Scaling laws and thermodynamic analysis for vascular branching of microvessels

When blood flows through small vessels, the two-phase nature of blood as a suspension of red cells (erythrocytes) in plasma cannot be neglected, and with decreasing vessel size, a homogeneous continuum model become less adequate in describing blood flow. Following the Haynes’ marginal zone theory, and viewing the flow as the result of concentric laminae of fluid moving axially, the present work provides models for fluid flow in dichotomous branching composed by larger and smaller vessels, respectively. Expressions for the branching sizes of parent and daughter vessels, that provides easier flow access, are obtained by means of a constrained optimization approach using the Lagrange multipliers. This study shows that when blood behaves as a Newtonian fluid, Hess – Murray law that states that the daughters-to-parent diameter ratio must equal to 2^(-1/3) is valid. However, when the nature of blood as a suspension becomes important, the expression for optimum branching diameters of vessels is dependent on the separation phase lengths. It is also shown that the same effect occurs for the relative lengths of daughters and parent vessels. For smaller vessels (e. g., arterioles and capillaries), it is found that the daughters-to-parent diameter ratio may varies from 0,741 to 0,849, and the daughters-to-parent length ratio varies from 0,260 to 2,42. For larger vessels (e. g., arteries), the daughters-to-parent diameter ratio and the daughters-to-parent length ratio range from 0,458 to 0,819, and from 0,100 to 6,27, respectively. In this paper, it is also demonstrated that the entropy generated when blood behaves as a single phase fluid (i. e., continuum viscous fluid) is greater than the entropy generated when the nature of blood as a suspension becomes important. Another important finding is that the manifestation of the particulate nature of blood in small vessels reduces entropy generation due to fluid friction, thereby maintaining the flow through dichotomous branching vessels at a relatively lower cost.

On The Use of Genetic Algorithms for Parameter Identification in Anaerobic Digestion Modelling

Anaerobic digestion (AD) of wastewater is a very interesting option for waste valorization, energy production and environment protection. It is a complex, naturally occurring process that can take place inside bioreactors. The capability of predicting the operation of such bioreactors is important to optimize the design and the operation conditions of the reactors, which, in part, justifies the numerous AD models presently available. The existing AD models are not universal, have to be inferred from prior knowledge and rely on existing experimental data. Among the tasks involved in the process of developing a dynamical model for AD, the estimation of parameters is one of the most challenging. This paper presents the identifiability analysis of a nonlinear dynamical model for a batch reactor. Particular attention is given to the structural identifiability of the model, which considers the uniqueness of the estimated parameters. To perform this analysis, the GenSSI toolbox was used. The estimation of the model parameters is achieved with genetic algorithms (GA) which have already been used in the context of AD modelling, although not commonly. The paper discusses its advantages and disadvantages.

Confidence intervals for large non- centrality parameter

We use asymptotic linearity to derive confidence intervals for large noncentrality parameters. These results enable us to measure relevance of effects and interactions in multifactors models when we get highly statistically significant the values of F tests statistics. We show how to use our approach by considering two sets of data as application examples.

Cloud parameter retrievals from Meteosat and their effects on the shortwave radiation at the surface

A method based on Spinning Enhanced Visible and Infrared Imager (SEVIRI) measured reflectance at 0.6 and 3.9 µm is used to retrieve the cloud optical thickness (COT) and cloud effective radius (re) over the Iberian Peninsula. A sensitivity analysis of simulated retrievals to the input parameters demonstrates that the cloud top height is an important factor in satellite retrievals of COT and re with uncertainties around 10% for small values of COT and re; for water clouds these uncertainties can be greater than 10% for small values of re. The uncertainties found related with geometries are around 3%. The COT and re are assessed using well-known satellite cloud products, showing that the method used characterize the cloud field with more than 80% (82%) of the absolute differences between COT (re) mean values of all clouds (water plus ice clouds) centred in the range from ±10 (±10 µm), with absolute bias lower than 2 (2 μm) for COT (re) and root mean square error values lower than 10 (8 μm) for COT (re). The cloud water path (CWP), derived from satellite retrievals, and the shortwave cloud radiative effect at the surface (CRESW) are related for high fractional sky covers (Fsc >0.8), showing that water clouds produce more negative CRESW than ice clouds. The COT retrieved was also related to the cloud modification factor, which exhibits reductions and enhancements of the surface SW radiation of the order of 80% and 30%, respectively, for COT values lower than 10. A selected case study shows, using a ground-based sky camera that some situations classified by the satellite with high Fsc values correspond to situations of broken clouds where the enhancements actually occur. For this case study, a closure between the liquid water path (LWP) obtained from the satellite retrievals and the same cloud quantity obtained from ground-based microwave measurements was performed showing a good agreement between both LWP data set values.

Genetic Algorithms for Parameter Estimation in Circadian Model

This paper proposes an algorithm to estimate two parameter values vs, transcription of frq gene, and vd, maximum rate of FRQ protein degradation for an existing 3rd order Neurospora model in literature. Details of the algorithm with simulation results are shown in this paper.