Fractional Bayesian Lag Length Inference in Multivariate Autoregressive Processes

The posterior distribution of the number of lags in a multivariate autoregression is derived under an improper prior for the model parameters. The fractional Bayes approach is used to handle the indeterminacy in the model selection caused by the improper prior. An asymptotic equivalence between the fractional approach and the Schwarz Bayesian Criterion (SBC) is proved. Several priors and three loss functions are entertained in a simulation study which focuses on the choice of lag length. The fractional Bayes approach performs very well compared to the three most widely used information criteria, and it seems to be reasonably robust to changes in the prior distribution for the lag length, especially under the zero-one loss.     

Accounting for Lag Order Uncertainty in Autoregressions: the Endogenous Lag Order Bootstrap Algorithm

Conventional asymptotic and bootstrap methods for finite-order autoregressive models condition on the estimated lag order of the model as though it were known to be the true lag order. Even if the order is estimated correctly, this procedure ignores the sampling uncertainty about the lag order estimate and may result in spurious inferences. In this paper an appropriately modified bootstrap algorithm is introduced that reflects the true extent of sampling uncertainty in the regression estimates. This endogenous lag order bootstrap algorithm recognizes that lag order selection is an integral part of the sampling procedure by re-estimating the lag order in each bootstrap iteration. It is suggested that the endogenous lag order bootstrap algorithm should routinely replace the standard bootstrap algorithm in applications. Monte Carlo simulations show that ignoring lag order uncertainty may seriously undermine the coverage accuracy of bootstrap confidence intervals for vector autoregression impulse response estimates. Endogenizing the lag order choice is shown to improve coverage accuracy in small samples at negligible additional computational cost. As the lag order uncertainty declines in large samples, the performance of the endogenous lag order interval converges to that of the standard interval.     

尺度效应对三元复合驱色谱分离的影响

针对化学驱油剂存在色谱分离及评价三元复合驱效果的合适尺度模型问题,利用电位滴定法分别测定采出液中碱和表面活性剂的质量浓度,利用淀粉-碘化镉法定量测定聚合物的质量浓度。在油藏温度69℃的条件下,分别考察30,100和240 cm填砂管对ASP三元复合驱油体系色谱分离的影响。研究结果表明:填砂管尺度从30 cm增加到240 cm,聚合物、碱和表面活性剂的无因次突破时间依次增加;填砂管尺度从30 cm增加到100 cm,聚合物、碱和表面活性剂之间的运移滞后系数均相差较大,色谱分离严重,但色谱分离程度没有加剧;填砂管尺度从100 cm增加到240 cm,色谱分离程度有减弱的趋势。实验室及油田现场评价三元复合驱效果的模型尺度应超过100 cm。     

Model Selection in Threshold Models

This paper considers information criteria as model evaluation tools for nonlinear threshold models. Results concerning the consistency of information criteria in selecting the lag order of linear autoregressive models are extended to nonlinear autoregressive threshold models. Monte Carlo evidence of the small sample performance of a number of criteria is presented.
JEL. C15, C44, C52.     

A Bayesian Approach to Modelling Graphical Vector Autoregressions

Abstract. We introduce a Bayesian approach to model assessment in the class of graphical vector autoregressive processes. As a result of the very large number of model structures that may be considered, simulation‐based inference, such as Markov chain Monte Carlo, is not feasible. Therefore, we derive an approximate joint posterior distribution of the number of lags in the autoregression and the causality structure represented by graphs using a fractional Bayes approach. Some properties of the approximation are derived and our approach is illustrated on a four‐dimensional macroeconomic system and five‐dimensional air pollution data.     

Characteristic mixing length in bubble columns

Liquid-phase mixing in bubble columns is discussed on the basis of the mixing length theory. A characteristic mixing length defined as a lumped hydrodynamic parameter is estimated. The results indicate that the characteristic mixing length assumed previously by one of the authors is reasonable.     

Critical length of straight jet in electrospinning

In this paper the well-known Chauchy's inequality is applied to prediction of critical length of the straight jet in electrospinning. A critical relationship between radius r of jet and the axial distance z from nozzle is obtained for the straight jet. Critical length number and critical radius number are defined, which might be found potential applications in experiment and apparatus design.     

含时滞测量值下间歇过程的双维状态估计

基于粒子滤波研究了间歇过程的状态估计问题。根据间歇过程双维动态特性,针对关键参数在线检测精度低、离线分析时滞大等问题,分别建立一种双维状态转移模型和时滞测量模型,并利用贝叶斯方法及前/后向平滑,提出一种含时滞测量值下的双维状态估计算法。该算法通过融合先前批次和时滞测量值的信息提高估计精度,并且克服了离线采样周期和时滞时间不确定的问题。在数字仿真和啤酒发酵过程中的仿真应用验证了该算法的有效性。     

Chain length dependent termination in radical cross-linking polymerization

The work presents an evidence in support of chain length dependent termination during cross-linking polymerization. It is based on the behavior of the ratio of the bimolecular termination coefficient to propagation rate coefficient k_p during the after-effect of a photo-induced polymerization. The chain-length dependence was manifested by a decrease of the ratio with the increase in dark reaction time faster than that resulting from the conversion increase. Two monomethacrylate/dimethacrylate and one dimethacrylate/dimethacrylate systems were chosen, which enabled to study the chain-length dependence as a function of cross-link density of the polymer being formed and physical properties of the initial composition. The ratios of the polymerization rate coefficients were calculated for various postpolymerization processes as a function of dark reaction conversion using the mixed termination model (concerning the bimolecular and monomolecular termination occurring parallel). A rapid drop of the ratio during the dark reaction was observed at the beginning of the after-effect and in slightly cross-linked systems suggesting a significant chain length dependence, but when the cross-link density increased with conversion or with cross-linking agent concentration in the feed, the drop of the ratio became much slower indicating that the chain length dependence decreased.     

管道气体置换混合长度变化规律研究

采用低雷诺数k-ε模型对输气管道气体置换过程进行二维数值模拟。研究结果表明:混合区浓度在轴向呈非对称分布,呈"头短尾长"特征;流速、管径、管道长度是混合长度的主要影响因素。混合初始,混合长度增长速率大,随着主流向下游流动距离的增加,增长速率减小;流速是混合长度的重要控制参数,湍流时的混合长度小于层流,流速对混合长度的影响在高雷诺数湍流时比较小;同一湍流流速下,混合长度随管径增加而增加;管径对混合长度的影响随湍流度的降低而增大;氮气-天然气混合长度比氮气-空气混合长度大1%—2%。     

Consistent estimation and order selection for nonstationary autoregressive processes with stable innovations

Abstract. A possibly nonstationary autoregressive process, of unknown finite order, with possibly infinite‐variance innovations is studied. The ordinary least squares autoregressive parameter estimates are shown to be consistent, and their rate of convergence, which depends on the index of stability, α, is established. We also establish consistency of lag‐order selection criteria in the nonstationary case. A small experiment illustrates the relative performance of different lag‐length selection criteria in finite samples.     

Differences and limits in estimates of persistence length for semi-flexible macromolecules

Persistence length of (bio)macromolecules plays an increasingly important role in macromolecular science, especially in emerging fields like macromolecular biophysics. It is shown that using established approximate relations for the estimation of persistence length for semi-flexible macromolecules leads to differences between different methods or even to a modified behavior, especially at high chain stiffness. The approximate estimate obtained from the average bond angle (B) performs better than the estimate from the decay of bond orientation correlation (C) in chain but close to the coil-to-rod transition starts to fail. This approximate estimate is close to the estimate from the definition of persistence (D) (with minimum approximations) not only in the theta state or the random coil but also in the good solvent. The value of persistence from the decay of bond orientation correlation along the macromolecule is underestimated when compared to the exact value. The persistence obtained from the worm-like chain model (W) is close to the exact result in the coil regime (also in the good solvent) but near at and above the transition produces the largest values of all approximations. In systems with interactions this model starts to underestimate the persistence on decreasing temperature. We advocate using the estimate (D) of persistence length generally since it avoids limitations mentioned above and at the same time does not pose additional requirements on the evaluation itself.     

The kinetic substrate length in nucleation-controlled crystallization in polyethylene fractions

The concept of a substrate length L is essential in the understanding of the regime I→II growth rate transitions in melt-crystallized lamellar polymers. The present work deals with the actual magnitude of L in polyethylene fractions as determined strictly from the kinetics of crystallization. With the help of an improved value of the activation energy of transport in the melt, and a more precise method of analysis than was employed heretofore, it is found from published growth rate measurements on polyethylene fractions that L is within about a factor of two of 0.77 μm at the regime I→II transition. The value of L is independent of the equilibrium melting temperature T⁰_m(∞) assumed in the analysis. It is shown that L is much larger than a just stable surface nucleus. A brief summary is given of what is known about L from a kinetic point of view, and possible correlations with morphological features are mentioned. It is conjectured that L may relate to the mean distance between surface defects that have the capacity to terminate strip completion. In the course of the study, better values of the pre-exponential factors N₀ and C₀ that govern the absolute growth rates in regimes I and II, respectively, are obtained. A revised numerical value is given for the pre-exponential factor in the Lauritzen ‘Z’ test. This is based partly on the new value of C₀, and partly on a reformulation of the problem.     

输气管道二元气体混合长度变化规律分析

运用模拟试验、平推流建模、数值计算与现场数据对比等手段,对输气管道二元气体的混合系数和混合长度进行了研究。在平推流模型求解过程中,为提高计算精度,将Taylor公式中的摩擦系数进行了修正。通过国内外10条天然气管道气体置换实例的对比分析,可知粗糙度对混合系数影响很小。同时,采用不同方法计算得出了二元气体的混合系数,Taylor-CW得出的混合系数平均比Taylor公式大1.1倍。在大管径、长距离、高流速的置换工况下,GR I(美国天然气研究所)公式混合长度计算结果与实测值误差较小。而对于小管径、短距离或者低流速的工况,用Taylor-CW公式能获得更真实准确的结果。     

The entry length for slurries in horizontal pipeline flow

The entry length for horizontal slurry pipeline flows has been determined experimentally using a pipeline of diameter 50 mm. Concentration and velocity distributions have been measured in the vertical direction at positions 6, 50 and 185 diameters downstream of the entrance. The measurements show that the entry length is of the order of 50 pipe diameters for sand slurries. High particle settling velocities give somewhat shorter lengths than intermediate settling velocities. With lower density polystyrene particles for which dispersive effects are important, the entry length is significantly greater than 50 diameters. The velocity distributions show that the velocity profiles develop concurrently with the concentration profiles. For sand slurries, a two-dimensional simulation gives a satisfactory representation of the developing concentration profiles.     

Three‐dimensional imaging of large compressive deformations in elastomeric foams

Specimens of silica‐reinforced polysiloxane foam pads were three‐dimensionally imaged during axial compressive loading to densification. The foams' behavior was highly nonlinear and showed the three characteristic regions of linear elastic, elastic buckling, and densification. A finite‐element technique, based upon conversion of the image voxels to finite elements, was used to calculate the mechanical properties of the foams. The results were compared with conventional mechanical testing and theory. The finite‐element calculations were in excellent agreement with experimental stress–strain data over the entire range of compressive loading. Theoretical models, on the other hand, overestimated the stiffness of the foam above the elastic buckling stress by not correctly predicting the abruptness of the transition from elastic buckling to densification. Three‐dimensional analysis of the deformed microstructures indicated that there was a critical foam density beyond which the cell morphology suddenly changed from open‐celled to closed‐celled and that this “phase”‐like transition was responsible for the abrupt increase in stiffness near densification. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1746–1755, 2001     

Surfactant chain length effect on the hexagonal-to-cubic phase transition in mesoporous silica synthesis

In this study, silica-based mesoporous materials (the M41S family mesoporous molecular sieves) are synthesized using alkyltrimethylammonium bromide with different chain lengths (C_nH_2n+1N(CH₃)₃Br, n = 10, 12, 14, 16) as templates. The resulting silica structures are characterized by X-ray diffraction and are found to exhibit the phase transformation from the hexagonal mesophase MCM-41 to the cubic mesophase MCM-48 (with the space group of Ia3d). The structural phase transition in our study is controlled by the alkyl chain length of the surfactant: with an increase in the surfactant chain length (from C10 to C16), the structure goes from MCM-41 (synthesized by C10), through an intermediate structure (synthesized by C12), to MCM-48 (synthesized by C14 and C16). The amount of ethanol, which is used as a cosolvent, affects the pore size of the structured mesoporous silica, but only to a small extent. In the mean time, the autoclaving time has some effect, though not distinctively, on the structure integrity as well. With increased surfactant to silica ratio, the phase transformation can be shifted to longer chain template.     

链长法测定多聚磷酸中磷酸的含量

链长法是利用多聚磷酸在未水解时以氢氧化钠溶液为滴定溶液,用自动电位滴定仪滴定,并记录滴定曲线,根据曲线上的两个拐点处所消耗的氢氧化钠的体积,计算多聚磷酸中磷酸的含量。该法样品处理和分析过程简单、快速、准确、成本低,能满足多聚磷酸生产和产品检验的要求。