A Phase Space Approach to Gravitational Enropy

We examine the definition S = ln Omega as a candidate "gravitational entropy" function. We calculate its behavior for gravitationl and density perturbations in closed, open and flat cosmologies and find that in all cases it increases monotonically. Using the formalism to calculate the gravitational entropy produced during inflation gives the canonical answer. We compare the behavior of S with the behavior of the square of the Weyl tensor. Applying the formalism to black holes has proven more problematical.Comment: Talk delivered at South African Relativistic Cosmology Symposium, Feb 1999. Some new results over Rothman and Anninos 97. To appear in GRG, 17 page

Sources of oscillation frequency increase with rising solar activity

We analyze and interpret SOHO/MDI data on oscillation frequency changes between 1996 and 2004 focusing on differences between activity minimum and maximum of solar cycle 23. We study only the behavior of the centroid frequencies, which reflect changes averaged over spherical surfaces. Both the f-mode and p-mode frequencies are correlated with general measures of the sun's magnetic activity. However, the physics behind each of the two correlations is quite different. We show that for the f-modes the dominant cause of the frequency increase is the dynamical effect of the rising magnetic field. The relevant rise must occur in subphotospheric layers reaching to some 0.5 - 0.7 kG at a depth of about 5 Mm. However, the implied constraints also require the field change in the atmosphere to be so small that it has only a tiny dynamical effect on p-mode frequencies. For p-modes, the most plausible explanation of the frequency increase is a less than 2 percent decrease in the radial component of the turbulent velocity in the outer layers. Lower velocity implies a lower efficiency of the convective transport, hence lower temperature, which also contributes to the p-mode frequency increase.Comment: ApJ, accepte

Properties of Umbral Dots as Measured from the New Solar Telescope Data and MHD Simulations

We studied bright umbral dots (UDs) detected in a moderate size sunspot and compared their statistical properties to recent MHD models. The study is based on high resolution data recorded by the New Solar Telescope at the Big Bear Solar Observatory and 3D MHD simulations of sunspots. Observed UDs, living longer than 150 s, were detected and tracked in a 46 min long data set, using an automatic detection code. Total 1553 (620) UDs were detected in the photospheric (low chromospheric) data. Our main findings are: i) none of the analyzed UDs is precisely circular, ii) the diameter-intensity relationship only holds in bright umbral areas, and iii) UD velocities are inversely related to their lifetime. While nearly all photospheric UDs can be identified in the low chromospheric images, some small closely spaced UDs appear in the low chromosphere as a single cluster. Slow moving and long living UDs seem to exist in both the low chromosphere and photosphere, while fast moving and short living UDs are mainly detected in the photospheric images. Comparison to the 3D MHD simulations showed that both types of UDs display, on average, very similar statistical characteristics. However, i) the average number of observed UDs per unit area is smaller than that of the model UDs, and ii) on average, the diameter of model UDs is slightly larger than that of observed ones.Comment: Accepted by the AP

Does the Sun Shrink with Increasing Magnetic Activity?

We have analyzed the full set of SOHO/MDI f- and p-mode oscillation frequencies from 1996 to date in a search for evidence of solar radius evolution during the rising phase of the current activity cycle. Like Antia et al. (2000), we find that a significant fraction of the f-mode frequency changes scale with frequency; and that if these are interpreted in terms of a radius change, it implies a shrinking sun. Our inferred rate of shrinkage is about 1.5 km/y, which is somewhat smaller than found by Antia et al. We argue that this rate does not refer to the surface, but rather to a layer extending roughly from 4 to 8 Mm beneath the visible surface. The rate of shrinking may be accounted for by an increasing radial component of the rms random magnetic field at a rate that depends on its radial distribution. If it were uniform, the required field would be ~7 kG. However, if it were inwardly increasing, then a 1 kG field at 8 Mm would suffice. To assess contribution to the solar radius change arising above 4Mm, we analyzed the p-mode data. The evolution of the p-mode frequencies may be explained by a magnetic^M field growing with activity. The implications of the near-surface magnetic field changes depend on the anisotropy of the random magnetic field. If the field change is predominantly radial, then we infer an additional shrinking at a rate between 1.1-1.3 km/y at the photosphere. If on the other hand the increase is isotropic, we find a competing expansion at a rate of 2.3 km/y. In any case, variations in the sun's radius in the activity cycle are at the level of 10^{-5} or less, hence have a negligible contribution to the irradiance variations.Comment: 10 pages (ApJ preprint style), 4 figures; accepted for publication in Ap

Simulation and flight evaluation of a head-up landing aid for general aviation

A head-up general aviation landing aid called a landing site indicator (LASI) was tested in a fixed-base, visual simulator and in an airplane to determine the effectiveness of the LASI. The display, which had a simplified format and method of implementation, presented to the pilot in his line of sight through the windshield a graphic representation of the airplane's velocity vector. In each testing model (simulation of flight), each of 4 pilots made 20 landing approaches with the LASI and 20 approaches without it. The standard deviations of approach and touchdown parameters were considered an indication of pilot consistency. Use of the LASI improved consistency and also reduced elevator, aileron, and rudder control activity. Pilots' comments indicated that the LASI reduced work load. An appendix is included with a discussion of the simulator effectiveness for visual flight tasks

Diffuse reflectance imaging with astronomical applications

Diffuse objects generally tell us little about the surrounding lighting, since the radiance they reflect blurs together incident lighting from many directions. In this paper we discuss how occlusion geometry can help invert diffuse reflectance to recover lighting or surface albedo. Self-occlusion in the scene can be regarded as a form of coding, creating high frequencies that improve the conditioning of diffuse light transport. Our analysis builds on a basic observation that diffuse reflectors with sufficiently detailed geometry can fully resolve the incident lighting. Using a Bayesian framework, we propose a novel reconstruction method based on high-resolution photography, taking advantage of visibility changes near occlusion boundaries. We also explore the limits of single-pixel observations as the diffuse reflector (and potentially the lighting) vary over time. Diffuse reflectance imaging is particularly relevant for astronomy applications, where diffuse reflectors arise naturally but the incident lighting and camera position cannot be controlled. To test our approaches, we first study the feasibility of using the moon as a diffuse reflector to observe the earth as seen from space. Next we present a reconstruction of Mars using historical photometry measurements not previously used for this purpose. As our results suggest, diffuse reflectance imaging expands our notion of what can qualify as a camera.Natural Sciences and Engineering Research Council of Canada (NSERC) (Postdoctoral Fellowship)United States-Israel Binational Science Foundation (Grant 2008155)United States. National Geospatial-Intelligence Agency (NEGI-1582-04-0004)United States. Multidisciplinary University Research Initiative (Grant N00014-06-1-0734

Gravitational Entropy and Quantum Cosmology

We investigate the evolution of different measures of ``Gravitational Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models. A new quantity behaving in accordance with the second law of thermodynamics is introduced. We then go on and investigate whether a quantum calculation of initial conditions for the universe based upon the Wheeler-DeWitt equation supports Penrose's Weyl Curvature Conjecture, according to which the Ricci part of the curvature dominates over the Weyl part at the initial singularity of the universe. The theory is applied to the Bianchi type I universe models with dust and a cosmological constant and to the Lema\^itre-Tolman universe models. We investigate two different versions of the conjecture. First we investigate a local version which fails to support the conjecture. Thereafter we construct a non-local entity which shows more promising behaviour concerning the conjecture.Comment: 20 pages, 7 ps figure