Adsorption in columns packed with porous adsorbent particles having partially fractal structures

A mathematical model is constructed and solved that could describe the dynamic behavior of the adsorption of a solute of interest in single and stratified columns packed with partially fractal porous adsorbent particles. The results show that a stratified column bed whose length is the same as that of a single column bed, provides larger breakthrough times and a higher dynamic utilization of the adsorptive capacity of the particles than those obtained from the single column bed, and the superior performance of the stratified bed becomes especially more important when the superficial velocity of the flowing fluid stream in the column is increased to accommodate increases in the system throughput. This occurs because the stratified column bed provides larger average external and intraparticle mass transfer and adsorption rates per unit length of packed column. It is also shown that increases in the total number of recursions of the fractal and the ratio of the radii between larger and smaller microspheres that make up the partially fractal particles, increase the intraparticle mass transfer and adsorption rates and lead to larger breakthrough times and dynamic utilization of the adsorptive capacity of the particles. The results of this work indicate that highly efficient adsorption separations could be realized through the use of a stratified column comprised from a practically reasonable number of sections packed with partially fractal porous adsorbent particles having reasonably large (i) total number of recursions of the fractal and (ii) ratio of the radii between larger and smaller microspheres from which the partially fractal particles are made from. It is important to mention here that the physical concepts and modeling approaches presented in this work could be, after a few modifications of the model, applied in studying the dynamic behavior of chemical catalysis and biocatalysis in reactor beds packed with partially fractal porous catalyst particles.     

Fractal Aperture Distribution of Activated Carbon Fiber and Adsorption Behavior to Low‐Density Benzene Steam

Based on the J(x) fractal distribution function of aperture given by Jaroniec, this article suggests another function K(x), a variant of J(x) but offering new insight. We then use these two functions to characterize three kinds of activated carbon fiber (ACF) of different specific areas. This article also provides the fractal distribution of the aperture and the isotherm of nonpolarity benzene steam on the ACF specimens and the relationship between them.     

Contact Angle Determined by Spontaneous Imbibition in Porous Media: Experiment and Theory

In this paper, a theoretical model was established to determine the contact angle by introducing a new defined effective capillary radius into the Lucas–Washburn equation. Based on the theoretical model, capillary rise experiments of water imbibed by different glass beads were carried out to measure the contact angle; the results were similar to the available data published in the literature. In addition, the model was modified to take account of the dynamic contact angle, according to the experimental data. The influence of the dynamic contact angle on the movement of the spontaneous imbibition was studied.     

On global stability of an HIV pathogenesis model with cure rate

In this paper, applying both Lyapunov function techniques and monotone iterative techniques, we establish new sufficient conditions under which the infected equilibrium of an HIV pathogenesis model with cure rate is globally asymptotically stable. By giving an explicit expression for eventual lower bound of the concentration of susceptible CD4⁺ T cells, we establish an affirmative partial answer to the numerical simulations investigated in the recent paper [Liu, Wang, Hu and Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Analysis RWA (2011) 12 : 2947–2961]. Our monotone iterative techniques are applicable for the small and large growth rate in logistic functions for the proliferation rate of healthy and infected CD4⁺ T cells. Copyright © 2014 John Wiley & Sons, Ltd.     

On the stability of impulsive functional differential equations with infinite delays

In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results. Copyright © 2014 John Wiley & Sons, Ltd.     

Synchronization of multiple bursting neurons ring coupled via impulsive variables

Synchronization behavior of bursting neurons is investigated in a neuronal network ring impulsively coupled, in which each neuron exhibits chaotic bursting behavior. Based on the Lyapunov stability theory and impulsive control theory, sufficient conditions for synchronization of the multiple systems coupled with impulsive variables can be obtained. The neurons become synchronous via suitable impulsive strength and resetting period. Furthermore, the result is obtained that synchronization among neurons is weakened with the increasing of the reset period and the number of neurons. Finally, numerical simulations are provided to show the effectiveness of the theoretical results.© 2014 Wiley Periodicals, Inc. Complexity 21: 29–37, 2015     

Robust sampled‐data H∞ control for mechanical systems

This article addresses the issue of robust sampled‐data control for a class of uncertain mechanical systems with input delays and linear fractional uncertainties which appear in all the mass, damping, and stiffness matrices. Then, a novel Lyapunov–Krasovskii functional is constructed to obtain sufficient conditions under which the uncertain mechanical system is robustly, asymptotically stable with disturbance attenuation level about its equilibrium point for all admissible uncertainties. More precisely, Schur complement and Jenson's integral inequality are utilized to substantially simplify the derivation of the main results. In particular, a set of sampled‐data controller is designed in terms of the solution of certain linear matrix inequalities that can be solved effectively using available MATLAB software. Finally, a numerical example with simulation result is provided to show the effectiveness and less conservativeness of the proposed sampled‐data control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 19–29, 2015     

Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal

In this paper, we investigate the dynamical behavior of two nonlinear models for viral infection with humoral immune response. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cells. The intrinsic growth rate of uninfected cells, incidence rate of infection, removal rate of infected cells, production rate of viruses, neutralization rate of viruses, activation rate of B cells and removal rate of B cells are given by more general nonlinear functions. The second model is a modification of the first one by including an eclipse stage of infected cells. We assume that the latent-to-active conversion rate is also given by a more general nonlinear function. For each model we derive two threshold parameters and establish a set of conditions on the general functions which are sufficient to determine the global dynamics of the models. By using suitable Lyapunov functions and LaSalle’s invariance principle, we prove the global asymptotic stability of the all equilibria of the models. We perform some numerical simulations for the models with specific forms of the general functions and show that the numerical results are consistent with the theoretical results.     

Gelation Kinetics-Structure Analysis of pH-triggered Low Molecular Weight Hydrogelators

Properties such as shear modulus, gelation time, structure of supramolecular hydrogels are strongly dependent on self-assembly, gelation triggering mechanism and processes used to form the gel. In our work we extend reported rheology analysis methodologies to pH-triggered supramolecular gels to understand structural insight using a model system based on N−N’ Dibenzoyl-L-Cystine pH-triggered hydrogelator and Glucono-δ-Lactone as the trigger. We observed that Avrami growth model when applied to time-sweep rheological data of gels formed at lower trigger concentrations provide estimates of fractal dimension which agree well compared with visualization of the microstructure as seen via Confocal Laser Scanning Microscopy, for a range of gelator concentrations.     

初始状态对自组织演化过程的影响

从实验上系统研究了在强电场下处于介质中的大量金属小球从不同初始状态通过自组织演化为分形的过程;用Sandbox方法定量分析了最终形成的稳定树枝状分形的维数。结果表明:不同初始状态形成分形的过程完全不同,但最终的树枝状分形的维数基本相同。分析认为,小球之间的相互作用存在临界作用距离,不同初始状态相邻小球之间的平均间距不同,因而演化过程不同;而维数相同正是系统耗散相同的体现。