Simulations of multimode bolometric interferometers

We describe a procedure for the numerical modelling of astronomical interferometers, with particular relevance to far-infrared and submillimetre wavelengths. The scheme is based on identifying a set of modes that carry power from the sky to the detector. The procedure is extremely general, and can be used to model scalar or vector fields, in any state of coherence and polarization, the only limitation being that the propagation of a coherent field through the system be described by an integral transform, a constraint that is in practise always met.
We present simulations of ideal, multimode two-dimensional interferometers, and show that the modal theory reproduces the correct behaviour of both Michelson and Fizeau interferometers. We calculate simulated visibility data for a multimode bolometric Michelson interferometer, with a synthesized source, and produce a dirty map, recovering the original source with the usual artefacts associated with interferometers.     

Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling

In the last few decades hydrologists have made tremendous progress in using dynamic simulation models for the analysis and understanding of hydrologic systems. However, predictions with these models are often deterministic and as such they focus on the most probable forecast, without an explicit estimate of the associated uncertainty. This uncertainty arises from incomplete process representation, uncertainty in initial conditions, input, output and parameter error. The generalized likelihood uncertainty estimation (GLUE) framework was one of the first attempts to represent prediction uncertainty within the context of Monte Carlo (MC) analysis coupled with Bayesian estimation and propagation of uncertainty. Because of its flexibility, ease of implementation and its suitability for parallel implementation on distributed computer systems, the GLUE method has been used in a wide variety of applications. However, the MC based sampling strategy of the prior parameter space typically utilized in GLUE is not particularly efficient in finding behavioral simulations. This becomes especially problematic for high-dimensional parameter estimation problems, and in the case of complex simulation models that require significant computational time to run and produce the desired output. In this paper we improve the computational efficiency of GLUE by sampling the prior parameter space using an adaptive Markov Chain Monte Carlo scheme (the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm). Moreover, we propose an alternative strategy to determine the value of the cutoff threshold based on the appropriate coverage of the resulting uncertainty bounds. We demonstrate the superiority of this revised GLUE method with three different conceptual watershed models of increasing complexity, using both synthetic and real-world streamflow data from two catchments with different hydrologic regimes.     

Evolution of the mass function of dark matter haloes

We use a high-resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of 15, in a  50 h ⁻¹ Mpc  volume containing 80 million particles. Our low-redshift results allow us to probe low-σ density fluctuations significantly beyond the range of previous cosmological simulations. The Sheth & Tormen mass function provides an excellent match to all of our data except for redshifts of 10 and higher, where it overpredicts halo numbers increasingly with redshift, reaching roughly 50 per cent for the  10¹⁰–10¹¹ M_⊙  haloes sampled at redshift 15. Our results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. We provide an empirical fit to our data that corrects for the overprediction of extremely rare objects by the Sheth & Tormen mass function. This overprediction has implications for studies that use the number densities of similarly rare objects as cosmological probes. For example, the number density of high-redshift  ( z ≃ 6) QSOs  , which are thought to be hosted by haloes at 5σ peaks in the fluctuation field, are likely to be overpredicted by at least a factor of 50 per cent. We test the sensitivity of our results to force accuracy, starting redshift and halo-finding algorithm.     

Radiative transfer

Chandrasekhar’s work in radiative transfer theory began in 1944 and culminated with the publication of his influential treatiseRadiative Transfer in 1950. In this review his major contributions to radiative transfer will be recounted and evaluated. These include his development of the discrete ordinates method, the invariance principles, and his formulation and solution of the transfer equation for polarized light.     

Periodic orbits and escapes in dynamical systems

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central ??bumpy?? black hole. When the energy reaches its escape value, a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy.     

Tracing the Electron Density from the Corona to 1 au

We derive the electron density distribution in the ecliptic plane, from the corona to 1 AU, using observations from 13.8 MHz to a few kHz by the radio experiment WAVES aboard the spacecraft Wind. We concentrate on type III bursts whose trajectories intersect the spacecraft, as determined by the presence of burst-associated Langmuir waves, or by energetic electrons observed by the 3-D Plasma experiment. For these bursts we are able to determine the mode of emission, fundamental or harmonic, the electron density at 1 AU, the distance of emission regions along the spiral, and the time spent by the beams as they proceed from the low corona to 1 AU. For all of the bursts considered, the emission mode at burst onset was the fundamental; by contrast, in deriving many previous models, harmonic emission was assumed.By measuring the onset time of the burst at each frequency we are able to derive an electron density model all along the trajectory of the burst. Our density model, after normalizing the density at 1 AU to be ne(215 R0)=7.2 cm–3 (the average value at the minimum of solar activity when our measurements were made), is ne=3.3×105 r–2+4.1×106 r–4+8.0×107 r–6 cm–3, with r in units of R0. For other densities at 1 AU our result implies that the coefficients in the equation need to be multiplied by n _e (1 AU)/7.2.We compare this with existing models and those derived from direct, in-situ measurements (normalized to the same density at 1 AU) and find that it agrees very well with in-situ measurements and poorly with radio models based on apparent source positions or assumptions of the emission mode. One implication of our results is that isolated type III bursts do not usually propagate in dense regions of the corona and solar wind, as it is still sometimes assumed.     

Moonquakes and lunar tectonism

With the succesful installation of a geophysical station at Hadley Rille, on July 31, 1971, on the Apollo 15 mission, and the continued operation of stations 12 and 14 approximately 1100 km SW, the Apollo program for the first time achieved a network of seismic stations on the lunar surface. A network of at least three stations is essential for the location of natural events on the Moon. Thus, the establishment of this network was one of the most important milestones in the geophysical exploration of the Moon. The major discoveries that have resulted to date from the analysis of seismic data from this network can be summarized as follows:

1. Lunar seismic signals differ greatly from typical terrestrial seismic signals. It now appears that this can be explained almost entirely by the presence of a thin dry, heterogeneous layer which blankets the Moon to a probable depth of few km with a maximum possible depth of about 20 km. Seismic waves are highly scattered in this zone. Seismic wave propagation within the lunar interior, below the scattering zone, is highly efficient. As a result, it is probable that meteoroid impact signals are being received from the entire lunar surface.
2. The Moon possesses a crust and a mantle, at least in the region of the Apollo 12 and 14 stations. The thickness of the crust is between 55 and 70 km and may consist of two layers. The contrast in elastic properties of the rocks which comprise these major structural units is at least as great as that which exists between the crust and mantle of the earth. (See Toks?zet al., p. 490, for further discussion of seismic evidence of a lunar crust.)
3. Natural lunar events detected by the Apollo seismic network are moonquakes and meteoroid impacts. The average rate of release of seismic energy from moonquakes is far below that of the Earth. Although present data do not permit a completely unambiguous interpretation, the best solution obtainable places the most active moonquake focus at a depth of 800 km; slightly deeper than any known earthquake. These moonquakes occur in monthly cycles; triggered by lunar tides. There are at least 10 zones within which the repeating moonquakes originate.
4. In addition to the repeating moonquakes, moonquake ‘swarms’ have been discovered. During periods of swarm activity, events may occur as frequently as one event every two hours over intervals lasting several days. The source of these swarms is unknown at present. The occurrence of moonquake swarms also appears to be related to lunar tides; although, it is too soon to be certain of this point.

These findings have been discussed in eight previous papers (Lathamet al., 1969, 1970, 1971) The instrument has been described by Lathamet al. (1969) and Sutton and Latham (1964). The locations of the seismic stations are shown in Figure 1.     

Radiative transfer in spherical shell atmospheres: I. Rayleigh scattering

A comparison is made between the plane-parallel approximation and the more realistic spherical shell approximation for the radiance reflected from a planetary atmosphere. In this paper we have considered a planet of radius 6371 km (the Earth) with a homogeneous, conservative, Rayleigh scattering atmosphere extending to a height of 100 km. We have found significant departures from the plane-parallel approximation. Radiance versus height distributions for both single and multiple scattering are presented. Results are presented for the fractional radiance from altitudes in the atmosphere which contribute to the total unidirectional reflected radiance at the top of the atmosphere. We have referred to this as the radiance versus height distribution in the sequel. These data will be very useful for both remote sensing applications and planetary spectroscopy. We have also found that gross violations of the principle of reciprocity do occur in the spherical shell approximation.     

New 1982 — 1990 photometry of λ Andromedae and its 11-year cycle

We present photoelectric photometry of λ And never before published, obtained between February 1982 and December 1990 at 29 different observatories. Then we combine it with all other photometry available to us (previously published, contained in the I.A.U. Commission 27 Archives, and obtained with the Vanderbilt 16-inch automatic telescope but not yet published), to yield a 14.8-year data base. Analysis reveals a long-term cycle in mean brightness, with a full range of 0^m.15 and a period of 11.4 ± 0.4 years. Because most of our new photometry was concentrated in the 1983-84 observing season, we analyze that one well-defined light curve with a two-spot model. Spot A keeps a 0^m.04 amplitude throughout four rotation cycles whereas the amplitude of spot B diminishes from 0^m.09 down almost to 0^m.03. The spot rotation periods were 55^d.9 ± 0^d.6 and 520^d.8 ± 1^d.0, respectively.     

Hypervelocity capture of meteoritic particles in nonsilica aerogels

Abstract– The Stardust mission captured particles from the comet 81P/Wild 2 in gradient density silica aerogel and returned the collected samples to earth in 2006. The analyses of these particles have revealed several new insights into the formation of our solar system. However, since the aerogel used as the capture material was silica, the elemental analyses of the silica‐rich particles were made more complicated in certain ways due to the mixing of the silicon of the particles and that of the aerogel. By using a nonsilica aerogel, future elemental analyses of silica–rich particles captured in aerogel could be made more straightforward. Resorcinol/formaldehyde (RF), alumina, and zirconia aerogels were impact tested with meteoritic fragments and the captured fragments were mapped with synchrotron‐based X‐ray microprobe (XRM) and the particles were analyzed with X‐ray fluorescence (XRF). The resorcinol/formaldehyde aerogel proved to be the best capture material, in that it could be keystoned and XRF could be used to locate and analyze particles that were less than 10 μm.