Stochastic molecular descriptors for polymers. 2. Spherical truncation of electrostatic interactions on entropy based polymers 3D-QSAR

The spherical truncation of electrostatic field with different functions break down long-range interactions at a given cutoff distance (r_off) resulting in short-range ones. Consequently, a Markov Chain model may approach to the entropies of spatial distribution of charges within the polymer backbone. These entropies can be used to predict polymers properties [González-Díaz H, Molina RR, Uriarte E. Polymer 2004; 45: 3845 [53]]. Herein, we explore the effect of abrupt, shifting, force shifting, and switching truncation functions on QSAR models classifying 26 proteins with different function: lysozymes, dihydrofolate reductases, and alcohol dehydrogenases. Almost all methods have shown overall accuracies higher than 85% instead of 80.8% for models based on physicochemical parameters. The present result points to a acceptable robustness of the Markov model for different truncation schemes and r_off values. The results of best accuracy 92.3% with abrupt truncation coincides with our recent communication [Bioorg Med Chem Lett 2004; 14: 4691-4695]. Nonetheless, the simpler model with three variables and high accuracy (88%) was derived with a shifting function and r_off=10 Å.     

A study on metastability phenomena of passive films for corrosion resistant alloys

In chloride-containing environments, passive films on corrosion-resistant alloys (CRA) are characterised by instability phenomena. These in turn depend on environmental conditions, type of alloy, sample geometry and heterogeneities on the metal surface. The localised corrosion process for these systems can be described by a three-state model: (1) passivity, (2) metastability, and (3) localised corrosion. Corrosion resistance is based on the permanence of states 1 or 2, while transition to state 3 indicates the beginning of a localised attack. In this paper, the metastability state of passive films on CRA is studied in order to find a suitable model for predicting the transition from metastability (state 2) to localised corrosion (state 3). Samples are tested for properties such as frequency and charge quantity of metastability phenomena, and time versus survival probability distribution is also investigated. Our working hypothesis is that localised corrosion can be described by a Markov chain stochastic process. Using this model, two indexes are calculated for localised corrosion resistance, and their use in establishing a ranking of specific systems is considered.     

Collective dynamics modeling of polydisperse particulate systems via Markov chains

This paper develops an efficient approach to modeling and analyzing the overall dynamics of polydisperse particulate systems, exemplified using a rotating drum with horizontal axis, under both constant and time-varying operating conditions. This approach captures the collective dynamics using stochastic models in the form of Markov chains. The characteristics of such dynamics can be obtained from the Markov chains operator. It provides a systematic way to the analysis of collective dynamical features of particle movements. The obtained operators are used to estimate the spatial particle distribution and the degree of particulate mixing as examples of collective dynamic features of polydisperse particulate systems. In this paper, Markov chains models were developed from discrete element method simulation results to show the effectiveness of the proposed approach.     

振荡流反应器的物料停留时间分布模型研究

提出了一个基于马尔柯夫链（Markov chains）的考虑腔室间返混的振荡流反应器物料停留时间分布模型。通过对在内径50mm,长1．95m的振荡流反应器进行的理想脉冲示踪试验数据的统计分析,给出了模型的唯一参数回流比R的经验计算公式。发现在试验条件下,存在一个与最小回流比R相对应的振荡条件。这振荡条件可表示为振荡流雷诺数（Reo）与净流雷诺数（Ren）的比值ζ,其范围为1．6〈ζ〈2．5。     

Remarks on random residence time distributions

A discrete stochastic mixing model for chemical reactor; is presented here. The turbulent flow system has been modeled as a network of ideally mixed compartments with interconnecting flows that are random variables. The model is particularly useful for studying the statistics of RTD and of the output concentration in a chemical reactor. Some computations of confidence intervals of concentration using information about the stochastic nature of flows are presented.     

A TIME SERIES MODEL WITH SUDDENLY CHANGING PARAMETERS

Abstract. A process X_t = θ_t + e , is investigated where e_t is a strict white noise and θ_t is a Markov chain with two real states. A realization of X_t fluctuates around two levels which correspond to the two states of θ_t . Formulae for the extrapolation of the process X_t and for the mean square error of the extrapolation are derived. The moments of X_t and its covariance function are calculated. The results are used to derive moment estimators for the parameters of the model.     

Toxicity in sequential dose-response experiments

Often, in dose-response studies, it is desirable to arrange treatments in a region defined by the unknown surface. We accomplish such arrangements using sequential designs that are functions of previous outcomes. Here, for a class of randomized up-and-down designs for dichotomous responses (e.g., toxicity/no toxicity) and predetermined sample size, distributional results for the total number of toxic responses are derived. These results are useful in selecting sequential design parameters and have obvious ethical implications.     

RANDOM COEFFICIENT AUTOREGRESSIVE PROCESSES:A MARKOV CHAIN ANALYSIS OF STATIONARITY AND FINITENESS OF MOMENTS

Abstract. Simple yet practically efficient conditions for the ergodicity of a Markov chain on a general state space have recently been developed. We illustrate their application to non-linear time series models and, in particular, to random coefficient autoregressive models.
As well as ensuring the existence of a unique stationary distribution, geometric rates of convergence to stationarity are ensured. Moreover, sufficient conditions for the existence and convergence of moments can be determined by a closely related method. The latter conditions, in particular, are new.     

Modeling of Sewage Sludge Flow in a Continuous Paddle Dryer

A model based on the theory of Markov chains has been developed to represent the residence time distribution (RTD) of municipal sewage sludge in a continuous paddle dryer. The flow of dry solids is described by a chain of n perfectly mixed cells, n corresponding to the number of paddles attached to the shaft. The transition probabilities between the cells are governed by two parameters: the parameter of internal recirculation, R, and the solids hold-up, Hu. In the absence of available correlation, both parameters are identified by fitting the model to experimental RTD data. The model demonstrates its ability to describe the sludge flow in a continuous lab-scale paddle dryer. A sensitivity analysis highlights that R is critical for the treatment uniformity while Hu controls the mean residence time and thus the final moisture content.     

超声法提取甘草蔓籽油的研究

采用超声法提取甘草蔓籽油,通过单因素试验和正交试验,以甘草蔓籽油提取率为考察指标,对超声法提取甘草蔓籽油的工艺进行了优化。结果表明:选用石油醚作为萃取溶剂,料液比为1∶8(质量/体积)、超声功率为400W、温度为50℃、超声时间为30min,此条件下甘草蔓籽油的得率达35.37%,为进一步开发甘草蔓籽油提供了科学依据。     

Dynamic response of transiently trapped entanglements in polymer networks

The structure and viscoelastic response of polymer networks are highly sensitive to the presence of pendant chains. These imperfections, that are unavoidable produced during a cross-linking reaction, reduce the cross-linking density and affect the damping response of elastomers. In this work the dynamics of pendant chains present in a cross-linked network is investigated using end-linked poly(dimethyl-siloxane) networks with well defined structure. For this purpose, model networks containing 10 and 20 wt% of two different monodisperse pendant chains with molecular weights well above the critical entanglement molecular weight and some of their blends were prepared. It was found that, within this range of concentration of pendant chains, the long-time dynamic response of the networks was nearly insensitive to the content of pendant material but deeply influenced by the average molar mass of these defects. While the equilibrium behavior of the networks can be well described by a mean field theory for rubber elasticity, the long time relaxational dynamics can be rationalized in terms of the Pearson-Helfand picture for the arm retraction process. Within this theoretical picture, the dynamics can be explained in terms of the molecular architecture of the network, the Rouse time and the weight average molar mass of the pendant material.     

Different diffusion behavior of cyclic chains under confinement

Molecular dynamics simulations of merging process of two isolated cyclic chains and that of linear chains have been performed, in order to find the difference between the two kinds of chain in bulk and in vacuum, where surface of the system restrains thousands of configurations showing up. Analysis indicates that in such confinement the chain ends at most moments float on the surface layer, and their mobility is much larger than the mean value of all atoms in linear chains, or that in cyclic chains. Comparison of the merging processes of cyclic chains and their linear counterparts was intensively carried out by several means of analyzing the trajectory files in statics and in dynamics. It was found that the segments of cyclic chains showed almost the same behavior of motion with that of linear chains. This is different diffusion behavior from that in bulk systems, where the cyclic chain has much higher diffusion rate. This modeling therefore indicates that in these confined systems because of the surface energy, the end groups are involuntarily kept on the surface, and lost the capacity of leading chain reptation through the other polymer chains, which is possibly the origin that the difference of diffusion behavior between the linear chain and the cyclic chain in the bulk almost disappears in the case of the confinement.     

Configurational statistics of copolymers prepared by complex-radical polymerization

Radical copolymerization is considered theoretically taking into account the effect of complexing on the configurational statistics of macromolecules formed. Akinetic model has been developed that considers, apart from the ordinary addition of single monomer units to a propagating chain, the possible addition of monomer unit pairs along with a complexing agent in the form of a ternary complex. Within the framework of this model, the problem of calculating the probabilities of formation of any sequences of monomer units (taking into account their microtacticity) in a macromolecule has been rigorously solved as well as the problem of finding the composition distribution of the copolymer formed. It has been shown that this distribution is described by a conventional Gauss law and the appropriate parameters are given. Possible generalizations of the suggested approach are indicated.