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The case is considered of a matrix B which is k x n of rank k. Matrix equations are given which define the generalized inverse of B and are used to develop the transformed covariance matrix.
Human demand for food influences the water cycle through diversion and extraction of fresh water needed to support agriculture. Future population growth and economic development alone will substantially increase water demand and much of it for agricultural uses. For many semi-arid lands, socio-economic shifts are likely to exacerbate changes in climate as a driver of future water supply and demand. For these areas in particular, where the balance between water supply and demand is fragile, variations in regional climate can have potentially predictable effect on agricultural production. Satellite data and biophysically-based models provide a powerful method to quantify the interactions between local climate, plant growth and water resource requirements. In irrigated agricultural lands, satellite observations indicate high vegetation density while the precipitation amount indicates otherwise. This inconsistency between the observed precipitation and the observed canopy leaf density triggers the possibility that the observed high leaf density is due to an alternate source of water, irrigation. We explore an inverse process approach using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS), climatological data, and the NASA's Simple Biosphere model, SiB2, to quantitatively assess water demand in a semi-arid agricultural land by constraining the carbon and water cycles modeled under both equilibrium (balance between vegetation and prevailing local climate) and nonequilibrium (water added through irrigation) conditions. We postulate that the degree to which irrigated lands vary from equilibrium conditions is related to the amount of irrigation water used. We added water using two distribution methods: The first method adds water on top of the canopy and is a proxy for the traditional spray irrigation. The second method allows water to be applied directly into the soil layer and serves as proxy for drip irrigation. Our approach indicates that over the study site, for the month of July, spray irrigation resulted in an irrigation amount of about 1.4 mm per occurrence with an average frequency of occurrence of 24.6 hours. The simulated total monthly irrigation for July was 34.85 mm. In contrast, the drip irrigation resulted in less frequent irrigation events with an average water requirement about 57% less than that simulated during the spray irrigation case. The efficiency of the drip irrigation method rests on its reduction of the canopy interception loss compared to the spray irrigation method. When compared to a country-wide average estimate of irrigation water use, our numbers are quite low. We would have to revise the reported country level estimates downward to 17% or less
Recently, statistical distributions have been explored to provide estimates of the mineralogical diversity of Earth, and Earth-like planets. In this paper, a Bayesian approach is introduced to estimate Earth’s undiscovered mineralogical diversity. Samples are generated from a posterior distribution of the model parameters using Markov chain Monte Carlo simulations such that estimates and inference are directly obtained. It was previously shown that the mineral species frequency distribution conforms to a generalized inverse Gauss–Poisson (GIGP) large number of rare events model. Even though the model fit was good, the population size estimate obtained by using this model was found to be unreasonably low by mineralogists. In this paper, several zero-truncated, mixed Poisson distributions are fitted and compared, where the Poisson-lognormal distribution is found to provide the best fit. Subsequently, the population size estimates obtained by Bayesian methods are compared to the empirical Bayes estimates. Species accumulation curves are constructed and employed to estimate the population size as a function of sampling size. Finally, the relative abundances, and hence the occurrence probabilities of species in a random sample, are calculated numerically for all mineral species in Earth’s crust using the Poisson-lognormal distribution. These calculations are connected and compared to the calculations obtained in a previous paper using the GIGP model for which mineralogical criteria of an Earth-like planet were given.
Human epithelioid T-1E cells were cultured in suspension and subjected to density gradient electrophoresis upward in a vertical column. It is indicated that the most rapidly migrating cells were at the beginning of the cell cycle and the most slowly migrating cells were at the end of the cell cycle. The fastest migrating cells divided 24 hr later than the slowest migrating cells. Colonies developing from slowly migrating cells had twice as many cells during exponential growth as did the most rapidly migrating cells, and the numbers of cells per colony at any time was inversely related to the electrophoretic migration rate. The DNA measurements by fluorescence flow cytometry indicates that the slowest migrating cell populations are enriched in cells that have twice as much DNA as the fastest migrating cells. It is concluded that electrophoretic mobility of these cultured human cells declines steadily through the cell cycle and that the mobility is lowest at the end of G sub 2 phase and highest at the beginning of G sub 1 phase.
We study the X-ray emission in a Sample of galaxy clusters using the BeppoSAX PDS instrument in the 20 - 80 keV energy band. We estimate the non-thermal hard X-ray cluster emission (HXR) by modeling the thermal contribution from the cluster gas and the non-thermal contamination from the unobscured AGN in the clusters. We also evaluate the systematic uncertainties due to the background fluctuations. Assuming negligible contamination from the obscured AGN, the resulting non-thermal component is detected at a 2 sigma level in approx. 50% of the non-significantly AGN-contaminated clusters: A2142, A2199, A2256, A3376, Coma, Ophiuchus and Virgo. The data are consistent with a scenario whereby relaxed clusters have no hard X-ray component of non-thermal origin, whereas merger clusters do. The co-added spectrum of the above clusters indicates a power-law spectrum for the HXR with a photon index of 2.8+0.3-0.4 in the 12 - 115 keV band, and we find indication that it has extended distribution. These indications argue against significant contamination from obscured AGN, which have harder spectra and centrally concentrated distribution. These results are supportive of the assumption of the merger shock acceleration of electrons in clusters, which has been proposed as a possible origin of the non-thermal hard X-ray emission models. Assuming that the Cosmic Microwave Background photons experience Inverse Compton scattering from the merger-accelerated relativistic electrons, and thus produce the observed HXR, the measured hard X-ray slope corresponds to a differential momentum spectra of the relativistic electrons with a slope of mu = 3.8 - 5.0. In presence of cluster magnetic fields this relativistic electron population produces synchrotron emission with a spectral index of 1.4 - 2.1, consistent with radio halo observations of merger clusters. Thus both hard X-ray and radio observations of merger clusters are consistent with the Inverse Compton model. The observed slope of HXR is also consistent with that predicted by the non-thermal bremsstrahlung, which chus cannot be ruled by the fit to the current data, even though this model requires an extreme, untenable cluster energetics. Assuming centrally concentrated distribution of HXR, the data requires a harder slope for the HXR spectrum, which is consistent with secondary electron models, but this model yields a worse fit to the PDS data and thus seems to be disfavored over the primary electron Inverse Compton model.
We study the X-ray emission in a sample of galaxy clusters using the BeppoSAX PDS instrument in the 20-80 keV energy band. We estimate the nonthermal hard X-ray (HXR) cluster emission by modeling the thermal contribution from the cluster gas and the nonthermal contamination from the unobscured active galactic nuclei (AGNs) in the clusters. We also evaluate the systematic uncertainties due to the background fluctuations. Assuming negligible contamination from the obscured AGNs, the resulting nonthermal component is detected at a 2 sigma level in approx. 50% of the nonsignificantly AGN-contaminated clusters: A2142, A2199, A2256, A3376, Coma, Ophiuchus, and Virgo. The data are consistent with a scenario whereby relaxed clusters have no hard X-ray component of nonthermal origin, whereas merger clusters do, with a 20-80 keV luminosity of approx. 10(exp 43)-10(exp 44) h(sup -2 sub 50) ergs/s. The co-added spectrum of the above clusters indicates a power-law spectrum for the HXR emission with a photon index of 2.8(sup +0.3 sub -0.4) in the 12-115 keV band, and we find indication that it has extended distribution. These indications argue against significant contamination from obscured AGNs, which have harder spectra and a centrally concentrated distribution. These results are supportive of the assumption of the merger shock acceleration of electrons in clusters, which has been proposed as a possible origin of the nonthermal hard X-ray emission models. Assuming that the cosmic microwave background photons experience inverse Compton scattering from the merger-accelerated relativistic electrons and thus produce the observed HXR, the measured hard X-ray slope corresponds to a differential momentum spectra of the relativistic electrons with a slope of mu = 3.8-5.0. In presence of cluster magnetic fields this relativistic electron population produces synchrotron emission with a spectral index of 1.4-2.1, consistent with radio halo observations of merger clusters. Thus both hard X-ray and radio observations of merger clusters are consistent with the inverse Compton model.
A cosmological hydrodynamic code is described, which includes a routine to compute cosmic ray acceleration and transport in a simplified way. The routine was designed to follow explicitly diffusive, acceleration at shocks, and second-order Fermi acceleration and adiabatic loss in smooth flows. Synchrotron cooling of the electron population can also be followed. The updated code is intended to be used to study the properties of nonthermal synchrotron emission and inverse Compton scattering from electron cosmic rays in clusters of galaxies, in addition to the properties of thermal bremsstrahlung emission from hot gas. The results of a test simulation using a grid of 128 (exp 3) cells are presented, where cosmic rays and magnetic field have been treated passively and synchrotron cooling of cosmic ray electrons has not been included.
This article studies changes in microwave signals of oceanic snowfall in response to the formation of snow-covered sea ice using active and passive coincident data from the radar and radiometer onboard the CloudSat and the global precipitation measurement satellites. Using reanalysis data of liquid and ice water path as well as satellite retrievals of sea ice snow-cover depth, spectral regions are determined over which the snowfall signatures are likely to be obscured or falsely detected. Relying on an a priori database populated with the active–passive coincidences, a Bayesian snowfall retrieval algorithm is presented that links a k -nearest neighbor matching with the inverse Gaussian estimator used in the Goddard profiling algorithm. Without relying on any ancillary data of air temperature, the results demonstrate that over open oceans (sea ice), we can passively retrieve the CloudSat active snowfalls with a true positive rate of 92 (85%) and the root mean squared error of 0.24 (0.15) mm per h.
Two elements are essential in structural health monitoring utilizing dynamic responses: response measurement with high-frequency contents, i.e., small characteristic wavelengths, that can adequately reflect damage features, and effective inverse identification analysis that is however oftentimes under-determined. The advancement of smart structure integration has led to active interrogation through frequency-sweeping piezoelectric impedance measurement at high frequency range. In this research we develop a multi-objective optimization formulation for the identification of damage location and severity utilizing piezoelectric impedance. While one optimization objective is to match the response measurement with finite element model prediction in the damage parametric space, the other is the number of locations of damage, i.e., the sparsity of damage index as the solution vector, since damage usually occurs within a small number of locations. This multi-objective formulation fits well the under-determined nature of damage identification, as it naturally provides multiple solutions as basis for further elucidation. The challenge remaining is how to find a small solution set that can include the actual damage scenario. Here we develop a novel inverse identification framework utilizing the intelligent swarm optimizer which possesses flexibility for enhancement. We first embed a sparsity enforcement process into the population generation of the optimizer, which yields a solution repository intrinsically possessing sparsity. We then apply reinforcement learning so the agents can adaptively opt for local strategies with the aim of enriching the searching patterns to diversify the solutions. Through the incorporation of a Q-table, searching toward more promising directions will be rewarded. Our case analyses employing experimental data indicate that this sparsity-conscious multi-objective particle swarm optimization technique can lead to a small solution set which generally encompasses the true damage scenario. This effectively solves the structural damage identification problem with piezoelectric impedance measurement.
The use of a quantitative analysis of the dominant source of relaxation in ruby spin systems to make predictions of key maser amplifier parameters is described. The spin-lattice Hamiltonian which describes the interaction of the electron spins with the thermal vibrations of the surrounding lattice is obtained from the literature. Taking into account the vibrational anisotropy of ruby, Fermi's rule is used to calculate the spin transition rates between the maser energy levels. The spin population rate equations are solved for the spin transition relaxation times, and a comparison with previous calculations is made. Predictions of ruby gain, inversion ratio, and noise temperature as a function of physical temperature are made for 8.4-GHz and 32-GHz maser pumping schemes. The theory predicts that ruby oriented at 90 deg will have approximately 50 percent higher gain in dB and slightly lower noise temperature than a 54.7-deg ruby at 32 GHz (assuming pump saturation). A specific calculation relating pump power to inversion ratio is given for a single channel of the 32-GHz reflected wave maser.
New observational results on color and population gradients in the cores of several highly concentrated globular clusters are reported. The gradients are in the sense of blueing toward the cluster center, and appear to be caused mostly or entirely by population gradients in the number of blue horizontal branch and red giant branch stars. Taken at face value, such gradients would imply an inverse mass segregation, but this interpretation is not fully secure. In any case, their dynamical understanding remains a problem.
We describe a refined calculation of high-energy emission from rotation-powered pulsars based on the outer gap model of Cheng, Ho, & Ruderman (1986 a, b). In this calculation, vacuum gaps form in regions near the speed-of-light cylinder of the pulsar magnetosphere along the boundary between the closed and open field line zones. We have improved upon previous efforts to model the spectra from these pulsars (e.g., Cheng et al. 1986b; Ho 1989) by following the variation in particle production and radiation properties with position in the outer gap. Curvature, synchotron, and inverse-Compton scattering fluxes vary significantly over the gap, and their interactions via photon-photon pair production build up the radiating charge populations at varying rates. We have also incorporated an approximate treatment of the transport particle and photon fluxes between gap emission zones. These effects, along with improved computations of the particle and photon distribution, provide very important modifications of the model gamma-ray flux. In paticular, we attempt to make specific predictions of pulse profile shapes and spectral variations as a function of pulse phase and suggest further extensions to the model which may provide accurate computations of the observed high-energy emissions.
We report new Chandra hard X-ray (>2 keV) and Jansky Very Large Array C-band observations of the nuclear super bubble of NGC 3079, an analog of the “Fermi bubble” in our Milky Way. We detect extended hard X-ray emission on the southwest (SW)side of the galactic nucleus with coherent multiwavelength features in radio, Hα, and soft X-ray. The hard X-ray feature has a cone shape with possibly a weak cap, forming a bubble-like structure with a diameter of∼1.1 kpc. A similar extended feature, however, is not detected on the northeast (NE)side, which is brighter in all other wavelengths such as radio, Hα, and soft X-ray. Scattered photons from the nuclear region or other nearby point-like X-ray bright sources, inverse Compton emission from cosmic-ray(CR)electrons via interaction with the cosmic microwave background, or any individually faint stellar X-ray source populations, cannot explain the extended hard X-ray emission on the SW side and the strongly NE/SW asymmetry. A synchrotron emission model, plus a thermal component accounting for the excess at∼1 keV, can well characterize the broadband radio/hard X-ray spectra. The broadband synchrotron spectra do not show any significant cutoff, and even possibly slightly flatten at higher energy. This rule out a loss-limited scenario in the acceleration of the CR electrons in or around this superbubble. As the first detection of kiloparsec-scale extended hard X-ray emission associated with a galactic nuclear superbubble, the spatial and spectral properties of the multiwavelength emissions indicate that the CR leptons responsible for the broadband synchrotron emission from the SW bubble must be accelerated in situ, instead of transported from the nuclear region of the galaxy.
We investigate the origin of diffuse low-energy Galactic gamma-ray continuum down to about 30 keV. We calculate gamma-ray emission via bremsstrahlung and inverse Compton scattering by propagating an unbroken electron power law injection spectrum and employing a Galactic emmissivity model derived from COSB observations. To maintain the low energy electron population capable of producing the observed continuum via bremsstrahlung, a total power input of 4 x 10 exp 41 erg/s is required. This exceeds the total power supplied to the nuclear cosmic rays by about an order of magnitude.
The recent Fermi detection of the globular cluster (GC) 47 Tucanae highlighted the importance of modeling collective gamma-ray emission of millisecond pulsars (MSPs) in GCs. Steady flux from such populations is also expected in the very high energy (VHE) domain covered by ground-based Cherenkov telescopes. We present pulsed curvature radiation (CR) as well as unpulsed inverse Compton (IC) calculations for an ensemble of MSPs in the GCs 47 Tucanae and Terzan 5. We demonstrate that the CR from these GCs should be easily detectable for Fermi, while constraints on the total number of MSps and the nebular B-field may be derived using the IC flux components.
Column CO2 observations from current and future remote sensing missions represent a major advancement in our understanding of the carbon cycle and are expected to help constrain source and sink distributions. However, data assimilation and inversion methods are challenged by the difference in scale of models and observations. OCO-2 footprints represent an area of several square kilometers while NASA s future ASCENDS lidar mission is likely to have an even smaller footprint. In contrast, the resolution of models used in global inversions are typically hundreds of kilometers wide and often cover areas that include combinations of land, ocean and coastal areas and areas of significant topographic, land cover, and population density variations. To improve understanding of scales of atmospheric CO2 variability and representativeness of satellite observations, we will present results from a global, 10-km simulation of meteorology and atmospheric CO2 distributions performed using NASA s GEOS-5 general circulation model. This resolution, typical of mesoscale atmospheric models, represents an order of magnitude increase in resolution over typical global simulations of atmospheric composition allowing new insight into small scale CO2 variations across a wide range of surface flux and meteorological conditions. The simulation includes high resolution flux datasets provided by NASA s Carbon Monitoring System Flux Pilot Project at half degree resolution that have been down-scaled to 10-km using remote sensing datasets. Probability distribution functions are calculated over larger areas more typical of global models (100-400 km) to characterize subgrid-scale variability in these models. Particular emphasis is placed on coastal regions and regions containing megacities and fires to evaluate the ability of coarse resolution models to represent these small scale features. Additionally, model output are sampled using averaging kernels characteristic of OCO-2 and ASCENDS measurement concepts to create realistic pseudo-datasets. Pseudo-data are averaged over coarse model grid cell areas to better understand the ability of measurements to characterize CO2 distributions and spatial gradients on both short (daily to weekly) and long (monthly to seasonal) time scales
Absorption in the 2Pi sub 1/2 J = 1/2 Lambda doublet transitions of OH, 182 K above the ground state, is detected in the megamaser galaxies IC 4553 (Arp 220), MK 231, MK 273, MGC 3690, and IRAS 17208-0014. The 4660, 4751, and 4766 MHz lines have intensity ratios moderately deviating from the LTE values (1:2:1). The OH rotational temperatures appear to be close to the temperature of the dust, approx. 60 K. The common characteristics of these galaxies (absence of 6 cm inversion, the optical depths, the infrared properties, the systematic trends in the line parameters, and the rotational temperatures) all suggest that the same pump process is responsible for the 18 cm line inversion in the five megamaser sources. The inversion is probably not due to an excitation mechanism involving collisions with HI or H2. While excitation via photodissociation of H2O cannot entirely be ruled out, the most likely mechanism is considered to be to be a combination of the intense FIR field (populating higher excited OH rotational states) and the non-thermal radiation from the nuclei of the parent galaxies (affecting the excitation within the Lambda -doublets). According to an LVG model of the OH excitation of IC4553, the OH-cloud(s) have to be located close, within 200 to 300 pc, to the center of the galaxy. The excitation of the individual 18 cm lines depends critically on the effective background radiation field and hence on the galactocentric distance of the masing clump. With increasing distance first the 1720 MHz and then the 18 cm main line inversion is quenched, while 1612 MHz inversion is obtained up to approx. 600 pc. The 1612 MHz satellite line is predicted to be more intense than the 1720 MHz line. A critical test for our excitation model is to observe the 2 Pi 3/2 J = 5/2 Lambda-doublet transitions which are predicted to be detectable in absorption.
Charge exchange between xenon ions and calcium atoms may produce an inversion between the 5s or 4d and 4p energy levels of the calcium ions. A low power flowing xenon plasma seeded with calcium was utilized to determine if charge exchange or electron collisions populate the 5s and 4d levels Ca(+). Line intensity ratios proportional to the density ratios n5s/n4p and n4d/n4p were measured. From the dependence of these intensity ratios on power input to the xenon plasma it was concluded that charge exchange pumping of the 5s and 4d levels predominates over electron collisional pumping of these levels. Also, by comparing intensity ratios obtained using argon and krypton in place of xenon with those obtained in xenon the same conclusion was made.