Model for propagation speed in turbulent channel flows.

The propagation speed Vc of the streamwise velocity fluctuations u' in turbulent channel flows is calculated using direct numerical simulation (DNS) data at four Mach numbers (M=0, 0.8, 2.0, and 3.0). The profiles of Vc are shown to display remarkable similarity at different M. Quantitative models are developed based on a statistical structure called Velocity-Vorticity Correlation Structure (VVCS), defined as the vorticity region most correlated to velocity fluctuations at a fixed location. Good agreement with DNS-measured propagation velocities is obtained throughout the channel and for all M. The result confirms earlier speculation that the near-wall propagation is due to an advection by coherent vortex structures, and validates the concept of the VVCS.

Scalings and structures in turbulent Couette-Taylor flow.

The scaling of velocity structure functions in Couette-Taylor flow [Lewis and Swinney, Phys. Rev. E 59, 5457 (1999)] is revisited to obtain more accurate values of the scaling exponents for the Reynolds number range investigated, 12,000 to 540,000 (Taylor Reynolds numbers, 3410(5); this transition corresponds to a visually observed break up of the Taylor vortex roll structure with increasing R.

A mathematical model for synergistic eukaryotic gene activation.

The precise biochemical mechanism underlying the synergistic action of gene activators on eukaryotic transcription has eluded a solution, largely because of the technical difficulties inherent in analyzing the mechanics of a 2.5 MDa complex comprising greater than 50 polypeptide components. To complement the biochemical approach we have employed mathematical modeling as a means to understand the mechanism of synergy. Parameters relevant to activated transcription were varied in a simple biochemical system and the data were compared to the transcriptional response predicted by a multi-component statistical model. We found that the model achieved a consistent, semi-quantitative description of the measured transcriptional response, and enabled the characterization and measurement of thermodynamic parameters in the in vitro system. The results provide evidence for the existence of cooperativity in the activation process beyond what would be predicted from one current model suggesting that activators function solely by simple recruitment of the general transcription machinery to the promoter.