Unsteady hydromagnetic boundary-layer flow on a semi-infinite wall

Unsteady two-dimensional flow of a viscous, incompressible and electrically conducting fluid which is confined on one side of a semi-infinite wall, in presence of a transverse magnetic field is investigated. The wall is initially at rest and then it is suddenly accelerated in its own plane with a velocity which is an arbitrary function of the time. Solution of the problem is obtained, for two particular cases, i.e., corresponding to two free-stream velocities, with the help of the finite difference approximation technique using the explicit method for uniformly accelerated motion of the wall.     

The concept of limiting magnitude and the performance of the Isaac Newton telescope for prime focus photography

A quantitative definition of limiting magnitude for stellar photographs is proposed, together with a method of measurement employing a Racine prism. Limiting magnitudes inU, B andV for the Isaac Newton telescope at Herstmonceux derived from a total of 72 prime focus photographs are presented and the results correlated with the size of the photographed image. The limiting magnitude for an extrapolated value of the seeing of 1 isB=22^m.0, in good agreement with a value obtained by scaling the limiting magnitudes of the 200 inch telescope.     

Thick and thin models of the evolution of carbon dioxide on Mars

We present results from a new simulation code that accounts for the evolution of the reservoirs of carbon dioxide on Mars, from its early years to the present. We establish a baseline model parameter set that produces results compatible with the present (i.e., Patm?6.5 mbar with permanent CO₂ ice cap) for a wide range of initial inventories. We find that the initial inventory of CO₂ broadly determines the evolutionary course of the reservoirs of CO₂. The reservoirs include the atmosphere, ice cap, adsorbed CO₂ in the regolith, and carbonate rocks. We track the evolution of the free inventory: the atmosphere, ice cap and regolith. Simulations begin at 4.53 Gyr before present with a rapid loss of free inventory to space in the early Noachian. Models that assume a relatively small initial inventory (?5 bar) have pronounced minima in the free inventory of CO₂ toward the end of the Noachian. Under baseline parameters, initial inventories below ∼4.5 bar result in a catastrophic loss of the free inventory to space. The current free inventory would be then determined by the balance between outgassing, sputtering losses and chemical weathering following the end of the late bombardment. We call these “thin” models. They generically predict small current free inventories in line with expectations of a small present CO₂ ice cap. For “thick” models, with initial inventories ?5 bar, a surplus of 300-700 mbar of free CO₂ remains during the late-Noachian. The histories of free inventory in time for thick models tend to converge within the last 3.5 Gyr toward a present with an ice cap plus atmospheric inventory of about 100 mbar. For thick models, the convergence is largely due to the effects of chemical weathering, which draws down higher free inventories more rapidly than the low. Thus, thick models have ?450 mbar carbonate reservoirs, while thin models have ?200 mbar. Though both thick and thin scenarios can reproduce the current atmospheric pressure, the thick models imply a relatively large current CO₂ ice cap and thin models, little or none. While the sublimation of a massive cap at a high obliquity would create a climate swing of greenhouse warming for thick models, under the thin model, mean temperatures and pressures would be essentially unaffected by increases in obliquity.     

Mineralogy and thermal properties of V-type Asteroid 956 Elisa: Evidence for diogenitic material from the Spitzer IRS (5-35 μm) spectrum

We present the thermal infrared (5-35 μm) spectrum of 956 Elisa as measured by the Spitzer Infrared Spectrograph (“IRS”; Houck, J.R. et al. [2004]. Astrophys. J. Suppl. 154, 18-24) together with new groundbased lightcurve data and near-IR spectra. From the visible lightcurve photometry, we determine a rotation period of 16.494 ± 0.001 h, identify the rotational phase of the Spitzer observations, and estimate the visible absolute magnitude (H_V) at that rotational phase to be 12.58 ± 0.04. From radiometric analysis of the thermal flux spectrum, we find that at the time of observation 956 Elisa had a projected radius of 5.3 ± 0.4 km with a visible albedo p_V = 0.142 ± 0.022, significantly lower than that of the prototype V-type asteroid, 4 Vesta. (This corresponds to a radius of 5.2 ± 0.4 km at lightcurve mean.) Analysis with the standard thermal model (STM) results in a sub-solar temperature of 292.3 ±  2.8 K and beaming parameter η = 1.16 ± 0.05. Thermophysical modeling places a lower limit of on the thermal inertia of the asteroid’s surface layer (if the surface is very smooth) but more likely values fall between 30 and depending on the sense of rotation.The emissivity spectrum, calculated by dividing the measured thermal flux spectrum by the modeled thermal continuum, exhibits mineralogically interpretable spectral features within the 9-12 μm reststrahlen band, the 15-16.5 μm Si-O-Si stretching region, and the 16-25 μm reststrahlen region that are consistent with pyroxene of diogenitic composition: extant diogenitic pyroxenes fall within the narrow compositional range Wo_2±1En_74±2Fs_24±1. Spectral deconvolution of the 9-12 μm reststrahlen features indicates that up to ≈20% olivine may also be present, suggesting an olivine-diogenite-like mineralogy. The mid-IR spectrum is inconsistent with non-cumulate eucrite as the major component on the surface of 956 Elisa, although cumulate eucrite material may be present at abundances lower than that of the diogenite component.Analysis of new near-IR spectra of 956 Elisa with the Modified Gaussian Model (MGM; Sunshine, J.M., Pieters, C.M., Pratt, S.F. [1990]. J. Geophys. Res. 95 (May), 6955-6966) results in two pyroxene compositions: 75% magnesian low-Ca pyroxene and 25% high-Ca pyroxene. High-Ca pyroxene is not evident in the mid-IR data, but may belong to a component that is underrepresented in the mid-IR spectrum either because of its spatial distribution on the asteroid or because of its particle size. High-Ca pyroxenes that occur as exsolution lamellae may also be more evident spectrally in the NIR than in the mid-IR. In any case, we find that the mid-IR spectrum of 956 Elisa is dominated by emission from material of diogenite-like composition, which has very rarely been observed among asteroids.     

Simulations of deep pencil-beam redshift surveys

We create mock pencil-beam redshift surveys from very large cosmological N -body simulations of two cold dark matter (CDM) cosmogonies, an Einstein–de Sitter model ( τ CDM) and a flat model with Ω₀=0.3 and a cosmological constant (ΛCDM). We use these to assess the significance of the apparent periodicity discovered by Broadhurst et al. Simulation particles are tagged as 'galaxies' so as to reproduce observed present-day correlations. They are then identified along the past light-cones of hypothetical observers to create mock catalogues with the geometry and the distance distribution of the Broadhurst et al. data. We produce 1936 (2625) quasi-independent catalogues from our τ CDM (ΛCDM) simulation. A couple of large clumps in a catalogue can produce a high peak at low wavenumbers in the corresponding one-dimensional power spectrum, without any apparent large-scale periodicity in the original redshift histogram. Although the simulated redshift histograms frequently display regularly spaced clumps, the spacing of these clumps varies between catalogues and there is no 'preferred' period over our many realizations. We find only a 0.72 (0.49) per cent chance that the highest peak in the power spectrum of a τ CDM (ΛCDM) catalogue has a peak-to-noise ratio higher than that in the Broadhurst et al. data. None of the simulated catalogues with such high peaks shows coherently spaced clumps with a significance as high as that of the real data. We conclude that in CDM universes, the regularity on a scale of ∼130  h ⁻¹ Mpc observed by Broadhurst et al. has a priori probability well below 10⁻³.     

Motion of test particles in parabolic density distributions

A detailed study of the motion of test-particles [either having a nonzero rest-mass or zero rest-mass] has been carried out for Tolman's type VII solution with vanishing surface density, which is one of the few physically relevant exact solutions of Einstein's field equations for static and spherically symmetric mass distributions.The trapping angles, 0, at which the test-particles escape these configurations are calculated and the trajectories of test-particles are studied in detail. The types of trajectories found for this spacetime geometry are: (1) arc-like trajectories, (2) spiral-like trajectories ending into a circle of constant radius, (3) trajectories with a cusp at the minimum distance, (4) double-bounded trajectories, and (5) double-bounded trajectories with a cusp at the minimum distance. The test-particles following the trajectories of type (1) and type (3) escape the configuration while others are trapped within the structure. Besides the advancement of periastron of the orbits the retrogradation of periastrons are also observed.The stability of the structures is considered by using the variational method (Chandrasekhar, 1964a,b), and its is seen that the structures remain stable at least for a central redshift,z0, as large as 5.09.These studies may distinguish relativistic cluster from a Newtonian one and may find application to the local models of quasi-stellar objects (QSOs).     

Models of travel demand with endogenous preference change and heterogeneous agents

In the literatures of regional science, urban economics, and urban development planning, a working assumption is that individuals respond to incentives and regulations, given their preferences. Models for planning and policy analyses are used to consider what might occur if the incentives or regulations were different. In these models, however, preferences are usually assumed to be given and stable, and agents are usually assumed to be homogeneous. This paper focuses on the implications of making preferences in models of policy implementation endogenously determined and time varying heterogeneous agents. We consider first the recent literature on intertemporal choice and preference change, which cuts across many disciplines, and more briefly the literature on norm-regarding behavior. We then elaborate a simple model of transportation demand—from a static to a dynamic orientation, from fixed and exogenously given preferences of strictly self-regarding agents to endogenously determined and policy-induced preferences of heterogeneous agents—and illustrate its characteristics with simple numerical examples.     

Effect of hysteretic smoothness on inelastic response spectra with constant‐ductility

This paper presents an efficient methodology for computing constant‐ductility inelastic response spectra. The computation of constant‐ductility spectra involves numerical root‐finding algorithms to find the strongest structure providing a desired ductility response. Smooth inelastic structural behavior is modeled using a first‐order nonlinear differential equation and the transient structural response is solved using an implicit algorithm requiring Newton iterations at each time step. For structural models with smooth hysteretic behavior (not piece‐wise linear), a simple root‐finding method involving a combination of hyperbolic fits, linear interpolation, and Newton's method converges upon the highest strength (conservative) solution with a small number of iterations. The effect of the hysteretic smoothness on the occurrence of multiple roots is examined for two near‐fault and two far‐fault earthquake records, and for two measures of ductility and for normalized hysteretic energy. The results indicate how the smoothness of the hysteretic behavior affects ductility demand and constant‐ductility response spectra. Copyright © 2010 John Wiley & Sons, Ltd.