MICELLE FORMATION BY ANIONIC AND CATIONIC SURFACTANTS IN AQUEOUS 18-CROWN-6 ETHER,P-CYCLODEXTRIN,AND 1,10-PHENANTHROLINE SOLUTIONS AT DIFFERENT TEMPERATURES

The conductances of sodium perfluorooctanoate (SPFO), sodium dodecylsulphate (SDS), dodecyltrimethylammonium bromide (DTAB), and tetradecyltrimethylammonium bromide (TTAB) in 18-crown-6 ether + water (CR+W), p-cyclodextrin + water (CY+W), and 1,10-phenanthroIine + water (Phen+W) mixtures with fixed 4 mM of each additive were determined over the temperature range of 5-55 °C. The conductivity plots for all the surfactants showed single break from which the critical micellization concentration (cmc) and degree of micelle ionization (x) were computed. From the pre and the post micellar slopes of the conductivity curves, the equivalent conductivities of the monomeric (Aass) and the micellar states (Amjc), respectively, were calculated and discussed with respect to the surfactant-additive complexation. It was observed that the micelle formation of all the ionic surfactants irrespective of the nature of their head groups were delayed in CYC+W in comparison to that in CR+W and Phen+W systems over the temperature range studied. The micelle formation of SPFO and SDS in CR+W and Phen+W systems showed stabilization of the respective micelles due to the adsorption of Na⁺-CR and Na+-Phen complexes at the micelle solution interface in comparison to that of DTAB and TTAB.     

A uniqueness theorem of radially symmetric positive stationary solutions for a competition–diffusion system

In this paper, as a first step to study the global structure of solution, we treat a class of reaction–diffusion systems with competitive interaction, and discuss a uniqueness theorem of radially symmetric solutions for the system. To do this, the comparison principle and the shooting method are employed, and the spatial profile is investigated.     

三维多面体网格上扩散方程的保正格式

 针对三维任意(星形)多面体网格, 本文构造了扩散方程的一种单元中心型非线性有限体积格式, 证明了该格式具有保正性. 在该格式设计中, 除引入网格中心量外, 还引入网格节点量和网格面中心量作为中间未知量, 它们将用网格中心未知量线性组合表示, 使得格式仅有网格中心未知量作为基本未知量. 在节点量计算中, 利用网格面上的调和平均点, 设计了一种适用于三维多面体网格的局部显式加权方法. 该格式适用于求解非平面的网格表面和间断扩散系数的问题. 数值例子验证了它对光滑解具有二阶精度和保正性.     

Modeling and analysis of a marine plankton system with nutrient recycling and diffusion

This article describes a nutrient‐phytoplankton‐zooplankton system with nutrient recycling in the presence of toxicity. We have studied the dynamical behavior of the system with delayed nutrient recycling in the first part of the article. Uniform persistent of the system is examined. In the second part of the article, we have incorporated diffusion of the plankton population to the system and dynamical behavior of the system is analyzed with instantaneous nutrient recycling. The condition of the diffusion driven instability is obtained. The conditions for the occurrence of Hopf and Turing bifurcation critical line in a spatial domain are derived. Variation of the system with small periodicity of diffusive coefficient has been studied. Stability condition of the plankton system subject to the periodic diffusion coefficient of the zooplankton is derived. It is observed that nutrient‐phytoplankton‐zooplankton interactions are very complex and situation specific. Moreover, we have obtained different exciting results, ranging from stable situation to cyclic oscillatory behavior may occur under different favorable conditions, which may give some insights for predictive management. © 2014 Wiley Periodicals, Inc. Complexity 21: 229–241, 2015     

Analysis of an aggregation‐based algebraic two‐grid method for a rotated anisotropic diffusion problem

A two‐grid convergence analysis based on the paper [Algebraic analysis of aggregation‐based multigrid, by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), pp. 539–564] is derived for various aggregation schemes applied to a finite element discretization of a rotated anisotropic diffusion equation. As expected, it is shown that the best aggregation scheme is one in which aggregates are aligned with the anisotropy. In practice, however, this is not what automatic aggregation procedures do. We suggest approaches for determining appropriate aggregates based on eigenvectors associated with small eigenvalues of a block splitting matrix or based on minimizing a quantity related to the spectral radius of the iteration matrix. Copyright © 2015 John Wiley & Sons, Ltd.     

The Effects of CO2 Additional on Flame Characteristics in the CH4/N2/O2 Counterflow Diffusion Flame

The effects (chemical, thermal, transport, and radiative) of CO₂ added to the fuel side and oxidizer side on the flame temperature and the position of the flame front in a one-dimensional laminar counterflow diffusion flame of methane/N₂/O₂ were studied. Overall CO₂ resulted in a decrease in flame temperature whether on the fuel side or on the oxidizer side, with the negative effect being more obvious on the latter side. The prominent effects of CO₂ on the flame temperature were derived from its thermal properties on the fuel side and its radiative properties on the oxidizer side. The results also highlighted the differences in the four effects of CO₂ on the position of the flame front on different sides. In addition, an analysis of OH and H radicals and the heat release rate of the main reactions illustrated how CO₂ affects the flame temperature.     

3D MRI of non-Gaussian (3)He gas diffusion in the rat lung

In (3)He magnetic resonance images of pulmonary air spaces, the confining architecture of the parenchymal tissue results in a non-Gaussian distribution of signal phase that non-exponentially attenuates image intensity as diffusion weighting is increased. Here, two approaches previously used for the analysis of non-Gaussian effects in the lung are compared and related using diffusion-weighted (3)He MR images of mechanically ventilated rats. One approach is model-based and was presented by Yablonskiy et al., while the other approach utilizes the second order decay contribution that is predicted from the cumulant expansion theorem. Total lung coverage is achieved using a hybrid 3D pulse sequence that combines conventional phase encoding with sparse radial sampling for efficient gas usage. This enables the acquisition of nine 3D images using a total of only approximately 1 L of hyperpolarized (3)He gas. Diffusion weighting ranges from 0 s/cm(2) to 40 s/cm(2). Results show that the non-Gaussian effects of (3)He gas diffusion in healthy rat lungs are directly attributed to the anisotropic geometry of lung microstructure as predicted by the Yablonskiy model, and that quantitative analysis over the entire lung can be reliably repeated in time-course studies of the same animal.     

Some insights in superdiffusive transport

In a wide range of systems, the relaxation in response to an initial pulse has been experimentally found to follow a nonlinear relationship for the mean squared displacement, of the kind 〈x²(t)〉∝t^α$〈x^2(t)〉\propto t^{\alpha }$, where α$\alpha$ may be greater or smaller than 1. Such phenomena have been described under the generic term of anomalous diffusion. “Lévy flights” stochastic processes lead to superdiffusive behaviour (1<α<2)$(1<\alpha <2)$ and have been recently proposed to model—among the others—the subsurface contaminant spread in highly heterogeneous media under the effects of water flow. In this paper, within the continuous-time random walk (CTRW) approach to anomalous diffusion, we compare the analytical solution of the approximated fractional diffusion equation (FDE) with the Monte Carlo one, obtained by simulating the superdiffusive behaviour of an ensemble of particle in a medium. We show that the two are neatly different as the process approaches the standard diffusive behaviour. We argue that this is due to a truncation in the Fourier space expansion introduced by the FDE approach. We propose a second-order correction to this expansion and numerically solve the CTRW model under this hypothesis: the accuracy of the results thus obtained is validated through Monte Carlo simulation over all the superdiffusive range. The same kind of discrepancy is shown to occur also in the derivation of the fractional moments of the distribution: analogous corrections are proposed and validated through the Monte Carlo approach.     

Dynamics and optimal control in a spatially structured economic growth model with pollution diffusion and environmental taxation

In the first part of this paper we present a spatially structured dynamic economic growth model which takes into account the level of pollution and a possible taxation based on the amount of produced pollution. In the second part we analyze an optimal harvesting control problem with an objective function composed of three terms, namely the intertemporal utility of the decision maker, the space–time average of the level of pollution in the habitat, and the disutility due to the imposition of taxation.