Fast Mesh Refinement in Pseudospectral Optimal Control

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as $N$ increases, the condition number of the resulting linear algebra increases as $N^2$; hence, spectral efficiency and accuracy are lost in practice. In this paper, we advance Birkhoff interpolation concepts over an arbitrary grid to generate well-conditioned PS optimal control discretizations. We show that the condition number increases only as $\sqrt{N}$ in general, but is independent of $N$ for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as $N$ increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using \underline{polynomials of over a thousandth order} to solve a low-thrust, long-duration orbit transfer problem.Comment: 27 pages, 12 figures, JGCD April 201

Quasiharmonic elastic constants corrected for deviatoric thermal stresses

The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for non-cubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO$_3$-perovskite and MgSiO$_3$-post-perovskite, the major phases of the Earth's lower mantle. We show that this first order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond anvil cells.Comment: 4 figures, 1 table, submitted to Phys. Rev. B, July 200

Studies on the Weak Itinerant Ferromagnet SrRuO3 under High Pressure to 34 GPa

The dependence of the Curie temperature Tc on nearly hydrostatic pressure has been determined to 17.2 GPa for the weak itinerant ferromagnetic SrRuO3 in both polycrystalline and single-crystalline form. Tc is found to decrease under pressure from 162 K to 42.7 K at 17.2 GPa in nearly linear fashion at the rate dTc/dP = -6.8 K/GPa. No superconductivity was found above 4 K in the pressure range 17 to 34 GPa. Room-temperature X-ray diffraction studies to 25.3 GPa reveal no structural phase transition but indicate that the average Ru-O-Ru bond angle passes through a minimum near 15 GPa. The bulk modulus and its pressure derivative were determined to be B =192(3) GPa and B' = 5.0(3), respectively. Parallel ac susceptibility studies on polycrystalline CaRuO3 at 6 and 8 GPa pressure found no evidence for either ferromagnetism or superconductivity above 4 K

Stand Density in South Florida Tropical Forests: Implications for the Function and Management of Everglades Tree Islands

Within the continental US, the broadleaved forests of south Florida are exceptional in the abundance and diversity of tree species of tropical origin. Dry tropical forests are regionally most extensive in the upper Florida Keys, but are also represented on the mainland as fragments on limestone rocklands, and as “tree islands” embedded in the Everglades marsh. The exposed Everglades tree islands have a history of human use reaching back thousands of years, and are subject to frequent disturbance from tropical storms and hurricanes. They are sensitive to the hydrology of the surrounding marsh, which can lead to gradual changes in species composition or stand structure, or to the sudden loss of the woody component entirely, especially when low water tables are precursors to damaging fires. Tree islands serve as local hotspots of biodiversity, and as concentrators of phosphorus in a landscape defined by P-limitation. The mechanisms by which P reaches the tree islands and is sequestered there are complex and not completely understood, but may depend in part on transpiration and resupply of water from the adjacent wetlands. Since transpiration is a direct function of the transpiring leaf surface, which itself is expected to vary with stocking, we examined the relationship between leaf area index and stand density in 16 Everglades tree islands. To determine maximum stocking levels for such forests, we also calculated stand density for tropical forests throughout south Florida, using a protocol modified slightly from Woodard et al. 2003. Our results suggest that (1) stand density in many Everglades tree islands is well below the expressed potential of similar tropical assemblages, (2) low site occupancy may prevent such under-stocked forests from performing several ecosystem functions, and (3) stand density can serve as an effective metric of forest condition for management or restoration purposes

What children know about the source of their knowledge without reporting it as the source

We argue that, amongst 3- to 5- year-olds, failure to report the source of knowledge recently acquired in answer to “How do you know…?” is due to a specific failure to make a causal inference, in line with source monitoring theory but not fuzzy trace theory. In three Experiments, children (N = 37; 30; 59) identified a hidden toy by seeing, feeling, or by being told, having had two modes of access on each trial, one informative (e.g. seeing a toy identified by colour) and the other uninformative (e.g. being told the toy’s colour by the Experimenter who had only felt it). Children who answered the know question wrongly nevertheless reported accurately who saw and who felt the toy, and what the well-informed player had said. They also realised when the Experimenter’s uninformative access implied their own knowledge was unreliable, suggesting precocious working understanding of knowledge sources

Plasma deposition of constrained layer damping coatings

Plasma techniques are used to generate constrained layer damping (CLD) coatings on metallic substrates. The process involves the deposition of relatively thick, hard ceramic layers on to soft polymeric damping materials while maintaining the integrity of both layers. Reactive plasma sputter-deposition from an aluminium alloy target is used to deposit alumina layers, with Young's modulus in the range 77-220GPa and thickness up to 335 μ, on top of a silicone film. This methodology is also used to deposit a 40 μ alumina layer on a conventional viscoelastic damping film to produce an integral damping coating. Plasma CLD systems are shown to give at least 50 per cent more damping than equivalent metal-foil-based treatments. Numerical methods for rapid prediction of the performance of such coatings are discussed and validated by comparison with experimental results

Light Baryon Resonances: Restrictions and Perspectives

The problem of nucleon resonances N' with masses below the Delta is considered. We derive bounds for the properties of such states. Some of these are new, while others improve upon existing limits. We discuss the nature of N' states, and their unitary partners, assuming their existence can be verified.Comment: 11 pages, 11 figur

The X-ray luminosity function of Active Galactic Nuclei in the redshift interval z=3-5

We combine deep X-ray survey data from the Chandra observatory and the wide-area/shallow XMM-XXL field to estimate the AGN X-ray luminosity function in the redshift range z=3-5. The sample consists of nearly 340 sources with either photometric (212) or spectroscopic (128) redshift in the above range. The combination of deep and shallow survey fields provides a luminosity baseline of three orders of magnitude, Lx(2-10keV)~1e43-1e46erg/s at z>3. We follow a Bayesian approach to determine the binned AGN space density and explore their evolution in a model-independent way. Our methodology accounts for Poisson errors in the determination of X-ray fluxes and uncertainties in photometric redshift estimates. We demonstrate that the latter is essential for unbiased measurement of space densities. We find that the AGN X-ray luminosity function evolves strongly between the redshift intervals z=3-4 and z=4-5. There is also suggestive evidence that the amplitude of this evolution is luminosity dependent. The space density of AGN with Lx<1e45erg/s drops by a factor of 5 between the redshift intervals above, while the evolution of brighter AGN appears to be milder. Comparison of our X-ray luminosity function with that of UV/optical selected QSOs at similar redshifts shows broad agreement at bright luminosities, Lx>1e45erg/s. The faint-end slope of UV/optical luminosity functions however, is steeper than for X-ray selected AGN. This implies that the type-I AGN fraction increases with decreasing luminosity at z>3, opposite to trends established at lower redshift. We also assess the significance of AGN in keeping the hydrogen ionised at high redshift. Our X-ray luminosity function yields ionising photon rate densities that are insufficient to keep the Universe ionised at redshift z>4. A source of uncertainty in this calculation is the escape fraction of UV photons for X-ray selected AGN.Comment: MNRAS accepte

Implications for Metallographic Cooling Rates, Derived from Fine-Scale Analytical Traverses Across Kamacite, Taenite, and Tetrataenite in the Butler Iron Meteorite

The "M-shaped" Ni concentrations across Widmanstatten patterns in iron meteorites, mesosiderites, and ordinary chondrites are commonly used to calculate cooling rates. As Ni-poor kamacite exolves from Ni-rich taenite, Ni concentrations build up at the kamacite-taenite interface because of the sluggish diffusivity of Ni. Quantitative knowledge of experimentally-determined Ni diffusivities, coupled with the shape of the M-profile, have been used to allow calculation of cooling rates that pertained at low temperatures, less than or equal to 500 C. However, determining Ni metallographic cooling rates are challenging, due to the sluggish diffusivity of Ni at low temperatures. There are three potential difficulties in using Ni cooling rates at low temperatures: (i) Ni diffusivities are typically extrapolated from higher-temperature measurements; (ii) Phase changes occur at low temperatures that may be difficult to take into account; and (iii) It appears that Ge in kamacite and taenite has continued to equilibrate (or attempted to equilibrate) at temperatures below those that formed the M-shaped Ni profile. Combining Ni measurements with those of other elements has the potential to provide a way to confirm or challenge Ni-determined cooling rates, as well as provide insight into the partitioning behaviors of elements during the cooling of iron meteorites. Despite these benefits, studies that examine elemental profiles of Ni along with other elements in iron meteorites are limited, often due to the low concentration levels of the other elements and associated analytical challenges. The Butler iron meteorite provides a good opportunity to conduct a multi-element analytical study, due to the higher concentration levels of key elements in addition to Fe and Ni. In this work, we perform combined analysis for six elements in the Butler iron to determine the relative behaviors of these elements during the evolution of iron meteorites, with implications for metallographic cooling rates

Integrability and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the Quantum Inverse Scattering Method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.Comment: 14 pages, latex, no figure