Ballistic trajectory: parabola, ellipse, or what?

Mechanics texts tell us that a particle in a bound orbit under gravitational central force moves on an ellipse, while introductory physics texts approximate the earth as flat, and tell us that the particle moves in a parabola. The uniform-gravity, flat-earth parabola is clearly meant to be an approximation to a small segment of the true central-force/ellipse orbit. To look more deeply into this connection we convert earth-centered polar coordinates to ``flat-earth coordinates'' by treating radial lines as vertical, and by treating lines of constant radial distance as horizontal. With the exact trajectory and dynamics in this system, we consider such questions as whether gravity is purely vertical in this picture, and whether the central force nature of gravity is important only when the height or range of a ballistic trajectory is comparable to the earth radius. Somewhat surprisingly, the answers to both questions is ``no,'' and therein lie some interesting lessons.Comment: 7 pages, 3 figure

Search for supermassive magnetic monopoles using mica crystals

The survival of the Galactic magnetic field almost certainly sets an astrophysical upper bound of approx. 10 to the minus 15th power cm(-2) sr(-1) s(-1) on the flux of monopoles. To improve significantly upon this Parker limit with direct, real time searches would require a detector area of approx. 10,000 square meters and a collection time of years. Several such searches are being contemplated. A novel alternative scheme using large mica crystals capable of recording and storing tracks of slow monopoles over a time scale of approx. 10 to the 9th power years was proposed

Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices

We propose a general method by which experiments on ultracold gases can be used to determine the topological properties of the energy bands of optical lattices, as represented by the map of the Berry curvature across the Brillouin zone. The Berry curvature modifies the semiclassical dynamics and hence the trajectory of a wave packet undergoing Bloch oscillations. However, in two dimensions these trajectories may be complicated Lissajous-like figures, making it difficult to extract the effects of Berry curvature in general. We propose how this can be done using a "time-reversal" protocol. This compares the velocity of a wave packet under positive and negative external force, and allows a clean measurement of the Berry curvature over the Brillouin zone. We discuss how this protocol may be implemented and explore the semiclassical dynamics for three specific systems: the asymmetric hexagonal lattice, and two "optical flux" lattices in which the Chern number is nonzero. Finally, we discuss general experimental considerations for observing Berry curvature effects in ultracold gases.Comment: 12 page

Late time tails from momentarily stationary, compact initial data in Schwarzschild spacetimes

An L-pole perturbation in Schwarzschild spacetime generally falls off at late times t as t^{-2L-3}. It has recently been pointed out by Karkowski, Swierczynski and Malec, that for initial data that is of compact support, and is initially momentarily static, the late-time behavior is different, going as t^{-2L-4}. By considering the Laplace transforms of the fields, we show here why the momentarily stationary case is exceptional. We also explain, using a time-domain description, the special features of the time development in this exceptional case.Comment: 7 pages, 5 figure

The length of time's arrow

An unresolved problem in physics is how the thermodynamic arrow of time arises from an underlying time reversible dynamics. We contribute to this issue by developing a measure of time-symmetry breaking, and by using the work fluctuation relations, we determine the time asymmetry of recent single molecule RNA unfolding experiments. We define time asymmetry as the Jensen-Shannon divergence between trajectory probability distributions of an experiment and its time-reversed conjugate. Among other interesting properties, the length of time's arrow bounds the average dissipation and determines the difficulty of accurately estimating free energy differences in nonequilibrium experiments

Electron beam fluorescence measurements in the Boeing hypersonic shock tunnel

The Calspan electron beam fluorescence (EBF) measurement system is described along with the results of measurements made in hypersonic flow. Numerous self-emitting metallic species were identified, many of which may be associated with an aging/erosion process within the B30HST. Because there were only 16 tunnel runs, it was only possible to obtain spectral measurements over a limited range of wavelengths and time sampling periods. Many spectral features of the flow remain uninvestigated. Because flow self-emission is important to all optical diagnostic techniques, it is recommended that additional spectral studies by performed. The three electron beam-excited species that were identified are nitrogen, helium, and nitric oxide. The high metallic radiation background interfered with attempts to obtain the time-wise variation of N2 density and He radiation with the optical fiber/PMT channels. In the case of the N2 density measurements the result of interference was increased uncertainty. Unfortunately, the interference caused the time-wise He measurements to fail completely. It is recommended that the electron beam be modulated to provide discrimination against the background radiation in future N2 density measurements. Careful data reduction produced useful measurements of N2 vibrational temperature, even though the high background from metallic species significantly increased measurement uncertainty. Perhaps the recommended additional spectral studies would reveal N2(+) First Negative System band-pair regions having less background. Detection of the He arrival was easily accomplished with the spectrometer/array detector system. Because of this, it is recommended that this means of detecting He arrival be used in the future. With proper calibrations of the system an He number density could be obtained. Although the flow conditions were out of limits for the run in which the NO spectrum was recorded, the usefulness of the NO spectrum for determination of free-stream rotational temperature was demonstrated and should be exploited in future experiments. Indeed, based on the strong NO signals, it is recommended that lower resolution NO spectra be obtained to provide a measure of NO vibrational temperature in the same manner that the N2 temperature was obtained

Do Management Changes Matter? An Empirical Investigation of REIT Performance

Management’s (board of directors or executive officers) contribution to a firm is difficult to directly observe, although stock return performance can be a source of information. This study addresses this issue by extending the work of McIntosh, Rogers, Sirmans and Liang (1994) by analyzing management changes within REITs from 1984 to 2002. The findings indicate a significant relationship between negative performance and a management change from a period three months prior to the change in management. Logit and probit analysis are used to determine whether negative firm performance (measured by its relationship to market returns) can predict the likelihood of a management change. No predictive ability is found.

Does Inflation Provide Natural Initial Conditions for the Universe?

If our universe underwent inflation, its entropy during the inflationary phase was substantially lower than it is today. Because a low-entropy state is less likely to be chosen randomly than a high-entropy one, inflation is unlikely to arise through randomly-chosen initial conditions. To resolve this puzzle, we examine the notion of a natural state for the universe, and argue that it is a nearly-empty spacetime. If empty space has a small vacuum energy, however, inflation can begin spontaneously in this background. This scenario explains why a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time.Comment: Submitted to Gravity Research Foundation Essay Competition; based on hep-th/041027