Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG) --- a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume --- is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, \textit{viz.} the usual one-electron density parameter $\rho$ and a new two-electron parameter $\eta$. We outline a systematic strategy to determine a new density functional $E(\rho,\eta)$ across the spectrum of possible $\rho$ and $\eta$ values.Comment: 8 pages, 2 figures, 5 table

Transient integral boundary layer method to calculate the translesional pressure drop and the fractional flow reserve in myocardial bridges

BACKGROUND: The pressure drop – flow relations in myocardial bridges and the assessment of vascular heart disease via fractional flow reserve (FFR) have motivated many researchers the last decades. The aim of this study is to simulate several clinical conditions present in myocardial bridges to determine the flow reserve and consequently the clinical relevance of the disease. From a fluid mechanical point of view the pathophysiological situation in myocardial bridges involves fluid flow in a time dependent flow geometry, caused by contracting cardiac muscles overlying an intramural segment of the coronary artery. These flows mostly involve flow separation and secondary motions, which are difficult to calculate and analyse. METHODS: Because a three dimensional simulation of the haemodynamic conditions in myocardial bridges in a network of coronary arteries is time-consuming, we present a boundary layer model for the calculation of the pressure drop and flow separation. The approach is based on the assumption that the flow can be sufficiently well described by the interaction of an inviscid core and a viscous boundary layer. Under the assumption that the idealised flow through a constriction is given by near-equilibrium velocity profiles of the Falkner-Skan-Cooke (FSC) family, the evolution of the boundary layer is obtained by the simultaneous solution of the Falkner-Skan equation and the transient von-Kármán integral momentum equation. RESULTS: The model was used to investigate the relative importance of several physical parameters present in myocardial bridges. Results have been obtained for steady and unsteady flow through vessels with 0 – 85% diameter stenosis. We compare two clinical relevant cases of a myocardial bridge in the middle segment of the left anterior descending coronary artery (LAD). The pressure derived FFR of fixed and dynamic lesions has shown that the flow is less affected in the dynamic case, because the distal pressure partially recovers during re-opening of the vessel in diastole. We have further calculated the wall shear stress (WSS) distributions in addition to the location and length of the flow reversal zones in dependence on the severity of the disease. CONCLUSION: The described boundary layer method can be used to simulate frictional forces and wall shear stresses in the entrance region of vessels. Earlier models are supplemented by the viscous effects in a quasi three-dimensional vessel geometry with a prescribed wall motion. The results indicate that the translesional pressure drop and the mean FFR compares favourably to clinical findings in the literature. We have further shown that the mean FFR under the assumption of Hagen-Poiseuille flow is overestimated in developing flow conditions

Biological and Non-Biological Methods for Lignocellulosic Biomass Deconstruction

Owing to their abundance and cost-effectiveness, lignocellulosic materials have attracted increasing attention in clean energy technologies over the last decade. However, the complex polymer structure in these residues makes it difficult to extract the fermentable sugars. Therefore, various pretreatment regimes have been used resulting in the breaking of lignocelluloses’ physical and chemical structures, thereby enhancing the availability of the polysaccharides which are subsequently hydrolysed into different biocommodities. This chapter provides an evaluation of some of the latest exploited methodologies that are used in the pretreatment of lignocellulosic materials. Moreover, the chapter discusses the advantages and disadvantages of each method