Observing the Galaxy's massive black hole with gravitational wave bursts

An extreme-mass-ratio burst (EMRB) is a gravitational wave signal emitted when a compact object passes through periapsis on a highly eccentric orbit about a much more massive object, in our case a stellar mass object about a 10^6 M_sol black hole. EMRBs are a relatively unexplored means of probing the spacetime of massive black holes (MBHs). We conduct an investigation of the properties of EMRBs and how they could allow us to constrain the parameters, such as spin, of the Galaxy's MBH. We find that if an EMRB event occurs in the Galaxy, it should be detectable for periapse distances r_p < 65 r_g for a \mu = 10 M_sol orbiting object, where r_g = GM/c^2 is the gravitational radius. The signal-to-noise ratio scales as \rho ~ -2.7 log(r_p/r_g) + log(\mu/M_sol) + 4.9. For periapses r_p < 10 r_g, EMRBs can be informative, and provide good constraints on both the MBH's mass and spin. Closer orbits provide better constraints, with the best giving accuracies of better than one part in 10^4 for both the mass and spin parameter.Comment: 25 pages, 17 figures, 1 appendix. One more typo fixe

Expectations for extreme-mass-ratio bursts from the Galactic Centre

When a compact object on a highly eccentric orbit about a much more massive body passes through periapsis it emits a short gravitational wave signal known as an extreme-mass-ratio burst (EMRB). We consider stellar mass objects orbiting the massive black hole (MBH) found in the Galactic Centre. EMRBs provide a novel means of extracting information about the MBH; an EMRB from the Galactic MBH could be highly informative regarding the MBH's mass and spin if the orbital periapsis is small enough. However, to be a useful astronomical tool EMRBs must be both informative and sufficiently common to be detectable with a space-based interferometer. We construct a simple model to predict the event rate for Galactic EMRBs. We estimate there could be on average ~2 bursts in a two year mission lifetime for LISA. Stellar mass black holes dominate the event rate. Creating a sample of 100 mission realisations, we calculate what we could learn about the MBH. On average, we expect to be able to determine the MBH mass to ~1% and the spin to ~0.1 using EMRBs.Comment: 22 pages, 5 figures, 2 appendices. Minor changes to reflect published versio

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

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

Decimation and Harmonic Inversion of Periodic Orbit Signals

We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic orbit signal is obtained by analytical frequency windowing of the periodic orbit sum. In a second step, the frequencies and amplitudes of the decimated signal are determined by either Decimated Linear Predictor, Decimated Pade Approximant, or Decimated Signal Diagonalization. These techniques, which would have been numerically unstable without the windowing, provide numerically more accurate semiclassical spectra than does the filter-diagonalization method.Comment: 22 pages, 3 figures, submitted to J. Phys.

Superconductor-proximity effect in chaotic and integrable billiards

We explore the effects of the proximity to a superconductor on the level density of a billiard for the two extreme cases that the classical motion in the billiard is chaotic or integrable. In zero magnetic field and for a uniform phase in the superconductor, a chaotic billiard has an excitation gap equal to the Thouless energy. In contrast, an integrable (rectangular or circular) billiard has a reduced density of states near the Fermi level, but no gap. We present numerical calculations for both cases in support of our analytical results. For the chaotic case, we calculate how the gap closes as a function of magnetic field or phase difference.Comment: 4 pages, RevTeX, 2 Encapsulated Postscript figures. To be published by Physica Scripta in the proceedings of the "17th Nordic Semiconductor Meeting", held in Trondheim, June 199

Towards Economic Models for MOOC Pricing Strategy Design

MOOCs have brought unprecedented opportunities of making high-quality courses accessible to everybody. However, from the business point of view, MOOCs are often challenged for lacking of sustainable business models, and academic research for marketing strategies of MOOCs is also a blind spot currently. In this work, we try to formulate the business models and pricing strategies in a structured and scientific way. Based on both theoretical research and real marketing data analysis from a MOOC platform, we present the insights of the pricing strategies for existing MOOC markets. We focus on the pricing strategies for verified certificates in the B2C markets, and also give ideas of modeling the course sub-licensing services in B2B markets