Acoustic radiation patterns for a source in a hard-walled unflanged circular duct

Acoustic radiation patterns are measured over a 320 deg arc for a point source in a finite length, hard walled, unflanged circular duct. The measured results are compared with computed results which are based on the Wiener-Hopf solution for radiation from a semi-infinite unflanged duct. Measurements and computations are presented for frequencies slightly below and slightly above each of the first four higher order radial mode cutoff frequencies. It is found that the computed and measured patterns show better agreement below the mode cut-off frequencies than above and that the agreement is better at lower frequencies that at higher frequencies. The computed radiation patterns do not show fine lobes which are caused by diffraction from the back end of the duct

Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment

Elliptic instability in the Lagrangian-averaged Euler-Boussinesq-alpha equations

We examine the effects of turbulence on elliptic instability of rotating stratified incompressible flows, in the context of the Lagragian-averaged Euler-Boussinesq-alpha, or \laeba, model of turbulence. We find that the \laeba model alters the instability in a variety of ways for fixed Rossby number and Brunt-V\"ais\"al\"a frequency. First, it alters the location of the instability domains in the $(\gamma,\cos\theta)-$parameter plane, where $\theta$ is the angle of incidence the Kelvin wave makes with the axis of rotation and $\gamma$ is the eccentricity of the elliptic flow, as well as the size of the associated Lyapunov exponent. Second, the model shrinks the width of one instability band while simultaneously increasing another. Third, the model introduces bands of unstable eccentric flows when the Kelvin wave is two-dimensional. We introduce two similarity variables--one is a ratio of the Brunt-V\"ais\"al\"a frequency to the model parameter $\Upsilon_0 = 1+\alpha^2\beta^2$, and the other is the ratio of the adjusted inverse Rossby number to the same model parameter. Here, $\alpha$ is the turbulence correlation length, and $\beta$ is the Kelvin wave number. We show that by adjusting the Rossby number and Brunt-V\"ais\"al\"a frequency so that the similarity variables remain constant for a given value of $\Upsilon_0$, turbulence has little effect on elliptic instability for small eccentricities $(\gamma \ll 1)$. For moderate and large eccentricities, however, we see drastic changes of the unstable Arnold tongues due to the \laeba model.Comment: 23 pages (sigle spaced w/figure at the end), 9 figures--coarse quality, accepted by Phys. Fluid

The free rigid body dynamics: generalized versus classic

In this paper we analyze the normal forms of a general quadratic Hamiltonian system defined on the dual of the Lie algebra $\mathfrak{o}(K)$ of real $K$ - skew - symmetric matrices, where $K$ is an arbitrary $3\times 3$ real symmetric matrix. A consequence of the main results is that any first-order autonomous three-dimensional differential equation possessing two independent quadratic constants of motion which admits a positive/negative definite linear combination, is affinely equivalent to the classical "relaxed" free rigid body dynamics with linear controls.Comment: 12 page

Emissivity for CO_2 at Elevated Pressures

Total absorptivity measurements have been carried out at room temperature as a function of partial pressure of CO_2 and of total pressure using nitrogen as pressurizing gas

Scanning probe microscopy imaging of metallic nanocontacts

We show scanning probe microscopy measurements of metallic nanocontacts between controlled electromigration cycles. The nanowires used for the thinning process are fabricated by shadow evaporation. The highest resolution obtained using scanning force microscopy is about 3 nm. During the first few electromigration cycles the overall slit structure of the nanocontact is formed. The slit first passes along grain boundaries and then at a later stage vertically splits grains in the course of consuming them. We find that first the whole wire is heated and later during the thinning process as the slit forms the current runs over several smaller contacts which needs less power.Comment: 4 pages, 4 figure

The Square Root Depth Wave Equations

We introduce a set of coupled equations for multilayer water waves that removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the presence of shear. The new well-posed equations are Hamiltonian and in the absence of imposed background shear they retain the same travelling wave solutions as MGN. We call the new model the Square Root Depth equations, from the modified form of their kinetic energy of vertical motion. Our numerical results show how the Square Root Depth equations model the effects of multilayer wave propagation and interaction, with and without shear.Comment: 10 pages, 5 figure