Correspondence between one- and two-equation models for solute\ud transport in two-region heterogeneous porous media

In this work, we study the transient behavior of upscaled models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the time scale of interest (t) is smaller than the characteristic time (T1) for the relaxation of the effective macroscale parameters (i.e., when t ≤ T1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (T1) (i.e., when t » T1); and (3) a one-equation, time-asymptotic formulation (1eq∞). This model can be adopted when (t) is significantly larger than the time scale (T2) associated with exchange processes between the two regions (i.e., when t » T2). In order to obtain some physical insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in simple cases. The main result of this paper is to show that there is weak long-time convergence of the solution of (2eq) toward the solution of (1eq∞) in terms of standardized moments but, interestingly, not in terms of centered moments. Physically, our interpretation of this result is that the spreading of the solute is dominating higher order non-zero perturbations in the asymptotic regime

Quality Assessment for CRT and LCD Color Reproduction Using a Blind Metric

This paper deals with image quality assessment that is capturing the focus of several research teams from academic and industrial parts. This field has an important role in various applications related to image from acquisition to projection. A large numbers of objective image quality metrics have been developed during the last decade. These metrics are more or less correlated to end-user feedback and can be separated in three categories: 1) Full Reference (FR) trying to evaluate the impairment in comparison to the reference image, 2) Reduced Reference (RR) using some features extracted from an image to represent it and compare it with the distorted one and 3) No Reference (NR) measures known as distortions such as blockiness, blurriness,. . .without the use of a reference. Unfortunately, the quality assessment community have not achieved a universal image quality model and only empiricalmodels established on psychophysical experimentation are generally used. In this paper, we focus only on the third category to evaluate the quality of CRT (Cathode Ray Tube) and LCD (Liquid Crystal Display) color reproduction where a blind metric is, based on modeling a part of the human visual system behavior. The objective results are validated by single-media and cross-media subjective tests. This allows to study the ability of simulating displays on a reference one

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer

We present an analytical and numerical stability analysis of Soret-driven convection in a porous cavity saturated by a binary fluid. Both the mechanical equilibrium solution and the monocellular flow obtained for particular ranges of the physical parameters of the problem are considered. The porous cavity, bounded by horizontal infinite or finite boundaries, is heated from below or from above. The two horizontal plates are maintained at different constant temperatures while no mass flux is imposed. The influence of the governing parameters and more particularly the role of the separation ratio, characterizing the Soret effect and the normalized porosity, are investigated theoretically and numerically. From the linear stability analysis, we find that the equilibrium solution loses its stability via a stationary bifurcation or a Hopf bifurcation depending on the separation ratio and the normalized porosity of the medium. The role of the porosity is important, when it decreases, the stability of the equilibrium solution is reinforced. For a cell heated from below, the equilibrium solution loses its stability via a stationary bifurcation when the separation ratio >0(Le,), while for 0, while a stationary or an oscillatory bifurcation occurs if mono the monocellular flow loses stability via a Hopf bifurcation. As the Rayleigh number increases, the resulting oscillatory solution evolves to a stationary multicellular flow. For a cell heated from above and <0, the monocellular flow remains linearly stable. We verified numerically that this problem admits other stable multicellular stationary solutions for this range of parameters

A new model for molecule exchange in the brain microvascular system: consequences of capillary occlusions in Alzheimer's disease

The brain microvascular system is a key actor in Alzheimer’s disease (AD) development. Indeed, a significant decrease of cerebral blood flow is the earliest biomarker of AD. In vivo TPLSM of cortical vasculature in APP/PS1 mice suggests the mechanism underlying the blood flow reduction is capillary occlusions. Leucocytes adhere to inflamed vessel walls and limit the flow. The impact of capillary occlusions on blood flow has been quantified numerically in large (>10000 vessels) anatomical networks in humans and mice. The regional blood flow has been found to depend linearly with no threshold effect on the fraction of capillary occlusions, so that a small fraction of stalls (2-4%) yields a significant decrease in blood flow (5-12%). Such flow decrease has a strong impact on nutrient delivery and waste clearance. That is why we devised a new model to study the effect of capillary stalling on molecule transport. The geometry of anatomical networks is too complex to use classic numerical approaches like finite elements. Instead, our model, inspired by pore-network approaches, reduces computational costs while capturing most of the underlying physics. To derive this model, we apply upscaling methods to the 3D transport equations within each vessel to obtain 1D average equations along the axis. Contrary to previous models, this new formulation describes accurately radial concentration gradients, capturing effects like longitudinal dispersion. We further use a Green’s function formulation to calculate the concentration fields inside the tissue where diffusion and reaction occur. The coupling between vessels and tissues is modelled using a membrane condition representing the blood brain barrier. This new molecule transport model is coupled with our previously validated blood flow model to examine the effects of capillary stalling on molecular exchange in transient and stationary regimes in anatomical networks. In particular, in stationnary regimes, we demonstrate an increase of the extraction coefficient with the proportion of stalled capillaries, which does not compensate for the associated blood flow reduction

Synthesis and White-Light Emission of ZnO/HfO2: Eu Nanocables

ZnO/HfO2:Eu nanocables were prepared by radio frequency sputtering with electrospun ZnO nanofibers as cores. The well-crystallized ZnO/HfO2:Eu nanocables showed a uniform intact core–shell structure, which consisted of a hexagonal ZnO core and a monoclinic HfO2 shell. The photoluminescence properties of the samples were characterized. A white-light band emission consisted of blue, green, and red emissions was observed in the nanocables. The blue and green emissions can be attributed to the zinc vacancy and oxygen vacancy defects in ZnO/HfO2:Eu nanocables, and the yellow–red emissions are derived from the inner 4f-shell transitions of corresponding Eu3+ ions in HfO2:Eu shells. Enhanced white-light emission was observed in the nanocables. The enhancement of the emission is ascribed to the structural changes after coaxial synthesis

Upscaling Flow and Transport Processes

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