Steady Viscous Flow in a Trapezoidal Cavity

The flow in a trapezoidal cavity (including the rectangular and triangular cavities) with one moving wall is studied numerically by finite differences with special treatment in the corners. It is found that streamlines and vorticity distributions are sensitive to geometric changes. The mean square law for core vorticity is valid for the rectangle but ceases to be valid for the triangular cavity

Improvement in the Reproducibility and Accuracy of DNA Microarray Quantification by Optimizing Hybridization Conditions

BACKGROUND: DNA microarrays, which have been increasingly used to monitor mRNA transcripts at a global level, can provide detailed insight into cellular processes involved in response to drugs and toxins. This is leading to new understandings of signaling networks that operate in the cell, and the molecular basis of diseases. Custom printed oligonucleotide arrays have proven to be an effective way to facilitate the applications of DNA microarray technology. A successful microarray experiment, however, involves many steps: well-designed oligonucleotide probes, printing, RNA extraction and labeling, hybridization, and imaging. Optimization is essential to generate reliable microarray data. RESULTS: Hybridization and washing steps are crucial for a successful microarray experiment. By following the hybridization and washing conditions recommended by an oligonucleotide provider, it was found that the expression ratios were compressed greater than expected and data analysis revealed a high degree of non-specific binding. A series of experiments was conducted using rat mixed tissue RNA reference material (MTRRM) and other RNA samples to optimize the hybridization and washing conditions. The optimized hybridization and washing conditions greatly reduced the non-specific binding and improved the accuracy of spot intensity measurements. CONCLUSION: The results from the optimized hybridization and washing conditions greatly improved the reproducibility and accuracy of expression ratios. These experiments also suggested the importance of probe designs using better bioinformatics approaches and the need for common reference RNA samples for platform performance evaluation in order to fulfill the potential of DNA microarray technology

Preconditioned Iterative Methods for Sparse Linear Algebra Problems Arising in Circuit Simulation

The DC operating point of a circuit may be computed by tracking the zero curve of an associated artificial-parameter homotopy. Homotopy algorithms exist that are globally convergent with probability one for the DC operating point problem. These algorithms require computing the one-dimensional kernel of the Jacobian matrix of the homotopy mapping at each step along the zero curve, and hence the solution of a linear system of equations at each step. These linear systems are typically large, highly sparse, non-symmetric and indefinite. Several iterative methods which are applicable to such problems, including Craig's method, GMRES(k), BiCGSTAB, QMR, KACZ, and LSQR, are applied to a suite of test problems derived from simulations of actual bipolar circuits. Preconditioning techniques considered include incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method and preconditioner