A Complex-boundary Treatment Method for Finite Volume Schemes with Cut-Cartesian Cell Mesh

In this paper, a second-order accurate method was developed for calculating fluid flows in complex geometries. This method uses cut-Cartesian cell mesh in finite volume framework. Calculus is employed to relate fluxes and gradients along curved surfaces to cell-averaged values. The resultant finite difference equations are sparse diagonal systems of equations. This method does not need repeated polynomial interpolation or reconstruction. Two-dimensional incompressible lid-driven semi-circular cavity flow at two Reynolds numbers was simulated with the current method and second-order accuracy was reached. The current method might be extended to third-order accuracy

Accurate gradient computations at interfaces using finite element methods

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea from \cite{wheeler1974galerkin}. For 2D interface problems, the idea is to introduce a small tube near the interface and introduce the gradient as part of unknowns, which is similar to a mixed finite element method, except only at the interface. Thus the computational cost is just slightly higher than the standard finite element method. We present rigorous one dimensional analysis, which show second order convergence order for both of the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface

Different normalization strategies for microarray gene expression traits affect the heritability estimation

Abstract Several studies have been conducted to assess the influence of genetic variation on genome-wide gene expression profiles measured by the microarray technologies. Due to substantial noise in microarray-based experiments, it has long been recognized that proper normalization is a crucial step to ensure sensitive and reliable downstream analyses. This is especially true when large number of samples were collected and analyzed. In this study, we investigated the impact of different normalization strategies on genome wide linkage analyses, in particular, the estimation of heritability of gene expression traits. We used the Genetics Analysis Workshop 15 Problem 1 data. We found that there are significant differences in the estimated number of genes showing heritability when different normalization strategies were used. RMA (robust multiarray average) and dChip identify 45% and 13% more genes showing heritability than MAS 5.0, respectively. Our study also reveals that a large number of genes show strong "family effect" in their expression levels but no significant heritability. Analysis of their annotation indicates different types of genes were enriched in this group compared to genes showing strong heritability.http://deepblue.lib.umich.edu/bitstream/2027.42/117370/1/12919_2007_Article_2518.pd

Structural comparison of metabolic networks in selected single cell organisms

BACKGROUND: There has been tremendous interest in the study of biological network structure. An array of measurements has been conceived to assess the topological properties of these networks. In this study, we compared the metabolic network structures of eleven single cell organisms representing the three domains of life using these measurements, hoping to find out whether the intrinsic network design principle(s), reflected by these measurements, are different among species in the three domains of life. RESULTS: Three groups of topological properties were used in this study: network indices, degree distribution measures and motif profile measure. All of which are higher-level topological properties except for the marginal degree distribution. Metabolic networks in Archaeal species are found to be different from those in S. cerevisiae and the six Bacterial species in almost all measured higher-level topological properties. Our findings also indicate that the metabolic network in Archaeal species is similar to the exponential random network. CONCLUSION: If these metabolic network properties of the organisms studied can be extended to other species in their respective domains (which is likely), then the design principle(s) of Archaea are fundamentally different from those of Bacteria and Eukaryote. Furthermore, the functional mechanisms of Archaeal metabolic networks revealed in this study differentiate significantly from those of Bacterial and Eukaryotic organisms, which warrant further investigation

A Statistical Model of Pressure Drop Increase with Deposition in Granular Filters

As deposits accumulate in a granular filter, pressure drop across the filter bed required to maintain a constant fluid flow rate may increase. Two pressure drop increase patterns had been observed. In slow sand filters pressure drop remains unchanged for a certain period of time then increases exponentially with the volume of filtrate; in granular aerosol filters pressure drop increases linearly with the amount of deposits from the beginning of the filtration process. New concepts of homogeneous and heterogeneous depositions were introduced in this paper. A statistical model based on these new concepts was developed. This non-linear model was able to reproduce both observed pressure drop increase patterns, including the linear one. Excellent agreements between the present model and experimental measurements were obtained. It was concluded that the two pressure drop increase patterns were indeed caused by different deposit distributions rather than different pressure drop increase mechanisms.Comment: 14 pages, 9 figure

Jamming Transition of Point-to-Point Traffic Through Cooperative Mechanisms

We study the jamming transition of two-dimensional point-to-point traffic through cooperative mechanisms using computer simulation. We propose two decentralized cooperative mechanisms which are incorporated into the point-to-point traffic models: stepping aside (CM-SA) and choosing alternative routes (CM-CAR). Incorporating CM-SA is to prevent a type of ping-pong jumps from happening when two objects standing face-to-face want to move in opposite directions. Incorporating CM-CAR is to handle the conflict when more than one object competes for the same point in parallel update. We investigate and compare four models mainly from fundamental diagrams, jam patterns and the distribution of cooperation probability. It is found that although it decreases the average velocity a little, the CM-SA increases the critical density and the average flow. Despite increasing the average velocity, the CM-CAR decreases the average flow by creating substantially vacant areas inside jam clusters. We investigate the jam patterns of four models carefully and explain this result qualitatively. In addition, we discuss the advantage and applicability of decentralized cooperation modeling.Comment: 17 pages, 14 figure