A polyphonic acoustic vortex and its complementary chords

Using an annular phased array of eight loudspeakers, we generate sound beams that simultaneously contain phase singularities at a number of different frequencies. These frequencies correspond to different musical notes and the singularities can be set to overlap along the beam axis, creating a polyphonic acoustic vortex. Perturbing the drive amplitudes of the speakers means that the singularities no longer overlap, each note being nulled at a slightly different lateral position, where the volume of the other notes is now nonzero. The remaining notes form a tri-note chord. We contrast this acoustic phenomenon to the optical case where the perturbation of a white light vortex leads to a spectral spatial distribution

Microwave background constraints on inflationary parameters

We use a compilation of cosmic microwave anisotropy data (including the recent VSA, CBI and Archeops results), supplemented with an additional constraint on the expansion rate, to directly constrain the parameters of slow-roll inflation models. We find good agreement with other papers concerning the cosmological parameters, and display constraints on the power spectrum amplitude from inflation and the first two slow-roll parameters, finding in particular that $\epsilon_1 < 0.057$. The technique we use for parametrizing inflationary spectra may become essential once the data quality improves significantly.Comment: 6 pages LaTeX file with figures incorporated. Major revisions including incorporation of new datasets (CBI and Archeops). Slow-roll inflation module for use with the CAMB program can be found at http://astronomy.cpes.susx.ac.uk/~sleach/inflation

Gauge Variant Symmetries for the Schr\"odinger Equation

The last multiplier of Jacobi provides a route for the determination of families of Lagrangians for a given system. We show that the members of a family are equivalent in that they differ by a total time derivative. We derive the Schr\"odinger equation for a one-degree-of-freedom system with a constant multiplier. In the sequel we consider the particular example of the simple harmonic oscillator. In the case of the general equation for the simple harmonic oscillator which contains an arbitrary function we show that all Schr\"odinger equations possess the same number of Lie point symmetries with the same algebra. From the symmetries we construct the solutions of the Schr\"odinger equation and find that they differ only by a phase determined by the gauge.Comment: 12 page

CMB Constraints on Principal Components of the Inflaton Potential

We place functional constraints on the shape of the inflaton potential from the cosmic microwave background through a variant of the generalized slow roll approximation that allows large amplitude, rapidly changing deviations from scale-free conditions. Employing a principal component decomposition of the source function G'~3(V'/V)^2 - 2V''/V and keeping only those measured to better than 10% results in 5 nearly independent Gaussian constraints that maybe used to test any single-field inflationary model where such deviations are expected. The first component implies < 3% variations at the 100 Mpc scale. One component shows a 95% CL preference for deviations around the 300 Mpc scale at the ~10% level but the global significance is reduced considering the 5 components examined. This deviation also requires a change in the cold dark matter density which in a flat LCDM model is disfavored by current supernova and Hubble constant data and can be tested with future polarization or high multipole temperature data. Its impact resembles a local running of the tilt from multipoles 30-800 but is only marginally consistent with a constant running beyond this range. For this analysis, we have implemented a ~40x faster WMAP7 likelihood method which we have made publicly available.Comment: 12 pages, 14 figures, submitted to Phys.Rev.D. Optimized WMAP7 likelihood code and principal component functions of the GSR source function available at http://background.uchicago.edu/wmap_fast

Fabrication of Pd-Cr wire

Fabrication of Pd-13 percent Cr alloy wires is described. Melting, casting, swaging and annealing processes are discussed. Drawing to reach two diameters (0.003 inch and 0.00176 inch) of wire is described. Representative micrographs of the Pd-Cr alloy at selected stages during wire fabrication are included. The resistance of the wire was somewhat lower, by about 15 to 20 percent, than comparable wire of other alloys used for strain gages

From the production of primordial perturbations to the end of inflation

In addition to generating the appropriate perturbation power spectrum, an inflationary scenario must take into account the need for inflation to end subsequently. In the context of single-field inflation models where inflation ends by breaking of the slow-roll condition, we constrain the first and second derivatives of the inflaton potential using this additional requirement. We compare this with current observational constraints from the primordial spectrum and discuss several issues relating to our results.Comment: RevTex4, 6 pages, 7 figures. To match version accepted by PR