Blueprint XAS: a Matlab‐based toolbox for the fitting and analysis of XAS spectra

Blueprint XAS is a new Matlab‐based program developed to fit and analyse X‐ray absorption spectroscopy (XAS) data, most specifically in the near‐edge region of the spectrum. The program is based on a methodology that introduces a novel background model into the complete fit model and that is capable of generating any number of independent fits with minimal introduction of user bias [Delgado‐Jaime & Kennepohl (2010), J. Synchrotron Rad. 17 , 119–128]. The functions and settings on the five panels of its graphical user interface are designed to suit the needs of near‐edge XAS data analyzers. A batch function allows for the setting of multiple jobs to be run with Matlab in the background. A unique statistics panel allows the user to analyse a family of independent fits, to evaluate fit models and to draw statistically supported conclusions. The version introduced here (v0.2) is currently a toolbox for Matlab. Future stand‐alone versions of the program will also incorporate several other new features to create a full package of tools for XAS data processing.     

Paramagnetic Mössbauer relaxation spectra by simple ab initio and stochastic models

The stochastic and ab initio (resolvent) methods for the calculation of Mössbauer relaxation spectra are shortly reviewed. The relaxation matrix based on a first order dynamical Hamiltonian is calculated and corresponding simulations are presented. The spin-phonon interaction spectral bath densities are calculated in the Debye approximation for the direct one and two phonon processes. Some least squares fits are presented.     

A new estimator method for GARCH models

The GARCH (p, q) model is a very interesting stochastic process with widespread applications and a central role in empirical finance. The Markovian GARCH (1, 1) model has only 3 control parameters and a much discussed question is how to estimate them when a series of some financial asset is given. Besides the maximum likelihood estimator technique, there is another method which uses the variance, the kurtosis and the autocorrelation time to determine them. We propose here to use the standardized 6th moment. The set of parameters obtained in this way produces a very good probability density function and a much better time autocorrelation function. This is true for both studied indexes: NYSE Composite and FTSE 100. The probability of return to the origin is investigated at different time horizons for both Gaussian and Laplacian GARCH models. In spite of the fact that these models show almost identical performances with respect to the final probability density function and to the time autocorrelation function, their scaling properties are, however, very different. The Laplacian GARCH model gives a better scaling exponent for the NYSE time series, whereas the Gaussian dynamics fits better the FTSE scaling exponent.     

Fitting of deuterium quadrupole echo spectra with multiple motional models

Dynamic information is generally extracted from deuterium quadrupole echo spectra by matching a spectrum calculated for a particular motional model to the experimental spectrum. In this work, a set of computer programs has been written to facilitate fitting of calculated spectra to experimental spectra that represent from one to five motional models. The fitting program requires pre-calculated libraries of spectra for the models of interest, and accomplishes the fitting either by a systematic method or by simulated annealing. The systematic method is convenient for fitting with one or two motional models, but the simulated annealing method is faster for two or more models, if the libraries are made up of hundreds of spectra. The parameter Q, with the standard deviation of the spectral points estimated as the standard deviation of the baseline noise, provides a stringent measure of goodness of fit. Acceptable fits of experimental data as judged by this criterion have not been found, even in the case of ring flip motion in phenylalanine-d(5) in which the fit may be judged acceptable by eye. An example of fitting with isotropic and methyl rotation motional models of alanine-d(3), which have distinct spectral patterns, shows that it is possible to obtain reasonably accurate estimates of the relative amounts of deuterium representing the different models, even from poorly fitted spectra.     

蒙特卡罗计算中颗粒型燃料的随机分布模型比较

高温气冷堆是新一代反应堆系统的热门候选堆型，已经受到国际上越来越多的关注。为设计和分析这种堆型，因其特有的包覆颗粒燃料引入了双重非均匀性，需要应用随机分布模型。对粗网格模型、细网格随机(FLS)模型、随机顺序添加(RSA)模型、子网格随机(Sub-FLS)模型和Metropolis模型等进行了研究，通过计算分析比较给出了各种模型的优缺点。结果表明:子网格随机模型和连续的RSA模型非常接近参考值，但是连续RSA模型的建模时间随着燃料体积份额的增加连续快速上升。 Key words: coated particle fuels; stochastic transport model; Monte Carlo; random distribution     

A Girsanov particle filter in nonlinear engineering dynamics

In this Letter, we propose a novel variant of the particle filter (PF) for state and parameter estimations of nonlinear engineering dynamical systems, modelled through stochastic differential equations (SDEs). The aim is to address a possible loss of accuracy in the estimates due to the discretization errors, which are inevitable during numerical integration of the SDEs. In particular, we adopt an explicit local linearization of the governing nonlinear SDEs and the resulting linearization errors in the estimates are corrected using Girsanov transformation of measures. Indeed, the linearization scheme via transformation of measures provides a weak framework for computing moments and this fits in well with any stochastic filtering strategy wherein estimates are themselves statistical moments. We presently implement the strategy using a bootstrap PF and numerically illustrate its performance for state and parameter estimations of the Duffing oscillator with linear and nonlinear measurement equations.     

Island models and the catalytic oxidation of carbon monoxide and carbon monoxide-olefin mixtures

Simple kinetic models which take account of the formation of islands of adsorbate on a catalyst surface are proposed, and are compared with an elementary step model for CO oxidation and oxidation of a CO-butene or CO-propylene mixture. The island models give fits to data from step change transient experiments which are comparable with the elementary step model, and give better fits to steady-state and continuously oscillating data (the latter with hydrocarbon present). Theoretical predictions of chaotic behaviour in CO oxidation can be obtained with the island models. Comparisons between island models suggest that islands of CO have the most significant effect on simulations at the experimental conditions.     

IMP-8 observations of the spectra, composition, and variability of solar heavy ions at high energies relevant to manned space missions.

In more than 25 years of almost continuous observations, the University of Chicago's Cosmic Ray Telescope (CRT) on IMP-8 has amassed a unique database on high-energy solar heavy ions of potential relevance to manned spaceflight. In the very largest particle events, IMP-8/CRT has even observed solar Fe ions above the Galactic cosmic ray background up to approximately 800 MeV/nucleon, an energy sufficiently high to penetrate nearly 25 g/cm2 of shielding. IMP-8/CRT observations show that high-energy heavy-ion spectra are often surprisingly hard power laws, without the exponential roll-offs suggested by stochastic acceleration fits to lower energy measurements alone. Also, in many solar particle events the Fe/O ratio grows with increasing energy, contrary to the notion that ions with higher mass-to-charge ratios should be less abundant at higher energies. Previous studies of radiation hazards for manned spaceflight have often assumed heavy-ion composition and steeply-falling energy spectra inconsistent with these observations. Conclusions based on such studies should therefore be re-assessed. The significant event-to-event variability observed in the high-energy solar heavy ions also has important implications for strategies in building probabilistic models of solar particle radiation hazards.     

Non-Markovian dynamics in a dense potassium vapor

Transient four-wave mixing experiments on a dense potassium vapor, which has a dephasing time long compared to the collision duration, reveal distinct signatures of non-Markovian dynamics. Theoretical fits assuming stochastic fluctuation of the excited-state frequencies confirm that the two-time correlation function has a finite temporal width.     

Simulating feedback and reversibility in substrate-enzyme reactions

We extend discrete event models (DEM) of substrate-enzyme reactions to include regulatory feedback and reversible reactions. Steady state as well as transient systems are modeled and validated against ordinary differential equation (ODE) models. The approach is exemplified in a model of the first steps of glycolysis with the most common regulatory mechanisms. We find that in glycolysis, feedback and reversibility together act as a significant damper on the stochastic variations of the intermediate products as well as for the stochastic variation of the transit times. This suggests that these feedbacks have evolved to control both the overall rate of, as well as stochastic fluctuations in, glycolysis.     

A universal instability of many-dimensional oscillator systems

The purpose of this review article is to demonstrate via a few simple models the mechanism for a very general, universal instability - the Arnold diffusion—which occurs in the oscillating systems having more than two degrees of freedom. A peculiar feature of this instability results in an irregular, or stochastic, motion of the system as if the latter were influenced by a random perturbation even though, in fact, the motion is governed by purely dynamical equations. The instability takes place generally for very special initial conditions (inside the so-called stochastic layers) which are, however, everywhere dense in the phase space of the systsm.The basic and simplest one of the models considered is that of a pendulum under an external periodic perturbation. This model represents the behavior of nonlinear oscillations near a resonance, including the phenomenon of the stochastic instability within the stochastic layer of resonance. All models are treated both analytically and numerically. Some general regulations concerning the stochastic instability are presented, including a general, semi-quantitative method-the overlap criterion—to estimate the conditions for this stochastic instability as well as its main characteristics.     

Particle subgrid scale modelling in large-eddy simulations of particle-laden turbulence

This study is concerned with particle subgrid scale (SGS) modelling in large-eddy simulations (LESs) of particle-laden turbulence. Although many particle-laden LES studies have neglected the effect of the SGS on the particles, several particle SGS models have been proposed in the literature. In this research, the approximate deconvolution method (ADM) and the stochastic models of Fukagata et al. (Dynamics of Brownian particles in a turbulent channel flow, Heat Mass Transf. 40 (2004), 715–726) Shotorban and Mashayek (A stochastic model for particle motion in large-eddy simulation, J. Turbul. 7 (2006), 1–13) and Berrouk et al. (Stochastic modelling of inertial particle dispersion by subgrid motion for LES of high Reynolds number pipe flow, J. Turbul. 8 (2007), pp. 1–20) are analysed. The particle SGS models are assessed using both a priori and a posteriori simulations of inertial particles in a periodic box of decaying, homogeneous and isotropic turbulence with an initial Reynolds number of Re_λ = 74. The model results are compared with particle statistics from a direct numerical simulation (DNS). Particles with a large range of Stokes numbers are tested using various filter sizes and stochastic model constant values. Simulations with and without gravity are performed to evaluate the ability of the models to account for the crossing trajectory and continuity effects. The results show that ADM improves results but is only capable of recovering a portion of the SGS turbulent kinetic energy. Conversely, the stochastic models are able to recover sufficient SGS energy, but show a large range of results dependent on the Stokes number and filter size. The stochastic models generally perform best at small Stokes numbers, but are unable to predict preferential concentration.     

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters.     

Multiple time scales and the empirical models for stochastic volatility

The most common stochastic volatility models such as the Ornstein–Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull–White models define volatility as a Markovian process. In this work we check the applicability of the Markovian approximation at separate times scales and will try to answer the question which of the stochastic volatility models indicated above is the most realistic. To this end we consider the volatility at both short (a few days) and long (a few months) time scales as a Markovian process and estimate for it the coefficients of the Kramers–Moyal expansion using the data for Dow-Jones Index. It has been found that the empirical data allow to take only the first two coefficients of expansion to be non-zero that define form of the volatility stochastic differential equation of Itô. It proved to be that for the long time scale the empirical data support the ExpOU model. At the short time scale the empirical model coincides with ExpOU model for the small volatility quantities only.     

ISSDE:基于第一性原理随机微分方程的碰撞等离子体隐式模拟

开发一种适用于求解含库仑碰撞等离子体随机微分方程（SDE）的第一性原理隐式模拟程序——Implicit Stratonovich Stochastic Differential Equations （ISSDE）.该程序基于Fokker-Planck （FP）方程与Stratonovich SDE的等价性理论，通过精确求解Stratonovich SDE达到对FP方程的高效第一性原理计算的目标.ISSDE采用隐式格式保证求解的数值稳定性，同时可以保证粒子碰撞过程的能量守恒.ISSDE基于C++语言开发，具有标准接口和灵活的可扩展模组.通过模拟电子束在非磁化和磁化致密等离子体中的慢化过程验证ISSDE的正确性，并展示该程序在碰撞等离子体模拟中的应用.     

A new program based on stochastic Liouville equation for the analysis of superhyperfine interaction in CW-ESR spectroscopy

In the slow-motion region, ESR spectra cannot be expressed as a sum of simple Lorentzian lines. Studies of Freed and co-workers, on nitroxides in liquids gained information on the microscopic models of rotational dynamics, relying much on computer programs for simulation of ESR spectra based on the stochastic Liouville equation (SLE). However, application of Freed's method to copper system of biological interest has been for a long time precluded by lack of a full program able to simulate ESR spectra containing more than one hyperfine interaction. Direct extension of the Freed's approach in order to include superhyperfine interaction is not difficult from a theoretical point of view but the resulting algorithm is problematical because it leads to substantial increase in the dimensions of the matrix related to the spin-hamiltonian operator. In this paper preliminary results of a new program, written in C, which includes the superhyperfine interactions are presented. This preliminary version of the program does not take into account a restoring potential, so it can be used only in isotropic diffusion conditions. A comparison with an approximate method previously developed in our laboratory, based on a post-convolution approach, is discussed.     

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.     

ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

A Monte Carlo implicit simulation program, Implicit Stratonovich Stochastic Differential Equations(ISSDE), is developed for solving stochastic differential equations(SDEs) that describe plasmas with Coulomb collision. The basic idea of the program is the stochastic equivalence between the Fokker–Planck equation and the Stratonovich SDEs. The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision. The cases of Lorentzian plasma, Maxwellian plasma and arbitrary distribution function of background plasma have been considered. The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge–Kutta methods. ISSDE is built with C++ and has standard interfaces and extensible modules. The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE, which shows its correctness and reliability.     

两种群随机动力系统的信息熵和动力学研究

随机种群动力学模型是研究种群间以及种群与不确定性环境间相互作用的动力学行为的数学模型. 本文从概率密度以及信息熵流、熵产生的演化角度探讨了两种群生态系统的Itô (或Statonovich)意义下随机模型的动力学行为.利用Fokker-Planck方程及其边界条件 和信息熵定义导出信息熵流(平均散度)和熵产生的关系式,并通过数值路径积分法捕 捉到熵流的非线性变化趋势以及信息熵的极值点位置与概率密度的快速迁移和分岔的联系. 应用数值路径积分法计算结果表明Itô (或Statonovich)意义下两种随机模型的概率密度 和信息熵的极值点位置不同但演化趋势一致.