A Closed‐Loop Control Strategy for Producing Nitrile Rubber of Uniform Chemical Composition in a Semibatch Reactor: A Simulation Study

To improve the quality of industrial nitrile rubbers, the copolymer chemical composition, p_A(t), should ideally be kept constant along the reaction. This work proposes a closed‐loop control strategy for the semibatch operation of the reactor with the aim of regulating p_A(t) within a reduced range of variability. The proposed strategy is evaluated by simulating a mathematical model of the process. To this effect, a simplified mathematical model of the reaction is first derived and then utilized to obtain a suboptimal control law and a soft‐sensor that estimates the polymerization rates. The suboptimal control law is compensated by adding a term proportional to errors in p_A(t). The simulated example considers the production of the low‐composition AJLT grade, with the copolymerization reaction represented by a detailed mathematical model adjusted to an industrial plant. Due to the high performance of the soft‐sensor, the simulation results suggest that the proposed closed‐loop strategy is efficient to adequately regulate p_A(t) in spite of structural and parametric uncertainties, while other quality variables remained practically unaffected.     

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

Pattern formation in a variable diffusion predator–prey model with additive Allee effect

This paper deals with a variable diffusion predator–prey model with additive Allee effect. A good understanding of the existence of steady states is gained for the case  $\sigma =0$. The result shows that the reduce problem has multiple solutions. Moreover, by applying the singular perturbation method, we give a proof of existence of large amplitude solutions when  $\sigma$ is sufficiently small.     

Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation

We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time.     

An Insight into the Diffusion of Unsaturated Polyester (UP) Resin into Expanded Graphite (EG) to Improve the Mechanical Properties of the UP/EG Composites

Abstract

Polymer/expanded graphite (EG) nanocomposites have great importance in many industrial applications mainly due to their high electrical/thermal conductivity or flame retardancy. However, to fully employ the benefits of polymer/EG nanocomposites one must consider the high degree of porosity of EG. The high degree of porosity of EG can deteriorate the composites’ mechanical properties if the polymer chains cannot diffuse completely into the EG pores. In this article, an insight is given into the diffusion of unsaturated isophthalic polyester (UP) resin, consisting of a combination of maleic anhydride and isophthalic anhydride in the resin backbone, with two viscosities, into the pores of the EG particles of various degrees of porosity. The diffusion experiments were carried out on compressed EG tablets with the same density but different porosity due to the different porosity of the EG particles. The results showed that the diffusion rate of the UP resin with higher viscosity slightly decreased when the EG porosity decreased but, in the opposite way, it strongly increased for the low viscosity UP resin. The EG nanocomposites samples were molded at varying pressures. The micrographs of the fractured surfaces of the EG nanocomposites showed that the EG pores were not filled with resin, thus the EG nanocomposites had residual pores. It was found that composites containing EGs with higher expansion ratio and larger particles and pores showed larger residual pores. Furthermore, the composites prepared with the more viscous UP resin showed more residual pores. By applying a pressure of 10?bar instead of 1?bar, a reduction of 7–20% in the residual pores of the nanocomposites was observed which led to improved mechanical properties by up to 20% in flexural strength for the EG with the highest expansion ratio.     

Modelling non-equilibrium self-assembly from dissipation

Non-equilibrium self-assembly is ubiquitous in physico-chemical and biological systems, and manifests itself at different scales, ranging from the molecular to the cosmological. The formation of microtubules, gels, cells and living beings among many others takes place through self-assembly under nonequilibrium conditions. We propose a general thermodynamic non-equilibrium model to understand the formation of assembled structures such as gels and Liesegang patterns and at the same time able to describe the kinetics and the energetics of the structure formation process. The model is supported for a global mechanism to obtain self-assembled structures from building blocks via activation, deactivation, assembly, and disassembly processes. It is proposed that the resulting structures can be characterised by a structural parameter. Our model may contribute to a better understanding of non-equilibrium self-assembly processes and give deeper insight as to how to obtain a specific structural architecture to materials, such as hydrogels which are of great importance in the design of advanced devices and novel materials.     

基于Retinex理论与概率非局部均值的红外图像增强方法

针对传统红外图像增强算法中细节模糊及过度增强的问题,提出了一种基于Retinex理论与概率非局部均值相结合的红外图像增强方法.首先通过单尺度Retinex方法调整图像中过暗与过亮部分的灰度级;然后利用概率非局部均值对图像进行分解处理得到基本层与细节层,对基本层采用直方图均衡化拉伸对比度,对细节层采用非线性函数进行增强;最后,将不同层次的结果融合得到对比度与细节增强的红外图像.用该方法对多组不同场景的红外图像进行仿真实验,并将其与多种增强方法进行主、客观对比分析,结果表明所提方法在红外图像的细节及对比度增强方面都获得了更好的效果.     

砂岩方梁断裂过程区范围的实验确定方法

裂纹前端的断裂过程区是引起岩石非线性断裂及尺寸效应的主要原因。利用数字图像相关技术对砂岩开展了三点弯曲梁实验,获得观测区域高精度的全场位移和应变数据,根据断裂韧带区域水平位移和水平应变的分布特征,结合裂尖岩石颗粒变化的微观分析,提出采用裂纹尖端水平位移波动性和水平应变突变性所得到的波动系数和水平应变突变值,确定断裂过程区形状和临界尺寸的方法。结果表明:砂岩断裂过程区的形状为不规则的狭长带状区域,断裂过程区的临界长度为11~13mm,临界宽度为1.58~2.36mm。断裂过程区区域内形变在趋向裂尖时呈指数增加,但其单位区域内的形变增量呈波动状态。该方法能够更加准确判断岩石断裂过程区的范围,有助于分析岩石的非线性断裂特性。     

An inequality connecting entropy distance,Fisher Information and large deviations

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.     

Linearized filtering of affine processes using stochastic Riccati equations

We consider an affine process $X$ which is only observed up to an additive white noise, and we ask for the law of $X_t$, for some $t>0$, conditional on all observations up to time $t$. This is a general, possibly high dimensional filtering problem which is not even locally approximately Gaussian, whence essentially only particle filtering methods remain as solution techniques. In this work we present an efficient numerical solution by introducing an approximate filter for which conditional characteristic functions can be calculated by solving a system of generalized Riccati differential equations depending on the observation and the process characteristics of $X$. The quality of the approximation can be controlled by easily observable quantities in terms of a macro location of the signal in state space. Asymptotic techniques as well as maximization techniques can be directly applied to the solutions of the Riccati equations leading to novel very tractable filtering formulas. The efficiency of the method is illustrated with numerical experiments for Cox–Ingersoll–Ross and Wishart processes, for which Gaussian approximations usually fail.