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Inference in infinite-dimensional inverse problems - Discretization and duality

Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.

Stark, Philip B.↗

Study of multi-dimensional radiative energy transfer in molecular gases

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical arrow band model with an exponential-tailed inverse intensity distribution. Consideration of spectral correlation results in some distinguishing features of the Monte Carlo formulations. Validation of the Monte Carlo formulations has been conducted by comparing results of this method with other solutions. Extension of a one-dimensional problem to a multi-dimensional problem requires some special treatments in the Monte Carlo analysis. Use of different assumptions results in different sets of Monte Carlo formulations. The nongray narrow band formulations provide the most accurate results.

Liu, Jiwen↗

Investigation of radiative interaction in laminar flows using Monte Carlo simulation

The Monte Carlo method (MCM) is employed to study the radiative interactions in fully developed laminar flow between two parallel plates. Taking advantage of the characteristics of easy mathematical treatment of the MCM, a general numerical procedure is developed for nongray radiative interaction. The nongray model is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. To validate the Monte Carlo simulation for nongray radiation problems, the results of radiative dissipation from the MCM are compared with two available solutions for a given temperature profile between two plates. After this validation, the MCM is employed to solve the present physical problem and results for the bulk temperature are compared with available solutions. In general, good agreement is noted and reasons for some discrepancies in certain ranges of parameters are explained.

Liu, Jiwen↗

Radiative interactions in chemically reacting compressible nozzle flows using Monte Carlo simulations

The two-dimensional spatially elliptic Navier-Stokes equations have been used to investigate the radiative interactions in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The radiative heat transfer term in the energy equation is simulated using the Monte Carlo method (MCM). The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The spectral correlation has been considered in the Monte Carlo formulations. Results obtained demonstrate that the effect of radiation on the flow field is minimal but its effect on the wall heat transfer is significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and the nozzle size on the radiative and conductive wall fluxes.

Liu, J.↗

Laser action in far-infrared astrophysical sources

Employing new atomic data and a 15 level collisional-radiative model, it is shown that population inversion, and consequent laser action, can be achieved in far-infrared (FIR) lines (C II) 157 micrometer, (N III) 58 micrometer, (O IV) 26 micrometer, (Ne VI) 7.6 micrometer, and (Mg VIII) 3 micrometer. Coupling of the lasting transition 2s(sup 2)2p((sup 2)P(sup o sub 3/2)-(sup 2)P(sup o sub 1/2)) to higher energy levels of the 2s2p(sup 2) configuration in boron-like ions provides the dominant pumping flux. Lasing column lengths are found to be l approximately equal 10(exp -4)-1.0 pcs, at T(sub e) approximately equal 10(exp 4)-10(exp 6) K, N(sub e) approximately equal 10(exp 4)-10(exp 10)/cu cm, conditions and sizes prevalent in broad-line regions of active-galactic nuclei and novae. Detectable emission fluxes are estimated. Lasing activity in the source could significantly affect abundance determinations. The FIR line emission should be readily observable with the upcoming Infrared Space Observatory.

Peng, Jianfang↗

There aren't Non-Standard Solutions for the Braid Group Representations of the QYBE Associated with 10-D Representations of SU(4)

It is well known that the quantum Yang-Baxter equations (QYBE) play an important role in various theoretical and mathematical physics, such as completely integrable system in (1 + 1)-dimensions, exactly solvable models in statistical mechanics, the quantum inverse scattering method and the conformal field theories in 2-dimensions. Recently, much remarkable progress has been made in constructing the solutions of the QYBE associated with the representations of lie algebras. It is shown that for some cases except the standard solutions, there also exist new solutions, but the others have not non-standard solutions. In this paper by employing the weight conservation and the diagrammatic techniques we show that the solution associated with the 10-D representations of SU (4) are standard alone.

Yijun, Huang↗

Oceanic Fluxes of Mass, Heat and Freshwater: A Global Estimate and Perspective

Data from fifteen globally distributed, modern, high resolution, hydrographic oceanic transects are combined in an inverse calculation using large scale box models. The models provide estimates of the global meridional heat and freshwater budgets and are used to examine the sensitivity of the global circulation, both inter and intra-basin exchange rates, to a variety of external constraints provided by estimates of Ekman, boundary current and throughflow transports. A solution is found which is consistent with both the model physics and the global data set, despite a twenty five year time span and a lack of seasonal consistency among the data. The overall pattern of the global circulation suggested by the models is similar to that proposed in previously published local studies and regional reviews. However, significant qualitative and quantitative differences exist. These differences are due both to the model definition and to the global nature of the data set.

MacDonald, Alison Marguerite↗

Rendering Three-Dimensional Solar Coronal Structures

An X-ray or EUV image of the corona or chromosphere is a 2D representation of an extended 3D complex for which a general inversion process is impossible. A specific model must be incorporated in order to understand the full 3D structure. We approach this problem by modeling a set of optically-thin 3D plasma flux tubes which we render these as synthetic images. The resulting images allow the interpretation of the X-ray/EUV observations to obtain information on (1) the 3D structure of X-ray images, i.e., the geometric structure of the flux tubes, and on (2) the internal structure using specific plasma characteristics, i.e., the physical structure of the flux tubes. The data-analysis technique uses magnetograms to characterize photospheric magnetic fields and extrapolation techniques to form the field lines. Using a new set of software tools, we have generated 3D flux tube structures around these field lines and integrated the plasma emission along the line of sight to obtain a rendered image. A set of individual flux-tube images is selected by a non-negative least-squares technique to Provide a match with an observed X-ray image. The scheme minimizes the squares of the differences between the synthesized image and the observed image with a non-negative constraint on the coefficients of the brightness of the individual flux-tube loops. The derived images are used to determine the specific photospheric foot points and physical data, i.e., scaling laws for densities and loop lengths. The development has led to Computer efficient integration and display software that is compatible for comparison with observations (e.g., Yohkoh SXT data, NIXT, or EIT). This analysis is important in determining directly the magnetic field configuration, which provides the structure of coronal loops, and indirectly the electric currents or waves, which provide the energy for the heating of the plasma. We have used very simple assumptions (i.e., potential magnetic fields and isothermal corona) to provide an initial test of the techniques before complex models are introduced. We have separated the physical and geometric contributions of the emission for a set of flux tubes and concentrated, in this initial study, on the geometric contributions by making approximations to the physical contributions. The initial results are consistent with the scaling laws derived from Yohkoh SXT data.

Gary, G. Allen↗

Validation of a "Kane's Dynamics" Model for the Active Rack Isolation System

Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.

Beech, Geoffrey S.↗

An Improved Model of the Crustal Structure of Mars

The first reliable model of the structure of the crust and upper mantle of Mars from remote observations was produced using data from the Mars Orbiter Laser Altimeter (MOLA) and the Radio Science investigation of Mars Global Surveyor (MGS). That model assumed a uniform crustal density and solved for the global variations in crustal thickness using a gravity field derived from preliminary MGS tracking. In that study, spherical harmonic potential coefficients were derived to degree and order 80, but crustal structure was interpreted cautiously to degree 60, or 360 km wavelength, owing to the presence of noise. Tracking normal equations have since been generated to degree 75, to degree 80 (supplemented by altimetric crossovers), and recently to degree 90, using new constants for the orientation of the spin pole and the rotation rate of Mars provided by the IAU2000 rotation model. Gravity models now incorporate tracking data coverage from the Primary and Extended MGS missions and the early phases of the Mars Odyssey mission. In the present study we exploit these advances in gravity modeling to present a refined crustal inversion, which we also interpret in the context of Mars' internal structure and thermal evolution.

Zuber, M. T.↗

Optimization Of Ocean Color Algorithms: Application To Satellite And In Situ Data Merging

The objective of our program is to develop and validate a procedure for ocean color data merging which is one of the major goals of the SIMBIOS project (McClain et al., 1995). The need for a merging capability is dictated by the fact that since the launch of MODIS on the Terra platform and over the next decade, several global ocean color missions from various space agencies are or will be operational simultaneously. The apparent redundancy in simultaneous ocean color missions can actually be exploited to various benefits. The most obvious benefit is improved coverage (Gregg et al., 1998; Gregg & Woodward, 1998). The patchy and uneven daily coverage from any single sensor can be improved by using a combination of sensors. Beside improved coverage of the global ocean the merging of ocean color data should also result in new, improved, more diverse and better data products with lower uncertainties. Ultimately, ocean color data merging should result in the development of a unified, scientific quality, ocean color time series, from SeaWiFS to NPOESS and beyond. Various approaches can be used for ocean color data merging and several have been tested within the frame of the SIMBIOS program (see e.g. Kwiatkowska & Fargion, 2003, Franz et al., 2003). As part of the SIMBIOS Program, we have developed a merging method for ocean color data. Conversely to other methods our approach does not combine end-products like the subsurface chlorophyll concentration (chl) from different sensors to generate a unified product. Instead, our procedure uses the normalized waterleaving radiances (LwN( )) from single or multiple sensors and uses them in the inversion of a semianalytical ocean color model that allows the retrieval of several ocean color variables simultaneously. Beside ensuring simultaneity and consistency of the retrievals (all products are derived from a single algorithm), this model-based approach has various benefits over techniques that blend end-products (e.g. chlorophyll): 1) it works with single or multiple data sources regardless of their specific bands, 2) it exploits band redundancies and band differences, 3) it accounts for uncertainties in the LwN( ) data and, 4) it provides uncertainty estimates for the retrieved variables.

Maritorena, Stephane↗

Photosynthetic fractionation of 13C and concentrations of dissolved CO2 in the central equatorial Pacific during the last 255,000 years

Carbon isotopically based estimates of CO2 levels have been generated from a record of the photosynthetic fractionation of 13C [is equivalent to epsilon(p)] in a central equatorial Pacific sediment core that spans the last approximately 255 ka. Contents of 13C in phytoplanktonic biomass were determined by analysis of C37 alkadienones. These compounds are exclusive products of Prymnesiophyte algae which at present grow most abundantly at depths of 70-90 m in the central equatorial Pacific. A record of the isotopic composition of dissolved CO2 was constructed from isotopic analyses of the planktonic foraminifera Neogloboquadrina dutertrei, which calcifies at 70-90 m in the same region. Values of epsilon(p), derived by comparison of the organic and inorganic delta values, were transformed to yield concentrations of dissolved CO2 [is equivalent to c(e)] based on a new, site-specific calibration of the relationship between epsilon(p) and c(e). The calibration was based on reassessment of existing epsilon(p) versus c(e) data, which support a physiologically based model in which epsilon(p) is inversely related to c(e). Values of PCO2, the partial pressure of CO2 that would be in equilibrium with the estimated concentrations of dissolved CO2, were calculated using Henry's law and the temperature determined from the alkenone-unsaturation index U(K/37). Uncertainties in these values arise mainly from uncertainties about the appropriateness (particularly over time) of the site-specific relationship between epsilon(p) and 1/c(e). These are discussed in detail and it is concluded that the observed record of epsilon(p) most probably reflects significant variations in delta pCO2, the ocean-atmosphere disequilibrium, which appears to have ranged from approximately 110 microatmospheres during glacial intervals (ocean > atmosphere) to approximately 60 microatmospheres during interglacials. Fluxes of CO2 to the atmosphere would thus have been significantly larger during glacial intervals. If this were characteristic of large areas of the equatorial Pacific, then greater glacial sinks for the equatorially evaded CO2 must have existed elsewhere. Statistical analysis of air-sea pCO2 differences and other parameters revealed significant (p<0.01) inverse correlations of delta pCO2 with sea surface temperature and with the mass accumulation rate of opal. The former suggests response to the strength of upwelling, the latter may indicate either drawdown of CO2 by siliceous phytoplankton or variation of [CO2]/[Si(OH)4] ratios in upwelling waters.

NASA Discipline Exobiology↗

Flight Results of the NF-15B Intelligent Flight Control System (IFCS) Aircraft with Adaptation to a Longitudinally Destabilized Plant

Adaptive flight control systems have the potential to be resilient to extreme changes in airplane behavior. Extreme changes could be a result of a system failure or of damage to the airplane. The goal for the adaptive system is to provide an increase in survivability in the event that these extreme changes occur. A direct adaptive neural-network-based flight control system was developed for the National Aeronautics and Space Administration NF-15B Intelligent Flight Control System airplane. The adaptive element was incorporated into a dynamic inversion controller with explicit reference model-following. As a test the system was subjected to an abrupt change in plant stability simulating a destabilizing failure. Flight evaluations were performed with and without neural network adaptation. The results of these flight tests are presented. Comparison with simulation predictions and analysis of the performance of the adaptation system are discussed. The performance of the adaptation system is assessed in terms of its ability to stabilize the vehicle and reestablish good onboard reference model-following. Flight evaluation with the simulated destabilizing failure and adaptation engaged showed improvement in the vehicle stability margins. The convergent properties of this initial system warrant additional improvement since continued maneuvering caused continued adaptation change. Compared to the non-adaptive system the adaptive system provided better closed-loop behavior with improved matching of the onboard reference model. A detailed discussion of the flight results is presented.

Bosworth, John T.↗

Physics of Solar Prominences: I-Spectral Diagnostics and Non-LTE Modelling

This review paper outlines background information and covers recent advances made via the analysis of spectra and images of prominence plasma and the increased sophistication of non-LTE (i.e. when there is a departure from Local Thermodynamic Equilibrium) radiative transfer models. We first describe the spectral inversion techniques that have been used to infer the plasma parameters important for the general properties of the prominence plasma in both its cool core and the hotter prominence-corona transition region. We also review studies devoted to the observation of bulk motions of the prominence plasma and to the determination of prominence mass. However, a simple inversion of spectroscopic data usually fails when the lines become optically thick at certain wavelengths. Therefore, complex

Labrosse, N.↗

Method for Predicting and Optimizing System Parameters for Electrospinning System

An electrospinning system using a spinneret and a counter electrode is first operated for a fixed amount of time at known system and operational parameters to generate a fiber mat having a measured fiber mat width associated therewith. Next, acceleration of the fiberizable material at the spinneret is modeled to determine values of mass, drag, and surface tension associated with the fiberizable material at the spinneret output. The model is then applied in an inversion process to generate predicted values of an electric charge at the spinneret output and an electric field between the spinneret and electrode required to fabricate a selected fiber mat design. The electric charge and electric field are indicative of design values for system and operational parameters needed to fabricate the selected fiber mat design.

Wincheski, Russell A.↗

Satellite and In Situ Observations for Advancing Global Earth Surface Modelling: A Review

In this paper we review the use of satellite-based remote sensing in combination with in situ data to inform Earth surface modelling. This involves verification and optimization methods that can handle both random and systematic errors and result in effective model improvement for both surface monitoring and prediction applications. The reasons for diverse remote sensing data and products include (i) their complementary areal and temporal coverage, (ii) their diverse and covariant information content, and (iii) their ability to complement in situ observations, which are often sparse and only locally representative. To improve our understanding of the complex behavior of the Earth system at the surface and sub-surface, we need large volumes of data from high-resolution modelling and remote sensing, since the Earth surface exhibits a high degree of heterogeneity and discontinuities in space and time. The spatial and temporal variability of the biosphere, hydrosphere, cryosphere and anthroposphere calls for an increased use of Earth observation (EO) data attaining volumes previously considered prohibitive. We review data availability and discuss recent examples where satellite remote sensing is used to infer observable surface quantities directly or indirectly, with particular emphasis on key parameters necessary for weather and climate prediction. Coordinated high-resolution remote-sensing and modelling/assimilation capabilities for the Earth surface are required to support an international application-focused effort.

Earth observations↗

MMS Observation of Inverse Energy Dispersion in Shock Drift Accelerated Ions

The four Magnetospheric Multiscale (MMS) spacecraft observed a ∼1 min burst of energetic ions (50–1000 keV) in the region upstream from the subsolar quasi-perpendicular bow shock on 6 December 2015. The composition, flux levels, and spectral indices of these energetic protons, helium, and oxygen ions greatly resemble those seen in the outer magnetosphere earlier while MMS crossed the magnetopause and differ significantly from those simultaneously observed far upstream by Advanced Composition Explorer (ACE). However, the event cannot be explained solely in terms of leakage from the magnetosphere. The strongly southward orientation of the interplanetary magnetic field (IMF) lines at the time of the event precludes any connection to the magnetosphere. This point is confirmed by the presence of energetic electrons, known to occur on magnetic field lines that graze the bow shock rather than connect to the magnetosphere. We suggest that the ions gradient drifted out of the nearby quasi-parallel foreshock and into the quasi-perpendicular bow shock. Each of the ion species exhibited an inverse energy dispersion. As predicted by models for shock drift acceleration, the energies of the ions increased as 𝜃(sub Bn), the angle between the IMF and the shock normal, increased. Finally, we note that a similar event was observed a few minutes later in the subsolar magnetosheath, indicating that such events can be swept downstream of the bow shock.

Lee, S. H.↗

TPSAS-NF1676L-27604-DND

Satellite-based hyperspectral observations provide high information content for the Earth's atmospheric and surface properties; however, in order to analyze hyperspectral data efficiently, fast and accurate radiative transfer model is needed. We have developed a Principal Component-based radiative transfer model (PCRTM) which can simulate radiative transfer in the cloudy atmosphere from far IR to visible and UV spectral regions quickly and accurately. Multi-scattering of multiple layers of clouds/aerosols is included in the model. The computation speed is 3 to 4 orders of magnitude faster than the medium speed correlated-k option MODTRAN5 and LBLRTM. The PCRTM calculated radiance spectra agree with the Modtran and LBLRTM within 0.02%. We will demonstrate the application of the PCRTM forward model for atmospheric and surface property inversions and for climate observation studies.

X Liu↗