An optimal stopping time for a power law process

Exact reliability analysis for complex repairable systems are usually difficult because of the complicated failure process that can result from repair policy. A common approach in practice is to use a simplified process such as the Power Law process which, although not exact, yields useful practical results. In this paper we consider the problem of determining a stopping time when estimating parameters of a Power Law process. The Bayes method is used in order to obtain an optimal time.     

PREDICTION OF VELOCITY PROFILES OF SHEAR THINNING FLUIDS FLOWING IN ELASTIC TUBES

Non-Newtonian fluid flow characteristics in inflatable and collapsible elastic tubes are relevant to bio-fluid mechanics and other applications. The radial velocity profiles in an elastic tube during steady laminar flow of a shear thinning aqueous solution of 1.5% carboxy methyl cellulose (CMC) were investigated using ultrasound Doppler velocimetry. The shear rate–dependent viscosities obtained using a rheometer were well represented by the Carreau model. Measured storage and loss moduli indicated the CMC solution to be inelastic up to 2% concentration. The velocity profiles were predicted by integrating the theoretical equation derived by equating the shear stress along the tube radius involving pressure drop to that of the Carreau model using its parameters. The agreement between predicted and measured velocity profiles was good. The predicted pressure drop is about the same as the experimental value at lower flow rates. In contrast, the measured pressure drop is lower than that predicted at higher flow rates due to inflation of the tube. Good agreement between estimation (Hagen-Poiseuille's law) and measurement (tube shape image analysis) for the detection of elastic tube expansion while increasing flow rates is found.     

A QUASI NEWTONIAN MODEL FOR SIMULATING THE FLOW OF DILUTE POLYMER SOLUTIONS THROUGH A SUDDEN CONTRACTION

The flow of a quasi Newtonian model fluid, which allows shear thinning as well as extension thickening, through a sudden planar 4:1 contraction is studied numerically. Comparing with numerical results for a purely shear thinning fluid differences show up which follow the trend of experimental data.     

A Unified Model for the Mixing of Non‐Newtonian Fluids in the Laminar,Transition, and Turbulent Region

Summary: Non‐Newtonian fluid behavior has significant influence on quantities in chemical engineering like power input, mixing time, heat transfer etc. In the laminar flow region, the concept of effective viscosity by Metzner and Otto is well established. In the transition region between laminar and turbulent flow, the existing concepts use three and even more empirical parameters to determine the specific power input. Here, a unified and general but simple approach is introduced to calculate the power input for shear thinning fluids over the whole flow region using just one empirical parameter. The Metzner‐Otto relation is obtained as a limiting case for the laminar region. The empirical parameter of the new approach is related to the Metzner‐Otto constant. The concept is validated for eight different stirrer systems. Mixing time and maximum shear rate and heat transfer can also be calculated using this approach. The new concept presented should also be applicable for other apparatuses, e.g., static mixers.

Comparison of experimental data and a curve calculated according to the new method (solid line).     

整数值时间序列的拟似然推断

基于推广的负二项稀疏算子利用预设新息过程分布法构造一个一元 INAR(1) 模型,给出了模型的概率性质并利用拟似然估计方法对模型进行了参数估计,同时也考虑了最小二乘法、极大似然估计方法。通过数值模拟评估了这些估计方法的有效性,并应用实际数据给出模型的应用,通过比较得出基于推广的负二项稀疏算子带有几何新息过程的INAR(1)是更适合数据的模型。     

A p‐Order signed integer‐valued autoregressive (SINAR(p)) model

In this article, we propose an extension of integer‐valued autoregressive INAR models. Using a signed version of the thinning operator, we define a larger class of ‐valued processes, called SINAR, which can have positive as well as negative correlations. Using a Markov chain method, conditions for stationarity and the existence of moments are investigated. In particular, it is shown that the autocorrelation function of any real‐valued AR process can be recovered with a SINAR process, which improves INAR modeling.     

A simple scaling derivation of the shear thinning power-law exponent in entangled polymer melts

By suggesting that the polymer dynamics in entangled polymer melts possesses the property of dynamical self-similarity, we argue that the power-law exponent of the Carreau-Yasuda law, which empirically describes the shear thinning effect of the polymer melt viscosity, is inversely proportional to the exponent of the molecular mass dependence of the terminal relaxation time. This finding is obtained in cases where the shear rate dependence of the segmental relaxation time is negligible. If such dependence is essential, the Carreau-Yasuda law is slightly modified at high shear rates: instead of a power-law dependence with a small shear rate independent exponent, a weaker logarithmic dependence is found both for shear rate and molecular mass dependence, which resembles the approach to zero of an effective shear rate and molecular mass dependent power-law exponents at sufficiently high shear rates.     

基于图像的二次反射镜面形质量快速检测方法

针对二次反射塔式太阳能热发电技术中二次反射镜面形精度要求高的特性, 利用2种条纹方向正交的直条纹图案将待测面形分解为2个正交方向的像素偏差量, 通过二次反射镜面形快速解算模型将像素偏差转换成镜面反射法线的偏差角, 实现了待测面面形的快速检测。然后, 对二次反射镜样品进行面形检测, 再将检测结果与基于关节臂测量机的检测结果进行了对比, 结果表明2种检测方法的检测结果相符。     

循环加卸载下纤维增强泡沫轻质土变形特性

为了研究聚丙烯纤维增强泡沫轻质土的损伤变形特性,选用UNSAT非饱和土三轴仪开展50 kPa围压作用下的循环加卸载试验. 以泊松比、弹性模量提高率及弹塑性变形趋势为参数,分析不同纤维质量分数条件下聚丙烯纤维增强泡沫轻质土的力学特性和变形规律. 研究结果表明：当纤维质量分数达到0.50%~1.00%时,初次弹性模量提高率为56.88%~69.43%,纤维对泡沫轻质土内部初始缺陷的改善作用最佳;纤维增强泡沫轻质土试样的弹性模量提高率随着循环次数的增加呈先增大后减小的趋势,泊松比随着循环次数的增加而增大,在经历最初的2、3次循环荷载作用后趋于稳定直至试样破坏;随着循环次数的增加,纤维增强泡沫轻质土的轴向弹性应变与总应变之比逐渐降低,试样内部损伤变形逐渐累积.     

带有随机系数的双线性INAR(1)模型的统计推断

基于带有随机系数的二项稀疏算子构造双线性INAR(1)模型,推导了模型的统计性质．采用修正的矩估计法对模型进行参数估计并进行了模拟研究．最后给出一个实例应用,结果表明基于带有随机系数的二项稀疏算子的双线性INAR(1)模型是更适合数据的模型．