双声道波导中低频环境噪声分布特性

针对北极冰下双声道波导的噪声分布特性研究,采用垂直阵对双声道波导内的噪声场进行了观测,北极冰下噪声物理模型使用混合加性噪声模型描述,统计分布模型使用α稳定分布描述.并将噪声划分为3个频段,按噪声来源分为背景噪声、冲击噪声以及航船噪声3种场景,分析其统计特性,给出了直方图统计、核函数估计与正态分布的比较结果,α稳定分布参数估计结果,峰度与偏度的计算结果以及累积分布函数检验结果。经分析讨论,给出结论:双声道波导中的噪声统计分布可用α稳定分布来描述,但上下表面声道的分布参数具有明显差别,上表面波导背景噪声明显偏离高斯分布而下表面声道的背景噪声接近于高斯分布;上下表面声道中不同频带的噪声分布差异也很明显,其中2~30 Hz差异性最大,30~100 Hz差异性较大,而100~500 Hz差异性相对较小,并且可以认为是对称α稳定分布.此外,上下表面声道中不同频带噪声α稳定特征参数变化也存在差异,上表面波导受冲击噪声影响α值变大,拖尾变薄;而下表面波导受冲击噪声影响α值则会变小,拖尾变重。      

The distribution of first-passage times and durations in FOREX and future markets

Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag-Leffler survival function and the Weibull distribution. For the Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter t_max, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag-Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag-Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull law for short times and do not have too heavy a tail.     

Statistical Analysis of Pellet Size Variation in Commercial Catalysts

The size of commercial catalyst pellets is distributed over a range of values. The suitability of the normal, lognormal and Weibull distributions to model pellet size variation was judged by three quality‐of‐fit criteria: the coefficient of determination, Akaike information criterion and Kolmogorov‐Smirnov test, respectively. It is concluded that the normal distribution is most appropriate to represent the diameter distribution of the spherical pellets, though the lognormal distribution also gives a satisfactory fit. The Weibull distribution is the best one to represent the length distribution of the catalyst tablets. It is elucidated that a downward tail of the tablet length distribution results from the fluctuating characteristics of feeding for the individual tablets. It is also pointed out that pellet size distributed in a narrow window is beneficial to the industrial application of solid catalysts.     

Prediction of energy consumption and risk of excess demand in a distribution system

An empirical model for prediction of energy consumption in a distribution system is described. The model resembles a normalized radial basis function neural network whose neurons contain prototype joint data about the consumption process and the environment. A set of prototype patterns of consumption and environmental variables is formed from a record of a multi-component time series by a self-organized process. Prediction of energy consumption is performed by a conditional average estimator based upon known prototype patterns and given future values of environmental variables. Importance of these variables for the prediction is determined by a genetic algorithm. Prediction performance of the model is tested on a one-year-long consumption record of a gas distribution system. Prediction error is determined by the difference between predicted and actually observed consumption. Its value depends on time and amounts to a few percent of the actual consumption. The probability distribution of prediction error is estimated from a properly selected time interval of prediction. This distribution can be used to estimate the risk of energy demand beyond some prescribed value. For an optimization of the distribution process, a cost function that includes operation and control costs of a distribution system as well as penalties related to excess energy demand is proposed. Its minimum corresponds to an economically optimal energy distribution.     

光纤耦合LD输出光场特性研究

根据光纤传输的模式理论,分析了单芯光纤输出端面的光场分布.利用单模光纤测量了纤端光场的强度分布,拟合了光纤输出端面光强分布的近似表达式.根据此数值计算和实验测量了多芯光纤输出端面的强度分布,结果基本吻合.表明光纤出射端面的光强分布应是介于高斯分布和几何分布之间的一种准高斯分布.     

Field inside a random distribution of parallel dipoles

We determine the probability distribution for the field inside a random distribution of electric or magnetic dipoles. Although the average contribution from any spherical shell around the probe position vanishes, at the center of a spherical distribution of parallel dipoles, the Levy stable distribution of the field is symmetric around a nonvanishing field amplitude. Omission of contributions from a small volume around the probe leads to a field distribution with a vanishing mean, which, in the limit of vanishing excluded volume, converges to the shifted distribution.     

二次电子分布函数对绝缘壁面稳态鞘层特性的影响

由于缺乏详细的理论计算和实验结果,在研究绝缘壁面稳态流体鞘层特性时,通常假设壁面出射的总二次电子服从单能分布(0)、半Maxwellian分布等.在单能电子轰击壁面的详细二次电子发射模型基础上,采用Monte Carlo方法统计发现:当入射电子服从Maxwellian分布时,绝缘壁面发射的总二次电子服从三温Maxwellian分布.进而,采用一维稳态流体鞘层模型进行对比研究,结果表明:二次电子分布函数对鞘边离子能量、壁面电势、电势及电子/离子密度分布等均具有明显影响;总二次电子服从三温Maxwellian分布时,临界空间电荷饱和鞘层无解,表明随着壁面总二次电子发射系数的增加,鞘层直接从经典鞘层结构过渡到反鞘层结构.     

Depth of origin of sputtered atoms

Estimates are given for the distribution of the depth of origin of sputtered atoms in the low-fluence limit, as well as the corresponding distribution of atoms sputtered into a given energy interval. The former distribution is well described by an exponential profile, with the characteristic depth being consistent with previous results. The latter distribution is characterized by an energy-dependent depth scale and a shape that varies from exponential at low sputtered-atom energies to inverse-power form at higher energies.     

Statistical dynamics of early river networks

Based on local erosion rule and fluctuations in rainfall, geology and parameters of a river channel, a generalized Langevin equation is proposed to describe the random prolongation of a river channel. This equation is transformed into the Fokker–Plank equation to follow the early evolution of a river network and the variation of probability distribution of channel lengths. The general solution of the equation is in the product form of two terms. One term is in power form and the other is in exponent form. This distribution shows a complete history of a river network evolving from its infancy to “adulthood”). The infancy is characterized by the Gaussian distribution of the channel lengths, while the adulthood is marked by a power law distribution of the channel lengths. The variation of the distribution from the Gaussian to the power law displays a gradual developing progress of the river network. The distribution of basin areas is obtained by means of Hack’s law. These provide us with new understandings towards river networks.     

基于广义极值的混沌电场峰值分布研究

通过分析峰值分布及广义极值分布理论关于混沌电场峰值分布的特点,获得一种混沌电场峰值分布的计算方法,结合Bootstrap重采样技术,提出了混沌电场峰值分布参数估计方法,该方法吸取了重采样技术估计的优点,对分布参数置信区间的估计更为准确、实用。以蒙特卡罗仿真和某机械搅拌混响室内电场数据为实例,结果表明,与传统的正态近似法、百分位法、BC-t等方法相比,其计算结果与实际结果更为吻合,证明了该方法具有更高的准确度。     

Determination of the refractive index profile of polymer optical fiber preform by the transverse ray tracing method

In graded-index polymer optical fiber (GI-POF), the refractive index profile is an important parameter in defining its bandwidth. However, direct determination of the refractive index profile of GI-POF is difficult due to its extreme thinness. In this study, the refractive index distribution of the GI-POF is indirectly determined by measuring the refractive index distribution of the GI-POF perform by applying the transverse ray tracing method to a simplified measurement system that we developed.In this system, a parallel tabular ray is irradiated transversely to a GI-POF preform. The transverse ray from the preform is then projected on a screen, and its digital image is processed to calculate the refractive index distribution. The calculation is based on a transverse ray simulation, a computer program that we developed in which the refractive index distribution of the preform is determined by comparing the displacement of the transverse ray projected on the screen with the actual measurement.The accuracy of this new measurement method is validated by comparing the refractive index distribution of a GI-POF preform with the refractive index distribution measured by the conventional method using an interferometer. We find that the refractive index distribution measured by this novel method agrees well with that measured by the conventional method.     

同轴放电环形增益区谐振腔镜面的场分布

 对几类环形增益区谐振腔进行了比较，得出利用谐振腔两镜之一的全工作面输出的新型环形增益区谐振腔是适合的谐振腔。提出了一种计算全工作面输出的同轴放电环形增益区谐振腔镜面场分布的方法，利用几何方法对腔镜镜面进行划分,得出了基于菲涅尔-基尔霍夫衍射积分定理的积分区域，并对该区域进行了有限元划分，应用计算机编程计算出了同轴放电环形增益区谐振腔镜面处的光场分布和相位分布。近场分布在环形区中央部分近似地呈高斯分布，且沿径向出现高阶模场分布特点，沿角向无差别。     

Development of a Three-parameter Volume-based Spray Drop Size Distribution through the Application of the Maximum Entropy Formalism

This work is an extension of a previous investigation on the determination of mathematical volume-spray drop size distributions by the application of the maximum entropy formalism. A two-parameter drop size distribution was derived and was found to give reasonable fits with experimental distributions obtained under different experimental conditions. However, as it is discussed, this two-parameter distribution shows critical limitations and cannot be applied in any situations of interest as far as drop size distributions in liquid sprays are concerned. To overcome this problem, a third parameter, equivalent to a drop diameter, is introduced into the procedure. This correction leads to a three-parameter drop size distribution with independent mean, width and symmetry. This function is a generalized gamma distribution and it can cover more practical situations than the previous two-parameter distribution. Furthermore, it is found that, contrary to the two-parameter distribution, the new volume-based drop size distribution shows a corresponding number-based drop size distribution with a physical behavior as the drop diameter decreases. This last result shows the importance of using three parameters to describe spray drop size distributions and that one of these parameters must represent the population of small drops.     

Single source emission of proton projectile fragments in nucleus-emulsion interactions

The projected angular distribution and transverse momentum distribution of proton projectile fragments produced in 3.7A GeV 16O,500A MeV 56Fe,and 1.7A GeV 84Kr induced by different kinds of emulsion target(H,CNO,and AgBr) interactions are investigated.It is found that the projected angular distribution and transverse momentum distribution can be well represented by a single Gaussian distribution.Comparison of transverse momentum distribution with the Maxwell-Boltzmann distribution reveals that proton projectile fragments are emitted from a single-temperature emission source.The temperature is different for different colliding systems,and linearly depends on the target size.     

数值模拟抽运分布对端泵激光器晶体热透镜球差的影响

为了研究端面抽运情况下,激光晶体在不同分布的抽运光抽运时热透镜球差的变化,通过对稳态热传导方程和Zernike多项式的求解,建立了热透镜球差与抽运光强度分布的模型,对模型进行了理论分析和仿真研究,并对仿真结果做了进一步理论和仿真分析.结果表明:在相同的抽运功率下,二阶超高斯分布抽运光抽运时球差最大,且随着抽运分布系数k的增大(除高斯分布外)球差逐渐减小;随着抽运功率的增加,抽运分布系数k对球差的影响逐渐加重,且不同分布系数k所产生的球差差距逐渐增大;并对二阶超高斯分布抽运光抽运得到最强激光功率的照射范围进行了理论分析和仿真分析,得知在相同抽运功率下,二阶超高斯分布抽运光得到最强激光功率的范围最宽为0.30—0.63倍高斯半径.     

Influence of statistical distribution properties on ultrafast random-number generation using chaotic semiconductor lasers

We study the influence of statistical distribution properties on ultrafast random-number generators (RNGs) using chaotic laser system consisting of a semiconductor laser subject to dual-chaotic optical injections. Two completely different distributions are considered in this paper: one is a long-tailed distribution, and the other is a well-fitted Gaussian distribution. The numerical results show that, using minimum post-processing, symmetric distribution allows for the extraction of 4 least significant bits (LSBs) per sample; while for the asymmetric distribution the produced sequence based on the last LSB still exhibits certain bias. In other words, the important role of symmetric distribution in fast generation of random bits using multi-bit extraction scheme is demonstrated in numerical simulations.     

Simulations of large acoustic scintillations in the straits of Florida

Using a full-wave acoustic model, Monte Carlo numerical studies of intensity fluctuations in a realistic shallow water environment that simulates the Straits of Florida, including internal wave fluctuations and bottom roughness, have been performed. Results show that the sound intensity at distant receivers scintillates dramatically. The acoustic scintillation index SI increases rapidly with propagation range and is significantly greater than unity at ranges beyond about 10 km. This result supports a theoretical prediction by one of the authors. Statistical analyses show that the distribution of intensity of the random wave field saturates to the expected Rayleigh distribution with SI= 1 at short range due to multipath interference effects, and then SI continues to increase to large values. This effect, which is denoted supersaturation, is universal at long ranges in waveguides having lossy boundaries (where there is differential mode attenuation). The intensity distribution approaches a log-normal distribution to an excellent approximation; it may not be a universal distribution and comparison is also made to a K distribution. The long tails of the log-normal distribution cause "acoustic intermittency" in which very high, but rare, intensities occur.     

激光平行平面有源腔自再现模的探求

实际的激光腔不可避免有增益介质的存在，同时，也不可能保证光强的泵浦分布是均匀的。这样光强分布的不均匀必然导致增益分布的不均匀，因此，在考虑自再现模时有考虑增益系数分布状态的必要。本文给出数学公式以及若干个增益分布模型的实例验证这种假设的可行性和合理性。     

Structure of the direct-current magnetron discharge in neon at different polarities of the electrode system

A dc magnetron discharge in neon is studied at different polarities of the electrode system. It is found that the electron energy distribution function is composed of three groups of electrons: fast electrons accelerated by the strong field of a cathode sheath, slow electrons confined in a potential well due to the space-charge field, and intermediate-energy electrons. It is shown that the energy distribution of the confined electrons is a Maxwell-Boltzmann distribution function, whereas the energy distribution of the intermediate electrons is typical of electron diffusion at a constant total energy. The measured values of the cathode sheath thickness depend on the source polarity.     

Kinetics of electron cooling of positrons in a storage ring

Kinetic equations are derived for the positron velocity distribution in storage rings with electron cooling. Both drag force and components of the velocity diffusion tensor are calculated. The mechanism of approach to a steady-state positron velocity distribution via electron cooling is discussed. It is shown that the resulting steady-state positron distribution is very close to the electron distribution when the magnetic field is sufficiently strong.