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At least 19 records

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Coutsias, Evangelos A.↗

The mean Jovian temperature structure derived from spectral observations from 105 to 630 cm kaysers

Far infrared observations of the thermal emission of Jupiter are used to determine the temperature at 1 bar. High-altitude observations of the whole-disk brightness temperature of Jupiter in the range of 100 to 347 kaysers were inverted to obtain a P-T profile between 1.5 and 0.06 atm, assuming as opacity sources the H2 collisionally induced continuum and the rotation inversion bands of ammonia. The P-T profile derived from the spectrum reproduces the main features of the observed spectrum, with a slightly improved fit if the effects of ammonia haze opacity or NH3 supersaturation in the saturated region are taken into account. The Jovian temperature is found to be 160 + or - 7 K at 1 bar, and 105 + or - 3 K at the inversion level at 0.15 bar. The 1-bar temperature is shown to be consistent with Jovian interior models which match the observed gravitational moment.

Goorvitch, D.↗

HEAO 1 high energy X-ray observations of the Virgo cluster and A2142

Observations are reported of the Virgo cluster and Abell 2142 in the energy range of 15-150 keV, detected by using hard X-ray and low energy gamma-ray instruments on board the HEAO-1 spacecraft, during 1977 and 1978. The Virgo cluster was detected at a mean flux of (1.3 + or - 0.3) x 10 to the 0.001 photons/sq cm-s in the 20-100 keV band, and A2142 was detected marginally at a flux of (2 + or - 0.8) x 10 to the 0.001 photons/sq cm-s in the 15-40 keV band. Inverse Compton emission was not observed in these clusters. Results are used to derive limits to the intracluster magnetic field of B approximately greater than 5 x 10 to the -7th gauss and B approximately 5 x 10 to the -8th gauss in the Virgo cluster and A1242, respectively. There is some evidence for variability in these sources, which implies that the hard X-ray emission originates in a relatively compact object or region rather than from the cluster as a whole.

Lea, S. M.↗

The Jovian ammonia abundance from interferometric observations of limb darkening at 3.4 mm

The relative abundances of the various atomic and molecular constituents in the Jovian atmosphere are important data for studies of the origin of the solar system. The determination of the ammonia abundance presents a number of difficulties. However, difficulties related to a use of the microwave sensing technique can be largely overcome by measuring the brightness distribution across the disk. In particular, information about the atmosphere can be obtained from the degree of limb darkening, which requires only a relative brightness measurement as opposed to an absolute measurement. Valdes and Welch (1978) have used the considered approach in a study of Jupiter at 1.3 cm. In the present investigation a more general relation between the amount of limb darkening in the broad 1.25-cm inversion band of ammonia and the ammonia abundance is derived. The model is applied to new measurements of Jupiter's limb darkening at 3.4 mm.

Valdes, F.↗

Construction and Calibration of a Difference Frequency Laser Spectrometer and New THZ Frequency Measurements of water and Ammonia

A three laser system based on 852nm DBR lasers has been constructed and used to generate radiation in the 750 GHz to 1600 GHz frequency region. The system works by locking two of the three lasers to modes of an ultra low expansion Fabry-Perot cavity. The third laser is offset locked to one of the cavity locked lasers with conventional microwave techniques. The signal from the offset laser and the other cavity locked laser are injected into a Master Oscillator Power Amplifier (MOPA), amplified and focused on a low temperature grown GaAs photomixer, which radiates the difference frequency. The system has been calibrated with molecular lines to better than one part in 10(exp 7). In this paper we present the application of this system to the v(sub 2) in inversion band of Ammonia and the ground and v(sub 2) states of water. A discussion of the system design, the calibration and the new spectral measurements will be presented.

Pearson, J. C.↗

FORWARD AND INVERSE L-BAND RADIATIVE TRANSFER MODELING OVER THE DRY CHACO, USING SMOS OBSERVATIONS, LAND SURFACE MODELING AND IN SITU DATA

Passive microwave L-band remote sensing is well known for its sensitivity to surface soil moisture over land.The signal is also affected by other dynamic variables such as vegetation and soil salinity. In this research, L-band microwave observations of the Soil Moisture Ocean Salinity (SMOS) mission are used to explore soil surface salinity, moisture and vegetation, in the Argentinean Dry Chaco, an area with possible emerging dryland salinity. A Radiative Transfer Model (RTM) with inclusion of a correction to the soil’s dielectric constant for salinity was used in forward and inverse mode, using either in situ data or Catchment Land Surface Model (CLSM) simulations as RTM input. The forward analysis pointed out shortcomings in the modeled soil moisture and soil surface temperature estimates. The impact of salinity on forward simulations over the Dry Chaco was limited.The RTM inversion using 10 years of SMOS brightness temperature observations resulted in realistic estimates of vegetation and roughness, both with and withouto ptimizing a correction term for the dielectric constant in terms of salinity equivalents. However,the retrieval of the correction term to the dielectric constant was very uncertain and not representative of soil surface salinity, but rather of open water, texture uncertainty or soil moisture bias.

L-band↗

Relaxation Matrix for Symmetric Tops with Inversion Symmetry: Line Coupling and Line Mixing Effects on NH3 Lines in the V4 Band

Line shape parameters including the half-widths and the off-diagonal elements of the relaxation matrix have been calculated for self-broadened NH3 lines in the perpendicular v4 band. As in the pure rotational and the parallel v1 bands, the small inversion splitting in this band causes a complete failure of the isolated line approximation. As a result, one has to use formalisms not relying on this approximation. However, due to differences between parallel and perpendicular bands of NH3, the applicability of the formalism used in our previous studies of the v1 band and other parallel bands must be carefully verified. We have found that, as long as potential models only contain components with K1 equals K2 equals 0, whose matrix elements require the selection rule delta k equals 0, the formalism is applicable for the v4 band with some minor adjustments. Based on both theoretical considerations and results from numerical calculations, the non-diagonality of the relaxation matrices in all the PP, RP, PQ, RQ, PR, and RR branches is discussed. Theoretically calculated self-broadened half-widths are compared with measurements and the values listed in HITRAN 2012. With respect to line coupling effects, we have compared our calculated intra-doublet off-diagonal elements of the relaxation matrix with reliable measurements carried out in the PP branch where the spectral environment is favorable. The agreement is rather good since our results do well reproduce the observed k and j dependences of these elements, thus validating our formalism.

Absorption coefficient↗

A Parameterized Inversion Model for Soil Moisture and Biomass from Polarimetric Backscattering Coefficients

A semi-empirical algorithm for the retrieval of soil moisture, root mean square (RMS) height and biomass from polarimetric SAR data is explained and analyzed in this paper. The algorithm is a simplification of the distorted Born model. It takes into account the physical scattering phenomenon and has three major components: volume, double-bounce and surface. This simplified model uses the three backscattering coefficients ( sigma HH, sigma HV and sigma vv) at low-frequency (P-band). The inversion process uses the Levenberg-Marquardt non-linear least-squares method to estimate the structural parameters. The estimation process is entirely explained in this paper, from initialization of the unknowns to retrievals. A sensitivity analysis is also done where the initial values in the inversion process are varying randomly. The results show that the inversion process is not really sensitive to initial values and a major part of the retrievals has a root-mean-square error lower than 5% for soil moisture, 24 Mg/ha for biomass and 0.49 cm for roughness, considering a soil moisture of 40%, roughness equal to 3cm and biomass varying from 0 to 500 Mg/ha with a mean of 161 Mg/ha

soil moisture↗

Detection of the 2165 inverse centimeter (4.619 micron) XCN band in the spectrum of L1551 IRS 5

We report the detection of a broad absorption band at 2165/cm in the spectrum of L1551 IRS 5. New laboratory results over the 2200-2100/cm wavenumber interval, performed with realistic interstellar ice analogs, suggest that this feature is due to a CN-containing compound. We will refer to this compound as XCN. We also confirm the presence of frozen CO through absorption bands at 2140/cm and 2135/cm. The relative abundance of solid state CO to frozen H2O is about 0.13 while the abundance of XCN seems comparable to that of frozen CO.

Tegler, Stephen C.↗

Detection of the 2165 Inverse Centimeter (4.619 Micron) XCN Band in the Spectrum of L1551 IRS 5

We report the detection of a broad absorption band at 2165 cm (4.619 microns) in the spectrum of L1551 IRS 5. New laboratory results over the 2200-2100 /cm wavenumber interval (4.55-4.76 microns), performed with realistic interstellar ice analogs, suggest that this feature is due to a CN-containing compound. We will refer to this compound as XCN. We also confirm the presence of frozen CO (both in nonpolar and polar matrices) through absorption bands at 2140 /cm (4.67 microns) and 2135 /cm (4.68 microns). The relative abundance of solid-state CO to frozen H2O is approx. 0.13 while the abundance of XCN seems comparable to that of frozen CO.

Tegler, Stephen C.↗

Inverse Method for Estimation of Composite Kink-Band Toughness from Open-Hole Compression Strength Data

Fiber-reinforced polymer matrix composite materials can fail by kink-band propagation mechanism when subjected to in-plane compressive loading. This mode of failure is especially prevalent in compressive loading of laminates with holes, cut-outs, or impact damage. Most of the successful models for predicting compressive strength of such laminates require “fracture” toughness associated with kink-band propagation under in-plane compression. However, this property is difficult to measure experimentally, limiting the use of such models in design practice. In this paper an inverse method is proposed to estimate the kink-band toughness of the laminate from its open-hole compression strength data, which is an easier property to measure experimentally. Furthermore, a scaling relationship is proposed to estimate kink-band toughness for other laminate configurations of the same material.

Luke Borkowski↗

High dispersion spectroscopic observations of Venus near superior conjunction. IV - Results for the carbon dioxide bands in the IV-N photographic region

Phase curves for the CO2 bands at 7883, 7820, and 8689 A are presented. While the weaker bands at 7820 and 7883 A show a definite 'inverse phase effect,' the band at 8689 A shows a more normal phase curve; it also exhibited much larger day-to-day variations in the CO2 abundance near superior conjunction in 1971. Because the variation of the phase curves with band strength is comparable to temporal variations on Venus, simultaneous observations of strong and weak bands are still needed to determine the dependence on band strength accurately.

Young, L. D. G.↗

The Relaxation Matrix for Symmetric Tops with Inversion Symmetry: Line Mixing Effects in the V1 Band of NH3 - II

Line mixing effects have been calculated in the ν1 parallel band of self-broadened NH3. The theoretical approach is an extension of a semi-classical model to symmetric-top molecules with inversion symmetry developed in the companion paper [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. This model takes into account line coupling effects and hence enables the calculation of the entire relaxation matrix. A detailed analysis of the various coupling mechanisms is carried out for Q and R inversion doublets. The model has been applied to the calculation of the shape of the Q branch and of some R manifolds for which an obvious signature of line mixing effects has been experimentally demonstrated. Comparisons with measurements show that the present formalism leads to an accurate prediction of the available experimental line shapes. Discrepancies between the experimental and theoretical sets of first order mixing parameters are discussed as well as some extensions of both theory and experiment.

Boulet, C.↗

Using parallel banded linear system solvers in generalized eigenvalue problems

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speedup is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

DISTRIBUTED MEMORY MULTIPROCES↗

Using parallel banded linear system solvers in generalized eigenvalue problems

Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented.

Zhang, Hong↗

Quantitative determination of stratospheric aerosol characteristics

The author has identified the following significant results. The multiplicative scale factor needed to calibrate the recorded intensity is obtained by fitting the measured curve against a brightness model. The model was converted to the multispectral band scanner signal. Inversion of this measured signature is shown as the profile of attenuation coefficients versus altitude. Because of Gaussian noise, data were not measured directly. Data were fit with two exponential curves, one covering the lower altitude and the other covering the higher altitude. A twenty point curve was derived by selecting a data point and plotting its value from each of twenty adjacent scans. Noise from the lower altitudes was found to be erratic.

Tingey, D. L.↗

Inverse Solution to the Electronic Crosstalk Correction of Bands 27-30 in Terra MODIS

In the Terra MODIS Collection 6.1 (C6.1) Level-1B (L1B) product, an electronic crosstalk correction is implemented for bands 27 30 using a linear algorithm. In this algorithm, the measured (contaminated) signal from the detectors in the bands was used as a reference signal for deriving the correction coefficients from lunar images and for applying the correction to the calibration and L1B data. As the mission progressed, the level of contamination steadily increased in each detector, with an additional large increase associated with the Terra MODIS safe-mode anomaly in February of 2016. In this work, we developed a modified algorithm for deriving the crosstalk coefficients and applying the correction which uses the inverse crosstalk coefficient matrix in order to remove the contamination from the reference signal. We apply the coefficients using this modified algorithm to calibration and Earth-view data in order to assess the difference with the data in C6.1. We also perform calculations using simulated contamination to show the difference in the recovery of the corrected signal between the C6.1 algorithm and the modified algorithm. We will show, that although the current levels of contamination are much higher than early in the mission, the overall impact of having contamination on the reference signal for the correction is small. However, this impact is non-linear as a function of the magnitude of the contamination level, so it should be monitored as the mission continues.

Truman Wilson↗