HIRFL-CSRm纵向随机冷却-槽形滤波冷却模拟研究

　通过Fokker Planck方程,对拟在HIRFL CSRm上建造的纵向槽形滤波器(notchfilter)的冷却机理进行了研究,得出了冷却原理及冷却时间的表达式,并对影响冷却时间和冷却效果的因素进行了模拟和讨论,模拟结果表明,噪信比越小,冷却时间越短,冷却效果越好;带宽越宽冷却越快。该研究为具体纵向冷却系统的设计和优化提供了依据。

CSR随机冷却研究

随机冷却是用一个宽带反馈系统对束流进行衰减，位于束流上游的探测器探测到与粒子偏差成正比的电子学信号，这一输出信号经过放大滤波系统后被加到下游的冲击器上，粒子在冲击器上得到正比于偏差的校正，从而达到冷却的目的。随机冷却可以用于粒子储存环任意能区的冷却，尤其是对大动量分散的次级束、高能束、稀有粒子束有其独特的作用，并与电子冷却互补。本论文首先对随机冷却的发展历史及贡献作了叙述，并对国外研究现状以及随机冷却同其它冷却的不同作了描述，继而提出了在HIRFL-CSR上建立随机冷却的重要性、必要性以及条件的成熟性。接着本论文对Schottky噪声信号理论、随机冷却理论（分别在时域和频域下）作了详细的推导和描述，并对-Schoftky噪声诊断和用于随机冷却系统测量和束流稳定性分析的束流传输函数作了一定的分析和讨论。由于探测器和冲击器在随机冷却中起着核心作用，因此也对探测器和冲击器作了一定的研究。最后，也是本论文的核心部分，根据CSR的实际情况，如环的Lattice参数，环上元件布置，现有Sdhottky诊断装置以及资金等，对CSR随机冷却做了初步的设计和优化，用冷却方程和Fokker-Planck方程对CSR随机冷却做了详细的数值模拟计算，得到了最佳带宽、冷却时间、频谱上束流谱密度分布函数随时间的变化，以及在冷却过程中的束流分布变化等值，并且对功率限定情况作了讨论研究表明随机冷却对CSR束流冷却速度很快，冷却效果很好。并对电子冷却和随机冷却做了比较，提出对CSR束流冷却用电子冷却和随机冷却相结合的办法，先用随机冷却粗冷，再用电子冷却精细冷却，这样可以得到更高流强更好品质的束流。本文对具体冷却系统的设计补优代；健滇码运行有重要意义为CSR随机冷却系统的建造做了充分的准备，也为实验数据的分析提供了理论依据。

Complex potentials and singular integral equation for curve crack problem in antiplane elasticity

Four types of the fundamental complex potential in antiplane elasticity are introduced: (a) a point dislocation, (b) a concentrated force, (c) a dislocation doublet and (d) a concentrated force doublet. It is proven that if the axis of the concentrated force doublet is perpendicular to the direction of the dislocation doublet, the relevant complex potentials are equivalent. Using the obtained complex potentials, a singular integral equation for the curve crack problem is introduced. Some particular features of the obtained singular integral equation are discussed, and numerical solutions and examples are given.

Direct numerical test of the B-G-K model equation by the DSMC method

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

A lattice Boltzmann method for KDV equation

We prepose a 5-bit lattice Boltzmann model for KdV equation. Using Chapman-Enskog expansion and multiscale technique, we obtained high order moments of equilibrium distribution function, and the 3rd dispersion coefficient and 4th order viscosity. The parameters of this scheme can be determined by analysing the energy dissipation.

Modified Simplified Rate Equation Model of Flowing Chemical Oxygen-Iodine Laser and its Application

A modified simplified rate equation (RE) model of flowing chemical oxygen-iodine laser (COIL), which is adapted to both the condition of homogeneous broadening and inhomogeneous broadening being of importance and the condition of inhomogeneous broadening being predominant, is presented for performance analyses of a COIL. By using the Voigt profile function and the gain-equal-loss approximation, a gain expression has been deduced from the rate equations of upper and lower level laser species. This gain expression is adapted to the conditions of very low gas pressure up to quite high pressure and can deal with the condition of lasing frequency being not equal to the central one of spectral profile. The expressions of output power and extraction efficiency in a flowing COIL can be obtained by solving the coupling equations of the deduced gain expression and the energy equation which expresses the complete transformation of the energy stored in singlet delta state oxygen into laser energy. By using these expressions, the RotoCOIL experiment is simulated, and obtained results agree well with experiment data. Effects of various adjustable parameters on the performances of COIL are also presented.

A Continuation Method of Parameter Inversion for Non-Equilibrium Convection-Dispersion Equation

Based on the homotopy mapping, a globally convergent method of parameter inversion for non-equilibrium convection-dispersion equations (CDEs) is developed. Moreover, in order to further improve the computational efficiency of the algorithm, a properly smooth function, which is derived from the sigmoid function, is employed to update the homotopy parameter during iteration. Numerical results show the feature of global convergence and high performance of this method. In addition, even the measurement quantities are heavily contaminated by noises, and a good solution can be found.

A lattice Boltzmann equation for waves

We propose a lattice Boltzmann model for the wave equation. Using a lattice Boltzmann equation and the Chapman-Enskog expansion, we get 1D and 2D wave equations with truncation error of order two. The numerical tests show the method can be used to simulate the wave motions.

Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

A Variational Approach to the Burridge-Knopoff Equation

A variational principle is obtained for the Burridge-Knopoff model for earthquake faults, and this paper considers an analytic approach that does not require linearization or perturbation.

Variational Approach to the Thomas-Fermi Equation

By the semi-inverse method, a variational principle is obtained for the Thomas-Fermi equation, then the Ritz method is applied to solve an analytical solution, which is a much simpler and more efficient method.

A family of interesting exact solutions of the sine-Gordon equation

By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.

Dynamic constitutive equation of GFRP obtained by Lagrange experiment

The note presents a method of constructing dynamic constitutive equations of material by means of Lagrange experiment and analysis. Tests were carried out by a light gas gun and the stress history profiles were recorded on multiple Lagrange positions. The dynamic constitutive equations were deduced from the regression of a series of data which was obtained by Lagrange analysis based upon recorded multiple stress histories. Here constitutive equations of glass fibre reinforced phenolic resin composite(GFRP) in uniaxil strain state under dynamic loading are given. The proposed equations of the material agree well with experimental results.