a slab geometry. Equally sized filaments evolve independently in both the linear and non‐linear regimes. However, if filaments are initiated with slightly different heights from the reference flux surface, they interact with each other in the non‐linear regime: lower filaments are slowed down and are eventually completely suppressed, while the higher filaments grow faster because of the non‐linear interaction. In the second study, this model of non‐linear ballooning modes is examined quantitatively against experimental observations of ELMs in Mega Amp Spherical Tokamak (MAST) geometries. The results suggest that experimentally relevant results can only be obtained using modified equilibria.     

Second-order Green's function theory of a Heisenberg paramagnet

The Heisenberg paramagnet in one, two, and three dimensions is analyzed by a second-order Green's function theory similar to that used by Knapp and ter Haar. This theory, which incorporates the exact values for the zero, first, and second moments of the relaxation function as boundary conditions, yields results satisfying the rotational symmetry of the paramagnetic region as well as the principle of detailed balance. We find that our predictions for equal time properties in the classical limit are identical with the RPA Green's function theory of Liu as well as the spherical model results of Lax. The quantum limit is analyzed, and our predictions for the 1/T series coefficients for both internal energy and susceptibility are compared with exact results.Supported by National Science Foundation.