改进的单次散射相函数解析表达式

单次散射相函数对电磁辐射传输模拟过程的准确性和计算效率有重要的影响.基于电磁散射与辐射传输中的基本理论,对单次散射相函数的解析表达式进行了研究,提出了一种新的单次散射相函数解析表达式.比较了单个粒子的Henyey-Greenstein相函数、Henyey-Greenstein*相函数与新的相函数随角度的分布,发现新的散射相函数提高了后向散射峰值,可以更合理地描述单个粒子的散射特性.按三种气溶胶粒子谱分布模式计算了Henyey-Greenstein*相函数和新的相函数对应的数值结果,并与多分散系Mie散射相函数进行对比,发现新的相函数提高了与多分散系Mie散射相函数的符合程度.研究表明,对于大角度(大于90°)后向散射,新的相函数与Mie散射相函数均方根差较小的占73.3%,高于Henyey-Greenstein*相函数的26.7%,证明了新的相函数可以显著提高后向散射峰值.新的相函数对准确模拟辐射传输过程具有重要意义.     

A new procedure for obtaining the Voigt function dependent upon the complex error function

This work proposes a new method for obtaining the differential equation of the Voigt function and, from this equation, expressing the Voigt function as dependent upon the complex error function. In addition, the integral expression of the successive derivatives of the Voigt function is given, and from this a method is generalized which permits the representation, also, of other functions depending on the complex error function. This enables us to simplify other functions which are the convolution of a Gaussian function with rational polynomial functions. Moreover, the relationship between the Lorentzian (w_L), Gaussian (w_G) and Voigt (w_V) widths at half maximum for the function is given, which is of great interest in diverse branches of physics, such as plasma spectroscopy, astrophysics, nuclear magnetic resonance, etc.     

A Kind of Atomic Coherent State as a Two-Mode Squeezed State

We find that a kind of atomic coherent state, formed as exp[ ξJ＋-ξJ-]｜00〉,when the SU（2） generators J± are taken as Fan＇s form J＋=（1/2）（α1-α2）（α1-α2）,J-=（1/2）（α1＋α2）（α1＋α2）,and J0=（1/2）（α1α2-α1α2）,is simultaneously a two-mode squeezed state. We analyse this squeezed state＇s physical properites, such as the cross- correlation function, the Wigner function, and its marginal distribution as well as the Husimi function.     

Multistability of impact, utility and threshold concepts of binary choice models

The decision making problem in the context of binary choice is considered by means of impact function, utility function and threshold model approaches. The properties of generalized impact function and utility function are examined; it is shown that these two approaches are equivalent. Their relation to the threshold model is studied and the correspondence between respective cumulative distribution functions is displayed. The stationary state corresponding to the thermodynamic equilibrium is determined within mean field approximation. Multistability of the stationary state is expressed in terms of the distribution function of the random variable of impact/utility function. The correspondence with statistical physics predictions for Ising model is discussed: logistic distribution leads to the mean-field result, i.e. Curie-Weiss approximation. Variations of the distribution functions and/or other model parameters, of social character, self-support, nonlinearity of social interactions, etc., would break the direct correspondence to statistical physics of Ising model, leading in particular cases to richer structure of the multistability.     

量子相空间分布函数与压缩相干态表示间的变换关系

基于Husimi算符具有压缩相干态投影子形式, 首先介绍了一个新的量子算符表示, 即压缩相干态表示.当高斯展宽参数κ = 1时, 该函数约化为通常的P函数. 作为例子, 研究了热态的压缩相干态表示, 通过图示说明了压缩相干态表示与P函数的区别. 为更好地在量子光学问题中使用该表示, 我们揭示了压缩相干态表示与Wigner函数、Q函数以及Husimi函数间的积分变换关系.     

Many-body work distributions

The work distribution function for a non-relativistic, non-interacting quantum many-body system interacting with classical external sources is investigated. Exact expressions for the characteristic function corresponding to the work distribution function is obtained for arbitrary switching function and coupling functions. The many-body frequencies are assumed to be generally time-dependent in order to take into account the possibility of moving the boundaries of the system in a predefined process linking the characteristic function to the fluctuation-induced energies in confined geometries. Some limiting cases are considered and discussed.     

Modified scaling function projective synchronization of chaotic systems

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.     

非连续的线性耦合方法实现超混沌系统的同步

基于李亚普诺夫稳定性理论, 严格证明了一类超混沌系统在间歇线性单向耦合下可以实现完全同步. 线性控制器通过一个开关函数来调节来实现‘停’和‘控’. 第一类开关函数由一个等幅度矩形波来控制, 控制器的打开和关闭选取不同的间隔周期(T_a, T_b); 第二类开关函数由一个等幅度方波来控制, 方波间隔周期记为T₀; 首先通过构造指数类型的李亚普诺夫论证了两类开关函数调制下两个超混沌 系统在单向线性耦合下实现同步的可行性问题. 为了定量分析控制效果, 定义了一定周期内控制器的平均能耗. 在数值计算中, 对第一类矩形波函数情形则计算了二参数空间(T_a, T_b)下响应系统的最大李亚普诺夫指数分布, 同步区域/非同步区域分布, 控制器平均能耗分布, 确认在恰当的间隔周期(T_a, T_b)和耦合强度下,两个超混沌系统可以达到完全同步. 对第二类方波函数情形则计算了耦合强度和方波间隔周期T₀而参 数区域内响应系统最大条件李亚普诺夫指数分布, 给定耦合强度下选择不同间隔周期下误差函数演化和平均能耗, 研究结果表明: 在恰当的耦合强度和间隔周期T₀下两个超混沌系统可以达到完全同步. 同时发现, 在恰当的耦合强度下控制器的平均能耗最小, 数值计算结果验证了理论分析的可靠性. 关键词： 超混沌 脉冲函数 指数型李函数 线性耦合     

Function projective synchronization in partially linear drive-response chaotic systems

This paper gives the definition of function projective synchronization with less conservative demand for a scaling function,and investigates the function projective synchronization in partially linear drive-response chaotic systems.Based on the Lyapunov stability theory,it has been shown that the function projective synchronization with desired scaling function can be realized by simple control law.Moreover it does not need scaling function to be differentiable,bounded and non-vanished.The numerical simulations are provided to verify the theoretical result.     

A Kind of Atomic Coherent State as a Two-Mode Squeezed State

We find that a kind of atomic coherent state, formed as exp [ξ J₊- ξ^*J_-] |00>, when the SU(2) generators J_± are taken as Fan's form, J₊=(1/2)(a₁-a₂†)(a₁†-a₂), J_=(1/2) (a₁†+a₂)(a₁+a₂†), and J₀=(1/2) (a₁†a₂†-a₁a₂), is simultaneously a two-mode squeezed state. We analyse this squeezed state's physical properites, such as the cross-correlation function, the Wigner function, and its marginal distribution as well as the Husimi function.     

Research for Signal Power Spectrum Distribution in Laser Doppler Rotational Speed Measurement

ＲｅｓｅａｒｃｈｆｏｒＳｉｇｎａｌＰｏｗｅｒＳｐｅｃｔｒｕｍＤｉｓｔｒｉｂｕｔｉｏｎｉｎＬａｓｅｒＤｏｐｐｌｅｒＲｏｔａｔｉｏｎａｌＳｐｅｄＭｅａｓｕｒｅｍｅｎｔＬＵＯＤｅｙｕａｎＺＨＯＵＪｉａｎＴＡＮＹｕｓｈａｎ（ＬａｓｅｒａｎｄＩｎｆｒａｒｅｄＩ...     

Lyapunov function as potential function： A dynamical equivalence

For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization: a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.     

基于描述函数方法的神经群自激振荡特性分析

在无外界刺激时神经群表现为节律性自激振荡,自激振荡是非线性系统特有的一种运动形式.在非线性描述函数法理论框架下,对神经群模型自激振荡特性进行分析,并揭示其产生机理.神经群模型的sigmoid非线性函数(简称为S函数)是其自激振荡的根源.首先,求解S函数的描述函数;然后,基于S函数的描述函数得到神经群模型正反馈回路S函数和负反馈回路S函数的等效增益,在此基础上将神经群模型转化为可用描述函数法分析的典型结构形式;最后,应用描述函数法理论对神经群模型自激振荡特性进行理论分析,得到自激振荡特性的定量描述,并通过仿真分析对理论分析结果进行了验证.理论分析及仿真分析结果表明基于描述函数方法的神经群自激振荡特性分析方法是正确有效的.S函数是神经系统的典型非线性环节,S函数的处理方法及神经群自激振荡特性分析方法对于其他神经模型的自激振荡特性分析具有参考价值.     

半无界空间上函数的傅里叶-贝塞尔积分展开

柱坐标系中,本征函数族贝塞尔函数构成完备正交系,因此可作为广义傅里叶级数展开的基.本文从定义在有限区间[0,ρ0]上函数的广义傅里叶级数展开出发,利用贝塞尔函数的渐近展开公式以及贝塞尔函数零点的近似公式,讨论了半无界空间上函数的傅里叶-贝塞尔积分展开问题,得到了本征函数模方的近似表达式.当ρ0趋于无穷时,不连续参量变成连续参量,得到了函数的傅里叶-贝塞尔积分及其展开系数公式.     

光衍射数值模拟中不同抽样方法的适用性分析

基于标量衍射理论和快速傅里叶变换,分析了光衍射的数值模拟时可以采用的不同抽样方法及其适用性。理论分析表明,按照抽样对象的不同,存在三种适用范围不同的算法:传递函数抽样法、点扩展函数抽样法和加权函数抽样法。其适用范围分别为衍射距离小于、大于和等于特征距离的情况。在Matlab软件环境下给出了三种算法的模拟计算实例,并与相应的实验结果进行了比较,证明了理论分析的正确性。最后还给出了一种无需改变抽样点数和抽样间隔就可计算任意距离衍射过程的自适应抽样算法及其在数字全息再现中的应用实例。     

扩大景深的波前编码成像系统特性分析

从空域和频域两个方面利用新的数学工具对扩大景深的波前编码成像系统的一些重要特性进行了阐释和分析。空域中,主要利用维格纳分布函数的正则投影来分析系统的点扩展函数对离焦像差的变化不敏感特性;频域中,则利用考纽螺线的图解方法来分析系统的光学传递函数对离焦像差的变化不敏感特性。简单讨论了波前编码成像技术所涉及的数字图像处理方法,并且用数值仿真实验验证了波前编码成像系统的这些优越特性。     

Superstatistics of Modified Rosen-Morse Potential with Dirac Delta and Uniform Distributions

We discuss the thermodynamic properties of a modified Rosen-Morse potential using the $q$-deformed superstatistics approaches. We obtain the partition function with the help of the generalized Boltzmann factor from the modified Dirac delta distribution and uniform distribution. Other thermodynamic function is obtained for the superstatistics of the two distributions considered. We also discuss our results graphically and obtain the ordinary statistical quantities when the deformation parameter tends to zero.     

Rapid and accurate calculation of the Voigt function

Two general techniques significantly improve both the accuracy and speed of spectral line shapes that use only the complex Voigt function. Such line shape functions include the Voigt line profile, which is closely related to the real part of this function. The first technique is a new algorithm, which trades a small amount of RAM (at most 1.49 megabytes) for a considerable gain in speed and accuracy. The accuracy is one part in 10⁶ of the function itself. In addition, the derivatives of the function with respect to x and y are returned with an accuracy of 0.5%. The algorithm is up to nine times faster than the Drayson or Humlí?ek algorithms and about two orders of magnitude more accurate. A second independent improvement is a set of simple criteria to decide when an evaluation is required and when a value of zero can be assumed. This section alone can reduce the computation time by three orders of magnitude or more and it can be applied to algorithms using any Voigt approximation.     

光学综合孔径成像技术实验研究

根据光学综合孔径成像系统的成像质量与点扩散函数和光学传递函数的关系,以G o lay-3阵列结构为例,从空间域和频率域对光学综合孔径成像技术进行理论仿真和实验研究。在空间域从理论上分析光学综合孔径成像系统的点扩散函数,对复杂目标的成像通过目标函数与点扩散函数的卷积求得,点扩散函数决定了成像质量。通过数值仿真和模拟实验取得了点扩散函数强度分布图,两者分布规律一致证明理论分析正确。在频率域研究光学综合孔径调制传递函数,理论仿真和实验取得的调制传递函数表明,空间域和频率域内光学综合孔径成像技术的理论分析与实验结果具有较好的一致性。