Nonlinear gas oscillations in pipes. Part 1. Theory

The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. All these boundary conditions are modelled by two parameters: a length correction and a reflexion coefficient equivalent to the acoustic impedance. The linear theory predicts large amplitudes near resonance and nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and wave form of the oscillation are predicted there. In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end

Vertical motions in the disk of NGC 5668 as seen with optical Fabry-Perot spectroscopy

We have observed the nearly face-on spiral galaxy NGC 5668 with the TAURUS II Fabry-Perot interferometer at the William Herschel Telescope using the $H\alpha$ line to study the kinematics of the ionized gas. From the extracted data cube we construct intensity, velocity and velocity dispersion maps. We calculate the rotation curve in the innermost 2 arcmin and we use the residual velocity field to look for regions with important vertical motions. By comparing the geometry of these regions in the residual velocity field with the geometry in the intensity and velocity dispersion maps we are able to select some regions which are very likely to be shells or chimneys in the disk. The geometry and size of these regions are very similar to the shells or chimneys detected in other galaxies by different means. Moreover, it is worth noting than this galaxy has been reported to have a population of neutral hydrogen high velocity clouds (Schulman et al. 1996) which, according to these observations, could have been originated by chimneys similar to those reported in this paper.Comment: 7 pages with 9 figures. LaTeX file using A&A v4.0 macro

A computational approach to the D-module of meromorphic functions

Let $D$ be a divisor in ${\bf C}^n$. We present methods to compare the ${\mathcal D}$-module of the meromorphic functions ${\mathcal O}[* D]$ to some natural approximations. We show how the analytic case can be treated with computations in the Weyl algebra.Comment: 11 page