Comment on "Existence of Internal Modes of Sine-Gordon Kinks"

In Ref.[1] [Phys. Rev. B. {\bf 42}, 2290 (1990)] we used a rigorous projection operator collective variable formalism for nonlinear Klein-Gordon equations to prove the continuum Sine-Gordon (SG) equation has a long lived quasimode whose frequency $\omega_s$= 1.004 $\Gamma_0$ is in the continuum just above the lower phonon band edge with a lifetime ($1/\tau_s$) = 0.0017 $\Gamma_0$. We confirmed the analytic calculations by simulations which agreed very closely with the analytic results. In Ref.[3] [Phys. Rev. E. {\bf 62}, R60 (2000)] the authors performed two numerical investigations which they asserted ``show that neither intrinsic internal modes nor quasimodes exist in contrast to previous results.'' In this paper we prove their first numerical investigation could not possibly observe the quasimode in principle and their second numerical investigation actually demonstrates the existence of the SG quasimode. Our analytic calculations and verifying simulations were performed for a stationary Sine-Gordon soliton fixed at the origin. Yet the authors in Ref.[3] state the explanation of our analytic simulations and confirming simulations are due to the Doppler shift of the phonons emitted by our stationary Sine-Gordon soliton which thus has a zero Doppler shift.Comment: 5 pages, submitted to Phys. Rev.

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Uncertainty in phylogenetic tree estimates

Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly model the multivariate uncertainty of tree estimates. We consider both the cases where uncertainty information arises extrinsically (through covariate information) and intrinsically (through the tree estimates themselves). The importance of accounting for tree uncertainty in tree space is demonstrated in two case studies. In the first instance, differences between gene trees are small relative to their uncertainties, while in the second, the differences are relatively large. Our main goal is visualization of tree uncertainty, and we demonstrate advantages of our method with respect to reproducibility, speed and preservation of topological differences compared to visualization based on multidimensional scaling. The proposal highlights that phylogenetic trees are estimated in an extremely high-dimensional space, resulting in uncertainty information that cannot be discarded. Most importantly, it is a method that allows biologists to diagnose whether differences between gene trees are biologically meaningful, or due to uncertainty in estimation.Comment: Final version accepted to Journal of Computational and Graphical Statistic

Coherent structures in fully-developed pipe turbulence

A turbulent mean profile for pipe flow is prescribed which closely matches experimental observations. The nature of perturbations superimposed upon this profile is then considered. Optimal growth calculations predict two distinct classes of structures, clearly associated with near-wall and large-scale structures. Quantitative correspondence of the spanwise wavelength of wall-structures with experimental observations is very good. The response to harmonic forcing is also considered, and the linear growth tested with direct numerical simulation of forced turbulence. Despite the very simple eddy viscosity assumption, this linear approach predicts well the surprisingly large growth of outer-scale modes in the bulk flow. Un profil moyen turbulent est prescrit dans une conduite cylindrique, en adequation avec les observations experimentales. Nous considerons ensuite la nature des perturbations a cet ecoulement synthetique. Le calcul des croissances optimales predit deux types de structures, associees respectivement aux structures de proche-paroi et de grande echelle. Un excellent accord quantitatif est trouve avec les resultats experimentaux quant a la longueur d'onde transversale. La reponse harmonique est egalement etudiee, et la croissance lineaire observee comparee a des simulations numeriques directes de turbulence forcee. Malgre de l'hypothese simple de type `Eddy viscosity', cette approche lineaire predit efficacement la croissance spectaculaire des modes de grande echelle au coeur de l'ecoulement.Comment: 5 pages; Congres Francais de Mecanique, Marseille (2009

Experimental study of noise reduction for an unstiffened cylindrical model of an airplane fuselage

Noise reduction measurements were made for a simplified model of an airplane fuselage consisting of an unstiffened aluminum cylinder 0.5 m in diameter by 1.2 m long with a 1.6-mm-thick wall. Noise reduction was first measured with a reverberant field pink-noise load on the cylinder exterior. Next, noise reduction was measured by using a propeller to provide a more realistic noise load on the cylinder. Structural resonance frequencies and acoustic reverberation times for the cylinder interior volume were also measured. Comparison of data from the relatively simple test using reverberant-field noise with data from the more complex propeller-noise tests indicates some similarity in both the overall noise reduction and the spectral distribution. However, all of the test parameters investigated (propeller speed, blade pitch, and tip clearance) had some effect on the noise-reduction spectra. Thus, the amount of noise reduction achieved appears to be somewhat dependent upon the spectral and spatial characteristics of the flight conditions. Information is also presented on cyclinder resonance frequencies, damping, and characteristics of propeller-noise loads

Experimental study of acoustic loads on an upper-surface-blown STOL airplane configuration

Fluctuating pressure levels were measured on the flap and fuselage of an upper-surface-blown jet-flap airplane configuration in a wind tunnel. The model tested had turbofan engines with a bypass ratio of 3 and a thrust rating of 10 kN. Rectangular nozzles were mounted flush with the upper surface at 35 percent of the wing chord. Test parameters were flap deflection angle, jet impingement angle, angle of attack, free-stream velocity, spanwise location of the engine, and jet dynamic pressure. Load levels were high throughout the jet impingement region, with the highest levels (about 159 dB) occurring on the fuselage and near the knee of the flap. The magnitude of the forward-velocity effect appeared to depend upon the ratio of free-stream and jet velocities. Good agreement was obtained between fluctuating pressure spectra measured at jet dynamic pressures of 7 and 22 kPa when the spectra were scaled by nondimensional functions of dynamic pressure, velocity, and the empirical relationship between dynamic pressure and overall fluctuating pressure level