The parameters and measurements of the destabilizing actions of rotating machines, and the assumptions of the 1950's

The measurability of destabilizing actions is demonstrated for a rotor built to produce a forward circular, self excited malfunction (gas whip). It is argued that the continued use of past modeling technqiues is unfortunate in that it has led to the use of inappropriate words to express what is happening and a lack of full understanding of the category of forward circular whip instability mechanisms

Two Reflected Gray Code based orders on some restricted growth sequences

We consider two order relations: that induced by the m-ary reflected Gray code and a suffix partitioned variation of it. We show that both of them when applied to some sets of restricted growth sequences still yield Gray codes. These sets of sequences are: subexcedant or ascent sequences, restricted growth functions, and staircase words. In each case we give efficient exhaustive generating algorithms and compare the obtained results

The resonant damping of oscillations of coronal loops with elliptic cross-sections

Motivated by recent Transition Region and Coronal Explorer (TRACE) observations of damped oscillations in coronal loops, Ruderman & Roberts (2002), studied resonant damping of kink oscillations of thin straight magnetic tubes in a cold plasma. In their analysis, Ruderman & Roberts considered magnetic tubes with circular cross-sections. We extend their analysis for magnetic tubes with elliptic cross-sections. We find that there are two infinite sequences of the eigenfrequencies of the tube oscillations, {omega(nc)} and {omega(ns)}, n = 1,2,.... The eigenfrequencies {omega(nc)} and {omega(ns)} correspond to modes with 2n nodes at the tube boundary. In particular, omega(1c) and omega(1s) correspond to two kink modes. These modes are linearly polarized in the direction of the large and small axis of the tube elliptic cross-section respectively. The sequence {omega(nc)} is monotonically growing and {omega(ns)} monotonically decreasing, and they both tend to omega(k) as n --> infinity, where omega(k) is the frequency of the kink mode of tubes with circular cross-sections. In particular, omega(1c) < omega(k) < omega(1s). We calculate the decrements of the two kink modes and show that they are of the order of decrement of the kink mode of a tube with a circular cross-section

Sessile drop on oscillating incline

Natural or industrial flows of a fluid often involve droplets or bubbles of another fluid, pinned by physical or chemical impurities or by the roughness of the bounding walls. Here we study numerically one drop pinned on a circular hydrophilic patch, on an oscillating incline whose angle is proportional to $\sin(\omega\,t)$. The resulting deformation of the drop is measured by the displacement of its center of mass, which behaves like a driven over-damped linear oscillator with amplitude $A(\omega)$ and phase lag $\varphi(\omega)$. The phase lag is ${\cal O}(\omega)$ at small $\omega$ like a linear oscillator, but the amplitude is ${\cal O}(\omega^{-1})$ at large $\omega$ instead of ${\cal O}(\omega^{-2})$ for a linear oscillator. A heuristic explanation is given for this behaviour. The simulations were performed with the software Comsol in mode Laminar Two-Phase Flow, Level Set, with fluid 1 as engine oil and fluid 2 as water.Comment: 7 pages, 9 figure

Constraints on the Galactic bar from the Hercules stream as traced with RAVE across the Galaxy

Non-axisymmetries in the Galactic potential (spiral arms and bar) induce kinematic groups such as the Hercules stream. Assuming that Hercules is caused by the effects of the outer Lindblad resonance of the Galactic bar, we model analytically its properties as a function of position in the Galaxy and its dependence on the bar's pattern speed and orientation. Using data from the RAVE survey we find that the azimuthal velocity of the Hercules structure decreases as a function of Galactocentric radius, in a manner consistent with our analytical model. This allows us to obtain new estimates of the parameters of the Milky Way's bar. The combined likelihood function of the bar's pattern speed and angle has its maximum for a pattern speed of Omega(b) = (1.89 +/- 0.08) x Omega(0), where Omega(0) is the local circular frequency. Assuming a solar radius of 8.05 kpc and a local circular velocity of 238 km s(-1), this corresponds to Omega(b) = 56 +/- 2km s(-1) kpc(-1). On the other hand, the bar's orientation phi(b) cannot be constrained with the available data. In fact, the likelihood function shows that a tight correlation exists between the pattern speed and the orientation, implying that a better description of our best fit results is given by the linear relation Omega(b)/Omega(0) = 1.91+0.0044 (phi(b)(deg) - 48), with standard deviation of 0.02. For example, for an angle of phi(b) = 30 deg the pattern speed is 54.0 +/- 0.5 km s(-1) kpc(-1). These results are not very sensitive to the other Galactic parameters such as the circular velocity curve or the peculiar motion of the Sun, and are robust to biases in distance

On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets

Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert v_{\Omega}\Vert_{L^{\infty}(\Omega)}\lambda(\Omega)$, where $\lambda(\Omega)$ is the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Omega)$. The upper bound is sharp in the limit of a thinning sequence of convex sets. For planar rhombi and isosceles triangles with area $1$, it is shown that $\Vert v_{\Omega}\Vert_{L^{1}(\Omega)}\lambda(\Omega)\ge \frac{\pi^2}{24}$, and that this bound is sharp.Comment: 12 pages, 4 figure