Investigation of transport phenomena in a hybrid ion exchange-electrodialysis system for the removal of copper ions

Hybrid ion exchange electrodialysis processes allow the removal of metal ions from dilute waste liquids and the recovery of more concentrated solutions. The work reported here was aimed at investigating the two steps in the treatment process, namely, adsorption of metal ions onto the packed bed of resin and electromigration (i.e., the transport of these ions in the complex system under the applied electrical field). The case of copper sulfate was investigated. Dowex resins with a cross-linking degree of 2 and 8% were used. The flux of copper through the resin bed and the current efficiency for ion transfer to the cathode compartment were determined as a function of potential gradient and copper ionic fraction in the bed. Apparent diffusion coefficients of Cu²⁺ in the overall system were deduced from the experimental data.     

Averaged control

We analyze the problem of controlling parameter-dependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter.First we consider the problem of controllability for linear finite-dimensional systems and show that a necessary and sufficient condition for averaged controllability is an averaged rank condition, in the spirit of the classical rank condition for linear control systems, but involving averaged momenta of any order of the matrices generating the dynamics and representing the control action.We also describe some open problems and directions of possible research, in particular on the average controllability of evolution partial differential equations. In this context we analyze also the averaged version of a classical optimal control problem for a parameter dependent elliptic equation and derive the corresponding optimality system.     

FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

Solubility of Si3N4 in Liquid SiO2

The nitrogen solubility in the SiO₂-rich liquid in the metastable binary SiO₂-Si₃N₄ system has been determined by analytical TEM to be 1%–4% of N/(O + N) at 1973–2223 K. Analysis of the near edge structure of the electron energy loss peak indicates that nitrogen is incorporated into the silicate network rather than being present as molecular N₂. A regular solution model with a positive enthalpy of mixing for the liquid was used to match the data for the metastable solubility of N in the presence of crystalline Si₃N₄ and to adjust the computed phase diagram. The solubility of Si₃N₄ in fused SiO₂ is far less than reported in liquid silicates also containing Al, Mg, and/or Y. Apparently, these cations act as modifiers that break anion bridges in the silicate network and, thereby, allow further incorporation of Si₃N₄ without prohibitive amounts of network cross-linking. Finally, indications emerged regarding the diffuse nature of the Si₃N₄-SiO₂ interface that leads to amorphous regions of higher N content.     

Preparation of Silicon Carbide/Aluminum Nitride Ceramics Using Organometallic Precursors

Solid solutions of 2H -SiC/AlN can be prepared at temperatures less than 1600°C by rapid pyrolysis ("hot drop") of mixtures of [(Me₃Si)_0.80((CH₂=CH)MeSi)_1.0(MeHSi)_0.35] _n (VPS) or [MeHSiCH₂] _n (MPCS) with [R₂AlNH₂]₃, where R=Et, i -Bu or simply by slow pyrolysis of the precursor mixture in the case of [Et₂AlNH₂]₃. In contrast, slow pyrolysis of mixtures of VPS or MPCS with [ i -Bu₂AlNH₂]₃ yields a composite of 2 H -AlN and 3 C -SiC at 1600°C, which transforms into a single 2 H -SiC/AlN solid solution on heating to 2000°C. The influences of the nature of the precursor and processing conditions on the structure, composition, and purity of the SiC/AlN materials are discussed.     

A unified model for the structure of polymers in semidilute solution

A model is developed to analyse the concentration dependence of the range ξ_? of the monomer pair correlation function. In semidilute solution, three concentration regimes are found for semiflexible molecules and the crossover points between the various regimes are predicted in terms of the characteristic ratio of the chains in dilute solution and in terms of the Flory interaction parameter χ. A simple physical interpretation is given which explains the concentration dependence of ξ_? based on binary contacts initially and then ternary contacts at higher concentration. Temperature-concentration diagrams are developed for several common polymer-solvent systems.     

An efficient procedure for finding best compromise solutions to the multi-objective assignment problem

In this paper, we consider the problem of determining a best compromise solution for the multi-objective assignment problem. Such a solution minimizes a scalarizing function, such as the weighted Tchebychev norm or reference point achievement functions. To solve this problem, we resort to a ranking (or k-best) algorithm which enumerates feasible solutions according to an appropriate weighted sum until a condition, ensuring that an optimal solution has been found, is met. The ranking algorithm is based on a branch and bound scheme. We study how to implement efficiently this procedure by considering different algorithmic variants within the procedure: choice of the weighted sum, branching and bounding schemes. We present an experimental analysis that enables us to point out the best variants, and we provide experimental results showing the remarkable efficiency of the procedure, even for large size instances.     

Smart grid coordination in building HVAC systems: EMPC and the impact of forecasting

Energy consumption by heating, ventilation, and air conditioning (HVAC) systems exhibits a clear correlation with electricity prices. The method of economic model predictive control (EMPC) can be used in conjunction with thermal energy storage (TES) to time-shift power consumption away from periods of high demand to periods of low energy cost. Dynamic electricity pricing and weather condition forecasts can be readily incorporated within this methodology. Unfortunately, the receding horizon nature of this control strategy makes it very susceptible to the quality of the forecasts used. To this end, the development and implementation of several forecasting methods will be discussed. Finally, the EMPC performance of these methods will be assessed on a simple building example using active TES.     

压缩感知中高斯矩阵的优化研究

为了优化高斯矩阵,对部分哈达玛矩阵与高斯矩阵的统计学参数作了对比分析,确定了导致部分哈达玛矩阵信号重构能力好的主要因素,并提出了高斯矩阵优化算法.验证了优化算法对不同规模高斯矩阵的通用性和有效性,确定了优化矩阵对各种稀疏信号重构算法的适用性.最后对优化矩阵的性能作了初步的理论和实验分析,优化矩阵的信号重构能力可达到、甚至超过哈达玛矩阵.研究成果为测量矩阵的分析、设计和优化提供了新的思路和方法.