The boundary value problem of Poisson’s equation with Stokes’ boundary condition

The following Poisson’s equation with the Stokes’ boundary condition is dealt with $$\left\{ \begin{gathered} \nabla ^2 T = - 4\pi Gp outside S, \hfill \\ \left. {\frac{{\partial T}}{{\partial h}} = \frac{1}{\gamma }\frac{{\partial y}}{{\partial h}}T} \right|_s = - \Delta g, \hfill \\ T = O\left( {r^{ - 3} } \right) at infinity, \hfill \\ \end{gathered} \right.$$ whereS is reference ellipsord. Under spherical approximation transformation, the ellipsoidal correction terms about the boundary condition, the equation and the density in the above BVP are respectively given. Therefore, the disturbing potentialT can he obtained if the magnitudes aboveO(ε⁴) are neglected.     

Investigation by backscatter radar of artificial irregularities produced in ionospheric plasma heating experiments

The artificial ionospheric turbulence occurs in the ionosphere illuminated by high power HF radio waves. There are a lot of irregularities stretched along the geomagnetic field in this region. The investigation of the artificially disturbed ionospheric region is based on the reception of back scattered signals (BSS) which permits the basic parameters of this region to be estimated and its inhomogeneous structure to be described.Experiments were carried out using ‘Sura’ heating facility in the frequency range of ? = 4.7–9 MHz (ordinary mode) with the effective radiated power P_eff = 50–70 MW beamed vertically upwards. The most important dynamic and statistical BSS characteristics (the built-up time, the relaxation and autocorrelation times, the BSS amplitude spatial correlation function and power spectra) were measured using probe waves in the frequency range of that made it possible to obtain the basic parameters of the artificial irregularities. The model representation of a disturbed region in a form of a periodic structure gives a possibity to evaluate the scale of the structure, the whole size of the disturbance and its power and to calculate the main BSS characteristics.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Crystallization processes in an artificial magma: variations in crystal shape,growth rate and composition with melt cooling history

A large (4.8 m³, 1.3x10⁷ g) artificial mafic melt with a bulk composition similar to that of a basalt (but with a high CaO content of 17 wt%) was generated during a demonstration of in situ vitrification and was allowed to cool naturally. During the melting process, convection was vigorous, resulting in a chemically and thermally homogeneous melt body. Once heating was complete, the cooling rate was rapid with the temperature dropping from 1500°C to 500°C in 6 days within the interior of the 3 m diameter, 1.5 m thick body. A 20 h period of constant temperature (1140°C) observed during colling was the result of latent heat released by widespread crystallization. The final crystalline assemblage consists of diopsidic to hedenbergitic pyroxene and anorthitic feldspar, with a subordinate amount of potassic feldspar, plus a small amount of evolved glass. The compositions and proportions of phases agree well with those predicted by the MELTS thermodynamic model. Thermal and textural evidence suggest that convection within the melt ceased coincident with formation of the first crystals. Textural investigation of core samples reveals large (up to 1 cm in length) acicular diopsidic pyroxenes in a matrix of smaller feldspar and zoned pyroxene crystals (500 m in length). Crystal shape and pyroxene composition vary as a function of position within the solidified body, as a function of cooling rate. Both crystal size and degree of crystallinity are highest in the central, most slowly-cooled parts of the rock. Crystal shape is characterized by tabular, equilibrium-growth forms in the slowly-cooled areas, grading to highly skeletal, dendritic forms at the rapidly-cooled edges of the body. The pyroxene crystals are dominantly homogeneous diopside, but crystals are characterized by thin Fe-rich hedenbergitic rims. These rims were deposited when Mg in the melt was depleted by diopside growth, and melt temperature had cooled sufficiently to allow Fe-rich pyroxene growth. Crystal growth rates can be calculated based on thermal behavior of the melt, reinforced by thermodynamic modelling, and are determined to be between 10^-7 and 10^-8 cm/s in the central part of the melt. These estimates agree well with growth rates in natural systems with similar cooling rates. Pyroxene crystals that formed at a higher cooling rates are characterized by higher Al and lower Mg contents relative to tabular equilibrium crystalline forms, presumably as a result of disequilibrium melt compositions at the crystal-melt interface.New Mexico Bureau of Mines and Mineral Resources, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA     

A study of bernalite,Fe(OH)3, using Mössbauer spectroscopy,optical spectroscopy and transmission electron microscopy

To study the crystal chemistry of bernalite, Fe(OH)₃, and the nature of the octahedral Fe³⁺ environment, Mössbauer spectra were recorded from 80 to 350 K, optical spectra were recorded at room temperature and a sample was studied using transmission electron microscopy. The Mössbauer spectrum of bernalite consists of a single six-line magnetic spectrum at 80 K. A broadened six-line magnetic spectrum with significantly less intensity is observed at higher temperatures, and is attributed to a small fraction of bernalite occurring as small particles. The variation of hyperfine magnetic field data for bulk bernalite with temperature is well described by the Weiss molecular field model with parameters of H ₀ = 55.7±0.3 T and T _N = 427±5K. The centre shift data were fitted to the Debye model with parameters ₀=0.482±0.005 mm/s (relative to -Fe) and _M=492±30 K. The quadrupole shift is near zero at 300 K, and does not vary significantly with temperature. Absorption spectra in the visible and near infrared range show three crystal field bands of Fe³⁺ at 11 300, 16000 and 23 200 cm^-1, giving a crystal field splitting of 14 570 cm^-1 and Racah parameters of B=629 cm^-1 and C=3381 cm^-1. Infrared reflection spectra show two distinct OH-stretching frequencies, which could correspond to two structurally different types of OH groups. A band was also observed at 2250 cm^-1, suggesting the presence of molecular CO₂ in the large cation site. Analytical transmission electron microscopy indicates that Si occurs within the bernalite structure as well as along domain boundaries. Electron diffraction and imaging show that bernalite is polysynthetically twinned along {100} planes with twin domains ranging from 3 to 20 nm in thickness. Results are discussed with respect to the nature of the octahedral Fe³⁺ site, and compared with values for other iron oxides and hydroxides.     

Episode 49 of the Pu'u 'O'o-Kupaianaha eruption of Kilauea volcano-breakdown of a steady-state eruptive era

The Pu'u 'O'o-Kupaianaha eruption (1983-present) is the longest lived rift eruption of either Kilauea or neighboring Mauna Loa in recorded history. The initial fissure opening in January 1983 was followed by three years of episodic fire fountaining at the Pu'u 'O'o vent on Kilauea's east rift zone 19km from the summit (episodes 4–47). These spectacular events gave way in July 1986 to five and a half years of nearcontinuous, low-level effusion from the Kupaianaha vent, 3km to the cast (episode 48). A 49th episode began in November 1991 with the opening of a new fissure between Pu'u 'O'o and Kupaianaha. this three week long outburst heralded an era of more erratic eruptive behavior characterized by the shut down of Kupaianaha in February 1992 and subsequent intermittent eruption from vents on the west flank of Pu'u 'O'o (episodes 50 and 51). The events occurring over this period are due to progressive shrinkage of the rift-zone reservoir beneath the eruption site, and had limited impact on eruption temperatures and lava composition.     

A search for ultra-high energy counterparts to gamma-ray bursts

A small air shower array operating over many years has been used to search for ultra-high energy (UHE) gamma radiation ( 50 TeV) associated with gamma-ray bursts (GRBs) detected by the BATSE instrument on the Compton Gamma-Ray Observatory (CGRO). Upper limits for a one minute interval after each burst are presented for seven GRBs located with zenith angles < 20°. A 4.3 excess over background was observed between 10 and 20 minutes following the onset of a GRB on 11 May 1991. The confidence level that this is due to a real effect and not a background fluctuation is 99.8%. If this effect is real then cosmological models are excluded for this burst because of absorption of UHE gamma rays by the intergalactic radiation fields.     

Search for low energyν e,μ,τ andv e,μ,τ in coincidence with BATSE gamma ray bursts

A search for low energy neutrinos of all flavours in correlation with 553 ray bursts detected by BATSE aboard the Compton Observatory has been performed by the LSD (Liquid Scintillator Detector) neutrino telescope. No excess ofe,, orv _e,, candidate has been detected by LSD during the time interval in which BATSE detected the 90% of the photon flux for any of the GRBs analyzed. Upper limits on the neutrino fluxes are given in the paper.     

Magnetically-aided evolution of protoplanetary disks

We investigate the global evolution of a turbulent protoplanetary disk incorporating the effects of Maxwell stress due to a large-scale magnetic field permeating the disk. A magnetic field is produced continuously by an dynamo and the resultant Maxwell stress assists the viscous stress in p roviding the means for disk evolution. The most striking feature of magnetized disk evolution is the presence of the surface density bulge located in the magnetic gap, the region of the disk where the degree of ionization is too low to allow for coupli ng between the magnetic field and the gas. The bulge persists for a time of the order of 10⁵–10⁶ yr. The presence and persistence of the surface density bulge may have important implications for the process of planet formation and the overall characteristics of resultant planetary systems.Operated by USRA under contract No. NASW-4574 with NASA.     

Plasma processing of interstellar PAHs into solar system kerogen

Processes resulting in the formation of hydrocarbons of carbonaceous chondrites and the identity of the interstellar molecular precursors involved are an objective of investigations into the origin of the solar system and perhaps even life on earth. We have combined the resources and experience of an astronomer and physicists doing laboratory simulations with those of a chemical expert in the analysis of meteoritic hydrocarbons, in a project that investigated the conversion of polycyclic aromatic hydrocarbons (PAHs) formed in stellar atmospheres into alkanes found in meteorites. Plasma hydrogenation has been found in the University of Alabama at Birmingham Astrophysics Laboratory to produce from the precursor PAH naphthalene, a new material having an IR absorption spectrum (Lee, W. and Wdowiak, T.J., Astrophys. J. 417, L49-L51, 1993) remarkably similar to that obtained at Arizona State University of the benzene-methanol extract of the Murchison meteorite (Cronin, J.R. and Pizzarello, S., Geochim. Cosmochim. Acta 54, 2859-2868, 1990). There are astrophysical and meteoritic arguments for PAH species from extra-solar sources being incorporated into the solar nebula, where plasma hydrogenation is highly plausible. Conversion of PAHs into alkanes could also have occurred in the interstellar medium. The synthesis of laboratory analogs of meteoritic hydrocarbons through plasma hydrogenation of PAH species is underway, as is chemical analysis of those analogs. The objective is to clarify this heretofore uninvestigated process and to understand its role during the origin of the solar system as a mechanism of production of hydrocarbon species now found in meteorites. Results have been obtained in the form of time-of-flight spectroscopy and chemical analysis of the lab analog prepared from naphthalene.