LS解法和Fisher方程行波系统的定性分析

提出了求解非线性发展方程的新方法——LS解法.LS解法是基于(G’/G)展开法和扩展的双曲正切函数展开法.并引入了Poincar定性理论的思想,然后以Fisher方程为例进行了试验.通过定性分析首先获得了Fisher方程行波系统积分曲线的性质,然后解得了Fisher方程作为耗散系统时单调减少的波前解和作为扩张系统时单调递增的波前解.一些试验结果与Ablowitz所得结果一致.也得到了Fisher方程作为扩张系统时的新结果.LS解法是在定性理论指导下,在已获知解曲线性质的情况下进行精确求解的,求解目标明确.LS解法揭示了线性系统也可以用作辅助方程来求解非线性系统.     

针孔单光子发射计算机断层成像的空间分辨率研究

针孔单光子发射计算机断层(SPECT)成像的空间分辨率通常是根据Anger经验公式来进行估算,与实际测量存在较大偏差.本文通过对针孔成像的物理过程进行分析,提出了一个近似度更高的计算公式.利用精确的蒙特卡罗方法模拟针孔SPECT成像,采用OSEM(ordered subsets expectation maximization)算法对投影数据进行图像重建,并与模具实验进行比较,验证了理论公式的适用性.同时还讨论了体素尺寸、几何映射获取投影矩阵以及探测器尺寸与成像物体尺寸比值对断层图像空间分辨率的影响.实验结果显示,该理论公式所估算的空间分辨率比实验值平均偏小约10%,而Anger经验公式所估算的空间分辨率比实验值平均偏大约60%.因此,该理论公式能更好地估算针孔SPECT成像的空间分辨率,可为针孔SPECT系统的设计和使用提供有价值的参考.     

Monte Carlo方法模拟光在生物组织中传播的新进展

Monte Carlo方法已被广泛用于模拟复杂的随机介质如生物组织中光的辐射传输.在生物光子应用中,早期的Monte Carlo模拟模型忽略了光在组织中传输的波动性,而用中性粒子光子包来模拟其传播过程.然而,许多光学诊断技术是基于光在组织中的偏振效应和多重散射的相干性来揭示组织的生理和病理信息,这就要涉及光辐射的波动性.本文阐述了用Monte Carlo方法模拟光在生物组织中传播的最新进展.     

高离化态类氖离子的电子碰撞激发特性研究

利用基于多组态Dirac-Fock(MCDF)理论方法的原子结构和性质计算程序GRASP92和全相对论扭曲波电子碰撞激发计算程序REIE06,系统计算了类氖离子(Z=50—57)激发组态2s22p53l和2s2p63l(l=s,p,d)的能级结构和碰撞激发截面,总结了碰撞激发截面随入射电子能量的变化规律,讨论了实验中感兴趣的(2p1/23d3/2)1→2s22p61S0(标记为3C线)与(2p3/23d5/2)1→2s22p61S0(标记为3D线)跃迁线强度比值的沿等电子系列特性和强组态相互作用对高离化态类氖离子截面的影响.     

双零色散光子晶体光纤结构参数的变化对其性能的影响

应用多极法,研究了正六边形结构光子晶体光纤的结构参数改变时,波长范围在0.8—1.8μm之间的双零色散光子晶体光纤的色散特性和非线系数随波长的变化规律.对具有相同结构参数的正六边形结构和正八边形结构进行比较,得到正六边形结构的双零色散光子晶体光纤的色散更加平坦,非线性系数有明显增大的结果.因此,正六边形结构更容易获得色散平坦的高非线性双零色散光子晶体光纤.最终设计了在800nm附近具有平坦色散和高非线性的正六边形双零色散光子晶体光纤.     

深海内波非线性薛定谔方程的研究

考虑以跃层为界的两层分层流体,在弱非线性条件下,从分层流体的动力学基本方程组出发,应用多重尺度方法推导出描述深海内波的非线性薛定谔方程,分析方程中频散和非线性系数,求出非线性薛定谔方程的孤子解,并通过数值实验验证了理论的正确性.     

Friction phenomena in a two-dimensional Frenkel-Kontorova model

By using the molecular dynamic simulation method with a fourth-order Runge--Kutta algorithm, a two-dimensional dc- and ac-driven Frenkel--Kontorova (FK) model with a square symmetry substrate potential for a square lattice layer has been investigated in this paper. For this system, the effects of many different parameters on the average velocity and the static friction force have been studied. It is found that not only the amplitude and frequency of ac-driven force, but also the direction of the external driving force and the misfit angle between two layers have some strong influences on the static friction force. It can be concluded that the superlubricity phenomenon appears easily with a larger ac amplitude and lower ac frequency for some special direction of the external force and misfit angle.     

Dispersion characteristics of two-dimensional unmagnetized dielectric plasma photonic crystal

This paper studies dispersion characteristics of the transverse magnetic (TM) mode for two-dimensional unmagnetized dielectric plasma photonic crystal by a modified plane wave method. First, the cutoff behaviour is made clear by using the Maxwell--Garnett effective medium theory, and the influences of dielectric filling factor and dielectric constant on effective plasma frequency are analysed. Moreover, the occurence of large gaps in dielectric plasma photonic crystal is demonstrated by comparing the skin depth with the lattice constant, and the influence of plasma frequency on the first three gaps is also studied. Finally, by using the particle-in-cell simulation method, a transmission curve in the \Gamma -X direction is obtained in dielectric plasma photonic crystal, which is in accordance with the dispersion curves calculated by the modified plane wave method, and the large gap between the transmission points of 27~GHz and 47~GHz is explained by comparing the electric field patterns in particle-in-cell simulation.     

Ti(SO_4)_2水解-水热法制备锐钛型纳米TiO_2及其光催化性能

以Ti(SO4)2水溶液为原料,在水热条件下直接水解合成了锐钛型纳米TiO2颗粒。利用透射电镜(TEM)、X射线衍射(XRD)、BET低温吸附和紫外-可见光谱(UV-Vis)等方法对产物进行了表征,并研究了样品光催化降解甲基橙(MO)的性能。结果表明所制得纳米TiO2颗粒为锐钛矿型,晶型良好,平均粒径为24 nm,BET比表面积约为56.20 m2.g-1。光催化活性与商品纳米TiO2(P25)相近,具有良好的工业应用前景。     

Variational iteration method for solving compressible Euler equations

This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics.This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional.Using this method,a rapid convergent sequence is produced which converges to the exact solutions of the problem.Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient.