Time-dependent radiative transfer using Chapman-Enskog maximum entropy method

The time-dependent problems of radiative transfer involve a coupling between radiation and material energy fields and are nonlinear because of proposed temperature dependence of the medium characteristics in semi-infinite medium with Rayleigh anisotropic scattering. By means of the limited flux, Chapman-Enskog and maximum entropy technique the time-dependent radiative transfer equation has been solved explicitly. The maximum entropy method is used to solve the resulting differential equation for radiative energy density. The calculations are carried out for temperature (normalized dimensionless) Θ(x,τ), radiative energy density and net flux with Rayleigh and anisotropic scattering for different space at different times.     

Two alternative methods for solving ion transport equation with anisotropic approximation

By means of two alternative methods namely, the maximum entropy and Chapman-Enskog, flux limited approach the ion transport equation for slowing-down problem of low-energy light ions in solid has been solved explicitly. Maximum entropy technique yields approximate solutions in the form of locally Maxwellian distribution function, based on moments expansion truncated upon entropy maximization.The behavior of the approximate maximum entropy and the flux limited solutions have the same tendency. Knowing the distribution function obtained by flux limited approach, allows us to calculate directly the path length distributions of backscattered ions, and compared with that found by other theories such as Laplace-transform and double Legendre polynomial approximation. One can see that the flux limited approach is better than the previous method namely, (DPN) Laplace-transform.The results reported in this article provide further evidence of the usefulness of both maximum entropy and flux limited for obtaining the solution of ion transport equation in compact form.     

On the solution of time-dependent transport equation with time-varying cross sections

The time-dependent neutron transport equation in an infinite medium with time-varying cross sections has been solved by means of two techniques namely, flux-limited approach and maximum entropy method. The behaviour of the distribution function are shown graphically. Knowing the distribution function allows us to calculate directly some physical parametres of special interest such as the reflection function. The results reported in this article provide further evidence of the usefulness of both maximum entropy and flux limited methods for obtaining time-dependent solution of neutron transport in compact form.     

On the solution of Fokker-Planck equation for electron transport

Two different techniques have been used to solve the Fokker-Planck equation for electron transport in infinite homogeneous medium namely, maximum entropy and flux-limited approach. The solutions obtained for the scalar flux function φ₀(x,s) by both methods are numerically compared.     

Time-series analysis of foreign exchange rates using time-dependent pattern entropy

Time-dependent pattern entropy is a method that reduces variations to binary symbolic dynamics and considers the pattern of symbols in a sliding temporal window. We use this method to analyze the instability of daily variations in foreign exchange rates, in particular, the dollar–yen rate. The time-dependent pattern entropy of the dollar–yen rate was found to be high in the following periods: before and after the turning points of the yen from strong to weak or from weak to strong, and the period after the Lehman shock.     

Preliminary study on CAD-based method of characteristics for neutron transport calculation

Our new method makes use of a CAD-based automatic modeling tool, MCAM, for geometry modeling and ray tracing of particle transport in method of characteristics （MOC）. It was found that it could considerably enhance the capability of MOC to deal with more complicated models for neutron transport calculation. In our study, the diamond-difference scheme was applied to MOC to reduce the spatial discretization errors of the fiat flux approximation. Based on MCAM and MOC, a new 2D MOC code was developed and integrated into the SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical results demonstrated the feasibility and effectiveness of the new method for neutron transport calculation in MOC.     

Preliminary study on CAD-based method of characteristics for neutron transport calculation

Our new method makes use of a CAD-based automatic modeling tool, MCAM, for geometry modeling and ray tracing of particle transport in method of characteristics (MOC). It was found that it could considerably enhance the capability of MOC to deal with more complicated models for neutron transport calculation. In our study, the diamond-difference scheme was applied to MOC to reduce the spatial discretization errors of the flat flux approximation. Based on MCAM and MOC, a new 2D MOC code was developed and integrated into the SuperMC system, which is a Super Multi-function Computational system for neutronics and radiation simulation. The numerical results demonstrated the feasibility and effectiveness of the new method for neutron transport calculation in MOC.     

The criteria for selecting a method for unfolding neutron spectra based on the information entropy theory

To further expand the application of an artificial neural network in the field of neutron spectrometry, the criteria for choosing between an artificial neural network and the maximum entropy method for the purpose of unfolding neutron spectra was presented. The counts of the Bonner spheres for IAEA neutron spectra were used as a database, and the artificial neural network and the maximum entropy method were used to unfold neutron spectra; the mean squares of the spectra were defined as the differences between the desired and unfolded spectra. After the information entropy of each spectrum was calculated using information entropy theory, the relationship between the mean squares of the spectra and the information entropy was acquired. Useful information from the information entropy guided the selection of unfolding methods. Due to the importance of the information entropy, the method for predicting the information entropy using the Bonner spheres' counts was established. The criteria based on the information entropy theory can be used to choose between the artificial neural network and the maximum entropy method unfolding methods. The application of an artificial neural network to unfold neutron spectra was expanded.     

Extraction of spectral functions from Dyson-Schwinger studies via the maximum entropy method

It is shown how to apply the Maximum Entropy Method (MEM) to numerical Dyson-Schwinger studies for the extraction of spectral functions of correlators from their corresponding Euclidean propagators. Differences to the application in lattice QCD are emphasized and, as an example, the spectral functions of massless quarks in cold and dense matter are presented.     

非定常输运问题适应于消息传递并行编程环境的香农熵计算方法

在多计算步的非定常输运问题的蒙特卡罗模拟中,为自动调整每一步的样本数以获得较高的计算效率,可以有多种准则.一种可选的方法是在每一步每隔若干样本监测一次系统中未死亡粒子属性分布对应的香农熵的收敛情况以决定何时停止追加样本,此种方法需要在每一步频繁计算香农熵值.由于在MPI消息传递并行编程环境下香农熵的经典计算方法必须广播大量的数据,导致每一步的计算时间随香农熵计算频率的提高而快速增大,这显然是不能满足实际需求的.本文提出了一种适应于消息传递并行编程环境的香农熵计算新方法,该方法计算得到的香农熵值并不等价于经典方法,但二者之间的差别会随着样本数的增加而趋于零.新方法的最大优势是高频计算香农熵值的时间代价大为降低,为最终实现基于香农熵收敛判断的每步样本数的自动调整奠定了必要的基础.     

Static potential renormalization in time-dependent fields

We consider the scattering of electrons at a static potential under the influence of an additional time-dependent, homogeneous electric field (‘microwave’). Starting from a plane wave basis, we derive a generalization of the Born (first) order approximation in arbitrary strong oscillating fields. As an example, we evaluate the Friedel density oscillations around a static scatterer whose potential is renormalized by the microwave. The microwave leads to a band of inelastic scattering channels with effective potentials, the shape of which can be ‘tuned’ by the microwave polarization and strength.     

The principle of the maximum entropy method

Abstract

The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of “entropy” is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.     

非定常输运基于香农熵的自动调整样本数策略

对于非定常输运问题提出了一种基于香农熵的自动调整样本数策略。将每一计算步的总样本数划分为若干批并逐步模拟每批中的粒子, 可以在每批粒子模拟结束后通过计算得到该时间步幸存粒子属性分布对应的香农熵值。采用在线收敛性诊断方法, 一旦通过香农熵值序列判断对应的幸存粒子属性分布已经收敛, 则可以提前结束本时间步的计算。对一个空间一维非定常输运模型的计算结果表明, 该策略可以显著减少每一计算步的实际样本数且保持最终的结果基本不变, 从而减少了计算时间, 提高了计算效率。     

聚变中子能谱测量系统脉冲中子灵敏度的实验研究

为多种复杂环境下的稳态和脉冲DT聚变中子能谱测量建立了一种灵敏度优化反冲质子磁谱仪. 使用成像板和同位素α源测量了谱仪的反冲质子能量-位置投影关系. 利用稳态加速器中子源平台、通过单粒子计数方法结合三维带电粒子输运程序模拟,研究了谱仪脉冲中子灵敏度能量响应. 通过高探测效率参数设置使谱仪对DT中子的探测效率达到2×10^-5 cm²水平,从而在较弱中子源上获得了较高统计精度实验数据. 程序模拟结果与谱仪α粒子刻度和DT中子标定实验结果取得了良好的一致性,可由此发展精细解谱技术,以提高脉冲中子能谱测量的灵敏度和能量分辨. 关键词： 聚变中子能谱 磁反冲质子 脉冲中子灵敏度 粒子输运     

Maximum-entropy states for magnetized ion transport

For a plasma with fixed total energy, number of particles, and momentum, the distribution function that maximizes entropy is a Boltzmann distribution. If, in addition, the rearrangement of charge is constrained, as happens on ion-ion collisional timescales for cross-field multiple-species transport, the maximum-entropy state is instead given by the classic impurity pinch relation. The maximum-entropy derivation, unlike previous approaches, does not rely on the details of the collision operator or the dynamics of the system, only on the presence of certain conservation properties.     

最大熵法在风廓线雷达谱分析中的应用研究

为了解现代谱分析技术在风廓线雷达中应用的可行性,通过采用实测的和模拟的风廓线雷达回波信号,对比研究了FFT法与最大熵法的谱分析效果。结果表明:(1)当回波信号比较强时,两者都可以得到较好的谱分析效果;但是当回波信号较弱时,最大熵法分析效果优于FFT法,最大熵法对地杂波具有较好的抑制能力。(2)最大熵谱比较光滑,表明最大熵法对随机白噪声也有一定的抑制作用。(3)最大熵法的递推阶数对谱分析结果有一定影响,最终预测误差准则确定的递推阶数一般偏小,采用15阶的递推阶数进行最大熵法分析取得了较好结果。由于风廓线雷达回波通常都较弱,因此研究结果可望用于改善信号处理效果。     

Recovery of lifetime distributions from frequency-domain fluorometry data by means of the quantified maximum entropy method

The new quantified version of the maximum entropy method allows one to recover lifetime distributions with a precise statement of the accuracy of position, surface, and broadness of peaks in the distribution. Applications to real data (2,6-ANS in aqueous solutions of sodium dodecyl sulfate micelles of -cyclodextrin) are presented.Died on September 1, 1993.     

Statistical approach of the irreversible entropy variation

The constructal theory is based on the thought that flow architecture is a consequence of a principle of maximization of flow access, in time, and in flow configuration that is free to be realised. The principle of maxima for the variation of the entropy due to irreversibility represents a general principle of investigation for the stability of open systems, by which it is possible to predict some macroscopic shapes, originated by the spatial organisation, in Nature, both in living and in non-living objects. Its statistical meaning has recently been introduced. Here a statistical and dynamical interpretation for the entropy due to irreversibility is proposed as a foundation of the constructal theory.     

不同水温下的中子输运等效质量热运动模型

为了解决蒙特卡罗模拟S(, )模型只能求解特定温度条件下中子输运问题的局限性,建立了中子在不同温度液态水中输运的等效质量热运动模型。在分析自由气体热运动模型的基础上,采用不同的等效质量对中子与水中氢原子的弹性散射模拟过程进行改进,对中子穿过水层后的流量进行模拟计算,通过与S(, )模型的计算结果的比较,得到了5个不同的温度点水中氢原子的最佳等效质量。根据5个不同温度点的数据拟合给出了最佳等效质量和温度的函数关系。采用该模型计算得到的中子在不同温度条件下水中输运参数与S(, )模型相符。等效质量热运动模型突破了S(, )模型只能计算有限温度点的局限性,能有效处理300～800 K任意温度水中的中子输运问题。