The Crystallographic study suggests a blending model of chemical solutions over a network of interconnected pipes and pumps. The master goal of this current study is to rationalize a number of quality requirements in the network´s output. It is well known that the traditional methodology and strategy used to tackle this kind of technical problem has been to consider a modeling methodology based upon flow and quality. In this study, we suggest a new model and the overall method has been focused on the actual feasibility and throughout the course of the current study it is shown that, the whole process is reduced to a non-convex problem.
A rather complete and informative analysis of the intermolecular and intermolecular potentials is put forward with reference to the lanthanide type systems, such as in the, space group. A particular situation occurs in both extreme of the series, say for and respectively. The thirteen trivalent lanthanide ions, moving along the series from to , for these ions the shell is not fully occupied and therefore the physical and chemical properties are indeed, somehow challenging and interesting to examine using structural, spectroscopic and theoretical methods and model calculations.
Using these methods of mining and mineralogy there has been development and many implementation in the new model by employing a numerical analysis method and the results obtained show up to be quite sensible and consistent so as to provide sound and realistic solutions. This area of research is quite relevant since new mobile technology; digital cameras, laptops and electro mobility and so forth have become essential to humankind. It is, well known that the operational availability is limited by the quality of the batteries employed. Prolonged operative life per load requirements has motivated research aimed to develop a new technology of energy storage. There are several options, nevertheless in this specific study we have chosen batteries based in Lithium since they have become attractive and highly efficient, due to the characteristic of this chemical element (Z=3). In this research a feasibility problem is modeling using a least square objective function over a convex polyhedral, where the only variables are the ones related to flow and the quality variables are “transferred” to the objective function, reducing the complexity of the constraints which makes the problem amenable to traditional techniques which are easy to implement. The Frank-Wolf´s method was used to solve the complex problem with a quite satisfactory performance. From a model viewpoint, this is a new approach and we believe that this methodology and strategy could seduce researchers to make improvements for the whole model presented in this article.
In this current research work, we have elaborated some physical models and carried out a substantial amount of calculations, so as to estimate the reticular energy and also, employing a thermodynamic Born-Haber cycle, we have been able to make some sound predictions and numerical estimate of heat of formations for the above series of lanthanide type crystals. The calculated energy values associated with these observables seems to be most reasonable, and these follow the expected trends, as may be anticipated from theoretical and experimental grounds. Both, the advantages and disadvantages of the current model calculations, have been tested against other previous calculations performed.