Decoupling the coupled DGLAP evolution equations: an analytic solution to pQCD

Using Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we decouple the solutions for the singlet structure function $F_s(x,Q^2)$ and $G(x,Q^2)$ of the two leading-order coupled singlet DGLAP equations, allowing us to write fully decoupled solutions: F_s(x,Q^2)={\cal F}_s(F_{s0}(x), G_0(x)), G(x,Q^2)={\cal G}(F_{s0}(x), G_0(x)). Here ${\cal F}_s$ and $\cal G$ are known functions---found using the DGLAP splitting functions---of the functions $F_{s0}(x) \equiv F_s(x,Q_0^2)$ and $G_{0}(x) \equiv G(x,Q_0^2)$, the chosen starting functions at the virtuality $Q_0^2$. As a proof of method, we compare our numerical results from the above equations with the published MSTW LO gluon and singlet $F_s$ distributions, starting from their initial values at $Q_0^2=1 GeV^2$. Our method completely decouples the two LO distributions, at the same time guaranteeing that both distributions satisfy the singlet coupled DGLAP equations. It furnishes us with a new tool for readily obtaining the effects of the starting functions (independently) on the gluon and singlet structure functions, as functions of both $Q^2$ and $Q_0^2$. In addition, it can also be used for non-singlet distributions, thus allowing one to solve analytically for individual quark and gluon distributions values at a given $x$ and $Q^2$, with typical numerical accuracies of about 1 part in $10^5$, rather than having to evolve numerically coupled integral-differential equations on a two-dimensional grid in $x, Q^2$, as is currently done.Comment: 6 pages, 2 figure

Measurements of farfield sound generation from a flow-excited cavity

Results of 1/3-octave-band spectral measurements of internal pressures and the external acoustic field of a tangentially blown rectangular cavity are compared. Proposed mechanisms for sound generation are reviewed, and spectra and directivity plots of cavity noise are presented. Directivity plots show a slightly modified monopole pattern. Frequencies of cavity response are calculated using existing predictions and are compared with those obtained experimentally. The effect of modifying the upstream boundary layer on the noise was investigated, and its effectiveness was found to be a function of cavity geometry and flow velocity

Evaluation of the Langley 4- by 7-meter tunnel for propeller noise measurements

An experimental and theoretical evaluation of the Langley 4- by 7- Meter Tunnel was conducted to determine its suitability for obtaining propeller noise data. The tunnel circuit and open test section are described. An experimental evaluation is performed using microphones placed in and on the tunnel floor. The reflection characteristics and background noise are determined. The predicted source (propeller) near-field/far-field boundary is given using a first-principles method. The effect of the tunnel-floor boundry layer on the noise from the propeller is also predicted. A propeller test stand used for part of his evaluation is also described. The measured propeller performance characteristics are compared with those obtained at a larger scale, and the effect of the test-section configuration on the propeller performance is examined. Finally, propeller noise measurements were obtained on an eight-bladed SR-2 propeller operating at angles of attack -8 deg, 0 deg, and 4.6 deg to give an indication of attainable signal-to-noise ratios

All Adults Once Were Children

Issue Editor, Robert Block\u27s, point of view and summary of the articles in New Morbidities 2.