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.     

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.     

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.     

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.     

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.     

熵的一种通俗教法

熵如力、能量和动量一样是物理学中一个重要概念,若能用一种通俗易懂的方法设计熵的教学,对文科物理的教学有重要意义.为此本文提出了一种通俗的熵的教法,这一教法不需要学生学习热力学第二定律也可以建立熵的概念.具体教学设计如下:通过日常生活例子引入熵的概念(也就是玻尔兹曼熵),设计两个例子让学生会计算熵,通过具体问题的讨论让学...     

Lattice Boltzmann method for the generalized Kuramoto-Sivashinsky equation

In this paper, a lattice Boltzmann model with an amending function is proposed for the generalized Kuramoto-Sivashinsky equation that has the form u_t+uu_x+αu_xx+βu_xxx+γu_xxxx=0. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. It is found that the numerical results agree well with the analytical solutions.     

Maximum entropy algorithm with inexact upper entropy bound based on Fup basis functions with compact support

The maximum entropy (MaxEnt) principle is a versatile tool for statistical inference of the probability density function (pdf) from its moments as a least-biased estimation among all other possible pdf’s. It maximizes Shannon entropy, satisfying the moment constraints. Thus, the MaxEnt algorithm transforms the original constrained optimization problem to the unconstrained dual optimization problem using Lagrangian multipliers. The Classic Moment Problem (CMP) uses algebraic power moments, causing typical conventional numerical methods to fail for higher-order moments (m>5–10)$(m>5''–''10)$ due to different sensitivities of Lagrangian multipliers and unbalanced nonlinearities. Classic MaxEnt algorithms overcome these difficulties by using orthogonal polynomials, which enable roughly the same sensitivity for all Lagrangian multipliers. In this paper, we employ an idea based on different principles, using Fup_n${\mathit{Fup}}_n$ basis functions with compact support, which can exactly describe algebraic polynomials, but only if the Fup order-n   is greater than or equal to the polynomial’s order. Our algorithm solves the CMP with respect to the moments of only low order Fup₂${\mathit{Fup}}_2$ basis functions, finding a Fup₂${\mathit{Fup}}_2$ optimal pdf with better balanced Lagrangian multipliers. The algorithm is numerically very efficient due to localized properties of Fup₂${\mathit{Fup}}_2$ basis functions implying a weaker dependence between Lagrangian multipliers and faster convergence. Only consequences are an iterative scheme of the algorithm where power moments are a sum of Fup₂${\mathit{Fup}}_2$ and residual moments and an inexact entropy upper bound. However, due to small residual moments, the algorithm converges very quickly as demonstrated on two continuous pdf examples – the beta distribution and a bi-modal pdf, and two discontinuous pdf examples – the step and double Dirac pdf. Finally, these pdf examples present that Fup MaxEnt algorithm yields smaller entropy value than classic MaxEnt algorithm, but differences are very small for all practical engineering purposes.     

Utility function estimation: The entropy approach

The maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker’s preferences. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function. In this paper we explore the maximum entropy principle to estimate the utility function of a risk averse decision maker.     

Intermittency from maximum entropy distribution

A maximum entropy distribution has been formulated in which the imposed constraint contains a stochastic (rather than a deterministic) variable. The distribution depends on the observational bin size through the smoothing of population by intrabin averaging. Moments of fluctuations calculated with this distribution give bin-size dependences (intermittency exponents) that agree reasonably with those obtained from the size dependence in nuclear multifragmentation. The exponents depend on the spread of the stochastic mechanism (supposed to be a cascading, multiplicative process) and on the magnitude of the constraint imposed. An information-theoretic interpretation is provided for the relation between statistical and mechanism-induced (dynamic) fluctuations.     

Maximum entropy principle for rarefied polyatomic gases

The aim of this paper is to show that the procedure of maximum entropy principle for the closure of the moments equations for rarefied monatomic gases can be extended also to polyatomic gases. The main difference with respect to the usual procedure is the existence of two hierarchies of macroscopic equations for moments of suitable distribution function, in which the internal energy of a molecule is taken into account. The field equations for 14 moments of the distribution function, which include dynamic pressure, are derived. The entropy and the entropy flux are shown to be a generalization of the ones for classical Grad’s distribution. The results are in perfect agreement with the recent macroscopic approach of extended thermodynamics for real gases.