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General theorems concerning the strong consistency of the MLE of exponential mixture parameters are proved. These theorems imply the strong consistency of the MLE of normal mixture parameters when the data is organized into fields each of which is a random sample from one of the component normal distributions.
The paper presents a family of isothermal magnetostatic atmospheres with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model J is directed along the x-axis, where x is the horizontal ignorable coordinate. The current J is taken to be proportional to the cube of the magnetostatic potential A and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. A range of similarity solution examples are displayed depending on the values of the similarity parameters. Each similarity parameter corresponds to a symmetry of the underlying nonlinear elliptic equation for A. The similarity parameters also determine the source currents for the potential field solution of the family. The solutions show the interplay between the gravitational force, the J & B force (B, magnetic field induction) and the gas pressure gradient.
The shape of the oxygen abundance profile is examined for seven nearby spiral galaxies in which at least 15 H II regions have been observed. The radial abundance profile for three of these galaxies has a distinct change in slope. The others show no deviation from a single scale-length exponential. This behavior is explained within the framework of the star-forming viscous disk model of galaxy evolution. A prediction is made that radial abundance profiles of noninteracting unbarred spiral galaxies change slope at the radius where the rotation curve changes from linearly rising to flat. For barred and interacting galaxies the situation is complicated by additional mixing mechanisms of the interstellar medium.
Hemispherical dispersion of the SO2 cloud from the August 2008 Kasatochi eruption is analyzed using satellite data from the Ozone Monitoring Instrument (OMI) and the Goddard Trajectory Model (GTM). The operational OMI retrievals underestimate the total SO2 mass by 20-30% on 8-11 August, as compared with more accurate offline Extended Iterative Spectral Fit (EISF) retrievals, but the error decreases with time due to plume dispersion and a drop in peak SO2 column densities. The GTM runs were initialized with and compared to the operational OMI SO2 data during early plume dispersion to constrain SO2 plume heights and eruption times. The most probable SO2 heights during initial dispersion are estimated to be 10-12 km, in agreement with direct height retrievals using EISF algorithm and IR measurements. Using these height constraints a forward GTM run was initialized on 11 August to compare with the month-long Kasatochi SO2 cloud dispersion patterns. Predicted volcanic cloud locations generally agree with OMI observations, although some discrepancies were observed. Operational OMI SO2 burdens were refined using GTM-predicted mass-weighted probability density height distributions. The total refined SO2 mass was integrated over the Northern Hemisphere to place empirical constraints on the SO2 chemical decay rate. The resulting lower limit of the Kasatochi SO2 e-folding time is approx.8-9 days. Extrapolation of the exponential decay back in time yields an initial erupted SO2 mass of approx.2.2 Tg on 8 August, twice as much as the measured mass on that day.
The latter half of the last century has seen rapid advancements in semiconductor crystal growth powered by the demand for high performance electronics in myriad applications. The reduced gravity environment of space has also been used for crystal growth tests, especially in instances where terrestrial growth has largely been unsuccessful. While reduced gravity crystal growth affords some control of the gravity parameter, many crystals grown in space, to date, have structural flaws believed to result from convective motions during the growth phase. The character of these instabilities is not well understood but is associated with thermal and solutal density variations near the solidification interface in the presence of residual gravity and g-jitter. In order to study these instabilities in a separate, controlled space experiment, a concentration gradient would first have to be artificially established in a timely manner as an initial condition. This is generally difficult to accomplish in a microgravity environment because the momentum of the fluid injected into a test cell tends to swirl around and mix in the absence of a restoring force. The use of magnetic fields to control the motion and position of liquids has received growing interest in recent times. The possibility of using the force exerted by a non-uniform magnetic field on a ferrofluid to not only achieve fluid manipulation but also to actively control fluid motion makes it an attractive candidate for space applications. This paper describes a technique for quickly establishing a linear or exponential fluid concentration gradient using a magnetic field in place of gravity to stabilize the deployment. Also discussed is a photometric technique for measuring the concentration profile using light attenuation. Results of the ground-based experiments indicate that the concentration distribution is within 3% of the predicted value. Although any range of concentations can be realized, photometric constraints are discussed which impose some limitations on measurements.
Since Alvarez et al., discovered a worldwide approx. cm-thick layer of fine sediments laden with platinum group elements in approximately chondritic proportions exactly at the Cretaceous-Tertiary (C-T) boundary, and proposed bolide-impact as triggering mass extinctions, many have studied this hypothesis and the layer itself with its associated spherules and shocked quartz. At issue is whether the mass extinctions, and this horizon has an impact versus volcanic origin. A critical feature of the Alvarez hypothesis is the suggestion that the bolide or possibly a shower of objects delivered to the earth approx. 0.6 x 10 to the 18th power g of material which resulted in aerosol-sized ejecta such that global insolation was drastically reduced for significant periods. Such an event would lower temperatures on continents and halt photosynthesis in the upper 200 m of th eocean. The latter would strangle the marine food chain and thus produce the major marine faunal extinctions which mark the C-T boundary. Crucial issues examined include: What are the dynamics of atmospheric flow occurring upon impact of a large bolide with the earth; What is the size distributions of the very fine impact ejecta and how do these compare to the models of ejecta which are used to model the earth's radiative thermal balance. The flow field due to passage of a 10 km diameter bolide through an exponential atmosphere and the interaction of the gas flow and bolide with the solid ear was calculated. The CO2 released upon impact onto shallow marine carbonate sections was modeled and found that the mass of CO2 released exceeds the present 10 to the 18th power g CO2 budget of the earth's atmosphere by several times. Using the calculations of Kasting and Toon it was found that to compute the temperature rise of the earth's surface as a function of CO2 content, it was found that sudden and prolonged global increases are induced from impact of 20 to 50 km radius projectiles and propose that sudden terrestrial greenhouse-induced heating, not cooling, produced the highly variable extinctions seen at the C-T boundary.
We present our temporal and spectral analyses of 29 bursts from SGRJ0501+4516, detected with the Gamma-ray Burst Monitor onboard the Fermi Gamma-ray Space Telescope during the 13 days of the source activation in 2008 (August 22 to September 3). We find that the T(sub 90) durations of the bursts can be fit with a log-normal distribution with a mean value of approx. 123 ms. We also estimate for the first time event durations of Soft Gamma Repeater (SGR) bursts in photon space (i.e., using their deconvolved spectra) and find that these are very similar to the T(sub 90)s estimated in count space (following a log-normal distribution with a mean value of approx. 124 ms). We fit the time-integrated spectra for each burst and the time-resolved spectra of the five brightest bursts with several models. We find that a single power law with an exponential cutoff model fits all 29 bursts well, while 18 of the events can also be fit with two black body functions. We expand on the physical interpretation of these two models and we compare their parameters and discuss their evolution. We show that the time-integrated and time-resolved spectra reveal that E(sub peak) decreases with energy flux (and fluence) to a minimum of approx. 30 keV at F = 8.7 x 10(exp -6)erg/sq cm/s, increasing steadily afterwards. Two more sources exhibit a similar trend: SGRs J1550 - 5418 and 1806 - 20. The isotropic luminosity, L(sub iso), corresponding to these flux values is roughly similar for all sources (0.4 - l.5 x 10(exp 40) erg/s.
We use only left eigenvectors to evaluate the matrix exponential in the method of discrete ordinates for the vector radiative transfer equation, which neglects circular polarization, in a plane-parallel atmosphere. This is contrary to a common practice of using the right eigenvectors to evaluate the matrix exponential combined with the left eigenvectors to avoid the inversion of the matrix of the right ones. Two numerical tests for Rayleigh and Aerosol scattering confirm our idea. For better explanation of our approach and for independent crosscheck of our results, we distribute an example in C/C++.
Organic microstructure production in Miller-Urey spark discharge flasks is an energy-dependent, autocatalytic process which follows first order kinetics similar to microbial growth curves. These relationships hold for all three major morphological types of microstructures observed. The three types are assembled from smaller precursor subunits which associate according to a binomial distribution. These structures could have formed bounded systems in which pre-biological processes might have occurred.
A numerical study is conducted of a reacting flowfield generated by a single hydrogen jet injected transversely behind a rearward facing step. A nonreacting mixing study was followed by a reacting simulation. The computation simulates a current experimental condition. The validation of the numerical solution was limited to a comparison of the wall-pressure distribution along the wall. The comparison indicates agreement between the experiment and the prediction with a maximum error of 7 percent. The addition of the reaction responsible for HO2 production (H + O2 + M = HO2 + M) to an initially simplified chemical mechanism reduced the exponential growth of the free radicals and reduced the amount of heat released by combustion; as a result, the flowfield was significantly changed. A reversed flow was obtained in limited regions of the flow.
An experimental study was undertaken to measure solutal distributions in the diffusion layer produced during the vertical directional solidification (VDS) of an ammonium chloride - water (NH4Cl-H2O) solution. Interferometry was used to obtain concentration measurements in the 1-2 millimeter region defining the diffusion layer. These measurements were fitted to an exponential form to extract the characteristic diffusion parameter for various times after the start of solidification. The diffusion parameters are within the limits predicted by steady state theory and suggest that the effective solutal diffusivity is increasing as solidification progresses.
If plotted on mass vs time diagrams, geologic entities (for example, continental and oceanic crust, sediments, and mineral resources) display an exponential (power law) relationship, with entity per unit time increasing toward the present. This relationship is consistent with the concept of recycling and can be simulated mathematically. The approach is based on the plate tectonic theory and considers area-age or mass-age distributions of crystalline basement and sediments for major global tectonic realms. Each tectonic realm is characterized by a specific lifespan, which is an inverse function of its recycling rate. The estimated average half-area of half-mass ages are given. The corresponding parameters for continental crust are 690 Ma for K/Ar, and approximately 1200 Ma for Rb/St and U-Th/Pb dating pairs. Tectonic diversity preserved in the geologic record is therefore a function of time, with oceanic tectonic realms, because of their rapid recycling, underrepresented in the rocks older than approximately 300 Ma. The Sm/Nd isotopic systematic of sediments suggest that, for a near steady-state post-Archean sedimentary mass, recycling is approximately 90 + or - 5 percent cannibalistic. This yields an estimated upper limit on crust-mantle exchange via sediment subduction of approximately 1.1 + or - 0.5 x 10 g a(sup -1) considerably less than demanded by isotopic constraints. The discrepancy may indicate the existence of additional loci, such as orogenic belts, for significant crust-mantle interaction.
The third EGRET catalog lists 84 sources within 10 deg of the Galactic Plane. Five of these are well-known spin-powered pulsars, 2 and possibly 3 others are blazars, and the remaining 74 are classified as unidentified, although 6 of these are likely to be artifacts of nearby strong sources. Several of the remaining 68 unidentified sources have been noted as having positional agreement with supernovae remnants and OB associations. Others may be radio-quiet pulsars like Geminga, and still others may belong to a totally new class of sources. The question of the energy spectral distributions of these sources is an important clue to their identification. In this paper, the spectra of the sources within 10 deg of Galactic Plane are fit with three different functional forms; a single power law, two power laws, and a power law with an exponential cutoff. Where possible, the best fit is selected with statistical tests. Twelve, and possibly an additional 5 sources, are found to have spectra that are fit by a breaking power law or by the power law with exponential cutoff function.
It is a common experience that rainfall is intermittent in space and time. This is reflected by the fact that the statistics of area- and/or time-averaged rain rate is described by a mixed distribution with a nonzero probability of having a sharp value zero. In this paper we have explored the dependence of the probability of zero rain on the averaging space and time scales in large multiyear data sets based on radar and rain gauge observations. A stretched exponential fannula fits the observed scale dependence of the zero-rain probability. The proposed formula makes it apparent that the space-time support of the rain field is not quite a set of measure zero as is sometimes supposed. We also give an ex.planation of the observed behavior in tenus of a simple probabilistic model based on the premise that rainfall process has an intrinsic memory.
Most gamma-ray bursts (GRBs) exhibit deficits of X-rays below approximately 200 keV. Here we consider a spectral model in which the burst source is shielded by an optically thick layer of circumburster material (CBM) rich in iron-group elements whose photoelectric absorption opacity exceeds the Thomson opacity below approximately 120 keV. For power-law distributions of absorption depths along the lines of sight the absorbed spectrum can indeed mimic the typial GRB spectrum. This model predicts that (a) the spectrum should evolve monotonically from hard to soft during each energy release, which is observed in most bursts, especially in fast rise exponential decay bursts; (b) Fe spectral features near 7 keV may be present in some bursts; and (c) the ratio of burst distances to the CBM and to Earth should be approximately 10(exp -11) if the spectral evolution is purely due to Fe stripping by the photons.
Long-slit spectra across the Orion Bar reveal significant differences in the spatial behavior of the components of the 3 microns polycyclic aromatic hydrocarbon (PAH) spectrum. The strong PAH band at 3.29 microns generally decreases exponentially with distance from the ionization front into the molecular cloud (scale height approximately 12"), although excesses appear approximately 10" and 20" behind the ionization front, close to layers of H2 and CO emission, respectively. The 3.40 microns PAH feature separates into two components with very different spatial distributions. The main component (at 3.395 microns), along with the 3.51 microns band and the PAH plateau (3.3-3.6 microns), shows excess emission approximately 10" and approximately 20" behind the ionization front, stronger than the excesses in the 3.29 microns band. The extra component of the 3.40 microns band, which peaks at approximately 3.405 microns, has a spatial distribution very similar to the H2 emission. Aromatic C-H stretches in PAHs most likely produce the 3.29 microns feature. Aliphatic C-H stretches in either attached methyl side-groups or superhydrogenated PAHs, or perhaps both, could produce the complicated spectral and spatial structure at 3.40 microns.
The mean ionization states of 44-260 keV per charge ions observed as bursts in and near the earth's magnetosphere have been determined by using the particle data collected by the University of Maryland experiment on Imp 8. We find that during the period from October 1973 to December 1976 (1) the abundance ratio of heavy ions (Z greater than 2) to alphas ranges from 0.04 to 0.10, with a mean value of 0.08 plus or minus 0.02; (2) the energy spectra of alphas and Z greater than 2 ions in these bursts are adequately represented as exponentials in energy per charge with e-folding energies of 30-50 keV/Q; (3) the e-folding energies of both alpha particles and heavier ions are generally harder upstream from the bow shock than in the magnetotail and magnetosheath; and (4) the elemental abundances and ionization state distribution of the heavy ions are consistent with those of the corona at an equilibrium coronal temperature of 1-2 x 10 to the 6th K, which tends to support a solar wind origin for these particles.
In an attempt to relate the observed crater frequencies on the saturnian satellites with absolute time, the cratering history of the Saturn system was modeled. The model is based upon several assumptions. First, the cumulative flux history at Saturn resembles that of the inner solar system. That is to say, a high cratering rate which rapidly (exponentially) decayed over the first few hundred million years followed by a significatly lower but more constant flux to the present. Second, the end of the heavy bombardment occured about 3.7-3.8 b.y. ago. Third, Population I craters, dominated by large diameters and having a shallow size-frequency distribution slope, were formed during the period of heavy bombardment. Population II craters, characterized by small craters and a steep distribution slope, have formed since the heavy bombardment ended.