Fundamental study of flow field generated by rotorcraft blades using wide-field shadowgraph

The vortex trajectory and vortex wake generated by helicopter rotors are visualized using a wide-field shadowgraph technique. Use of a retro-reflective Scotchlite screen makes it possible to investigate the flow field generated by full-scale rotors. Tip vortex trajectories are visible in shadowgraphs for a range of tip Mach number of 0.38 to 0.60. The effect of the angle of attack is substantial. At an angle of attack greater than 8 degrees, the visibility of the vortex core is significant even at relatively low tip Mach numbers. The theoretical analysis of the sensitivity is carried out for a rotating blade. This analysis demonstrates that the sensitivity decreases with increasing dimensionless core radius and increases with increasing tip Mach number. The threshold value of the sensitivity is found to be 0.0015, below which the vortex core is not visible and above which it is visible. The effect of the optical path length is also discussed. Based on this investigation, it is concluded that the application of this wide-field shadowgraph technique to a large wind tunnel test should be feasible. In addition, two simultaneous shadowgraph views would allow three-dimensional reconstruction of vortex trajectories

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

<b>Background</b>: We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. <b>Results</b>: The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and <i>mdm2</i> messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-κB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3. <b>Conclusion</b>: The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks

Monopoles and Knots in Skyrme Theory

We show that the Skyrme theory actually is a theory of monopoles which allows a new type of solitons, the topological knots made of monopole-anti-monopole pair,which is different from the well-known skyrmions. Furthermore, we derive a generalized Skyrme action from the Yang-Mills action of QCD, which we propose to be an effective action of QCD in the infra-red limit. We discuss the physical implications of our results.Comment: 4 pages. Phys. Rev. Lett. in pres

Gauge Independent Trace Anomaly for Gravitons

We show that the trace anomaly for gravitons calculated using the usual effective action formalism depends on the choice of gauge when the background spacetime is not a solution of the classical equation of motion, that is, when off-shell. We then use the gauge independent Vilkovisky-DeWitt effective action to restore gauge independence to the off-shell case. Additionally we explicitly evaluate trace anomalies for some N-sphere background spacetimes.Comment: 19 pages, additional references and title chang

Charged particle display

An optical shutter based on charged particles is presented. The output light intensity of the proposed device has an intrinsic dependence on the interparticle spacing between charged particles, which can be controlled by varying voltages applied to the control electrodes. The interparticle spacing between charged particles can be varied continuously and this opens up the possibility of particle based displays with continuous grayscale.Comment: typographic errors corrected in Eqs (37) and (39); published in Journal of Applied Physics; doi:10.1063/1.317648

Quasi-normal modes for doubly rotating black holes

Based on the work of Chen, L\"u and Pope, we derive expressions for the $D\geq 6$ dimensional metric for Kerr-(A)dS black holes with two independent rotation parameters and all others set equal to zero: $a_1\neq 0, a_2\neq0, a_3=a_4=...=0$. The Klein-Gordon equation is then explicitly separated on this background. For $D\geq 6$ this separation results in a radial equation coupled to two generalized spheroidal angular equations. We then develop a full numerical approach that utilizes the Asymptotic Iteration Method (AIM) to find radial Quasi-Normal Modes (QNMs) of doubly rotating flat Myers-Perry black holes for slow rotations. We also develop perturbative expansions for the angular quantum numbers in powers of the rotation parameters up to second order.Comment: RevTeX 4-1, various figure