Iterative Methods for the Elasticity Imaging Inverse Problem

Cancers of the soft tissue reign among the deadliest diseases throughout the world and effective treatments for such cancers rely on early and accurate detection of tumors within the interior of the body. One such diagnostic tool, known as elasticity imaging or elastography, uses measurements of tissue displacement to reconstruct the variable elasticity between healthy and unhealthy tissue inside the body. This gives rise to a challenging parameter identification inverse problem, that of identifying the Lamé parameter μ in a system of partial differential equations in linear elasticity. Due to the near incompressibility of human tissue, however, common techniques for solving the direct and inverse problems are rendered ineffective due to a phenomenon known as the “locking effect”. Alternative methods, such as mixed finite element methods, must be applied to overcome this complication. Using these methods, this work reposes the problem as a generalized saddle point problem along with a presentation of several optimization formulations, including the modified output least squares (MOLS), energy output least squares (EOLS), and equation error (EE) frameworks, for solving the elasticity imaging inverse problem. Subsequently, numerous iterative optimization methods, including gradient, extragradient, and proximal point methods, are explored and applied to solve the related optimization problem. Implementations of all of the iterative techniques under consideration are applied to all of the developed optimization frameworks using a representative numerical example in elasticity imaging. A thorough analysis and comparison of the methods is subsequently presented

The First Reported Infrared Emission from the SN 1006 Remnant

We report results of infrared imaging and spectroscopic observations of the SN 1006 remnant, carried out with the Spitzer Space Telescope. The 24 micron image from MIPS clearly shows faint filamentary emission along the northwest rim of the remnant shell, nearly coincident with the Balmer filaments that delineate the present position of the expanding shock. The 24 micron emission traces the Balmer filaments almost perfectly, but lies a few arcsec within, indicating an origin in interstellar dust heated by the shock. Subsequent decline in the IR behind the shock is presumably due largely to grain destruction through sputtering. The emission drops far more rapidly than current models predict, however, even for a higher proportion of small grains than would be found closer to the Galactic plane. The rapid drop may result in part from a grain density that has always been lower -- a relic effect from an earlier epoch when the shock was encountering a lower density -- but higher grain destruction rates still seem to be required. Spectra from three positions along the NW filament from the IRS instrument all show only a featureless continuum, consistent with thermal emission from warm dust. The dust-to-gas mass ratio in the pre-shock interstellar medium is lower than that expected for the Galactic ISM -- as has also been observed in the analysis of IR emission from other SNRs but whose cause remains unclear. As with other SN Ia remnants, SN 1006 shows no evidence for dust grain formation in the supernova ejecta.Comment: 24 pages, 6 figure

Guidance, Navigation, and Control Performance for the GOES-R Spacecraft

The Geostationary Operational Environmental Satellite-R Series (GOES-R) is the first of the next generation geostationary weather satellites, scheduled for delivery in late 2015 and launch in early 2016. Relative to the current generation of GOES satellites, GOES-R represents a dramatic increase in Earth and solar weather observation capabilities, with 4 times the resolution, 5 times the observation rate, and 3 times the number of spectral bands for Earth observations. GOES-R will also provide unprecedented availability, with less than 120 minutes per year of lost observation time. The Guidance Navigation & Control (GN&C) design requirements to achieve these expanded capabilities are extremely demanding. This paper first presents the pointing control, pointing stability, attitude knowledge, and orbit knowledge requirements necessary to realize the ambitious Image Navigation and Registration (INR) objectives of GOES-R. Because the GOES-R suite of instruments is sensitive to disturbances over a broad spectral range, a high fidelity simulation of the vehicle has been created with modal content over 500 Hz to assess the pointing stability requirements. Simulation results are presented showing acceleration, shock response spectrum (SRS), and line of sight responses for various disturbances from 0 Hz to 512 Hz. These disturbances include gimbal motion, reaction wheel disturbances, thruster firings for station keeping and momentum management, and internal instrument disturbances. Simulation results demonstrate excellent performance relative to the pointing and pointing stability requirements, with line of sight jitter of the isolated instrument platform of approximately 1 micro-rad. Low frequency motion of the isolated instrument platform is internally compensated within the primary instrument. Attitude knowledge and rate are provided directly to the instrument with an accuracy defined by the Integrated Rate Error (IRE) requirements. The allowable IRE ranges from 1 to 18.5 micro-rad, depending upon the time window of interest. The final piece of the INR performance is orbit knowledge. Extremely accurate orbital position is achieved by GPS navigation at Geosynchronous Earth Orbit (GEO). Performance results are shown demonstrating compliance with the 50 to 75 m orbit position accuracy requirements of GOES-R, including during station-keeping and momentum management maneuvers. As shown in this paper, the GN&C performance for the GOES-R series of spacecraft supports the challenging mission objectives of the next generation GEO Earth-observation satellites

Spatiotemporal pattern of global forest change over the past 60 years and the forest transition theory

Forest ecosystems play an indispensable role in addressing various pressing sustainability and social-ecological challenges such as climate change and biodiversity loss. However, global forest loss has been, and still is today, an important issue. Here, based on spatially explicit data, we show that over the past 60 years (1960–2019), the global forest area has declined by 81.7 million ha (i.e. 10% more than the size of the entire Borneo island), with forest loss (437.3 million ha) outweighing forest gain (355.6 million ha). With this forest decline and the population increase (4.68 billion) over the period, the global forest per capita has decreased by over 60%, from 1.4 ha in 1960 to 0.5 ha in 2019. The spatiotemporal pattern of forest change supports the forest transition theory, with forest losses occurring primarily in the lower income countries in the tropics and forest gains in the higher income countries in the extratropics. Furthermore, economic growth has a stronger association with net forest gain than with net forest loss. Our results highlight the need to strengthen the support given to lower income countries, especially in the tropics, to help improve their capacity to minimize or end their forest losses. To help address the displacement of forest losses to the lower income countries in the tropics, higher income nations need to reduce their dependence on imported tropical forest products

Dust Destruction in Type Ia Supernova Remnants in the Large Magellanic Cloud

We present first results from an extensive survey of Magellanic Clouds supernova remnants (SNRs) with the Spitzer Space Telescope. We describe IRAC and MIPS imaging observations at 3.6, 4.5, 5.8, 8, 24, and 70 microns of four Balmer-dominated Type Ia SNRs in the Large Magellanic Cloud (LMC): DEM L71 (0505-67.9), 0509--67.5, 0519--69.0, and 0548-70.4. None was detected in the four short-wavelength IRAC bands, but all four were clearly imaged at 24 microns, and two at 70 microns. A comparison of these images to Chandra broadband X-ray images shows a clear association with the blast wave, and not with internal X-ray emission associated with ejecta. Our observations are well described by 1-D shock models of collisionally heated dust emission, including grain size distributions appropriate for the LMC, grain heating by collisions with both ions and electrons, and sputtering of small grains. Model parameters are constrained by X-ray, optical, and far-ultraviolet observations. Our models can reproduce observed 70/24 micron flux ratios only by including sputtering, destroying most grains smaller than 0.03-0.04 microns in radius. We infer total dust masses swept up by the SNR blast waves, before sputtering, of order 0.01 solar masses, several times less than those implied by a dust/gas mass ratio of 0.3 percent as often assumed for the LMC. Substantial dust destruction has implications for gas-phase abundances.Comment: 11 pages, 1 figure, submitted to the Astrophysical Journal Letter

RCW 86: A Type Ia Supernova in a Wind-Blown Bubble

We report results from a multi-wavelength analysis of the Galactic SNR RCW 86, the proposed remnant of the supernova of 185 A.D. We report new infrared observations from {\it Spitzer} and {\it WISE}, where the entire shell is detected at 24 and 22 $\mu$m. We fit the infrared flux ratios with models of collisionally heated ambient dust, finding post-shock gas densities in the non-radiative shocks of 2.4 and 2.0 cm$^{-3}$ in the SW and NW portions of the remnant, respectively. The Balmer-dominated shocks around the periphery of the shell, large amount of iron in the X-ray emitting ejecta, and lack of a compact remnant support a Type Ia origin for this remnant. From hydrodynamic simulations, the observed characteristics of RCW 86 are successfully reproduced by an off-center explosion in a low-density cavity carved by the progenitor system. This would make RCW 86 the first known case of a Type Ia supernova in a wind-blown bubble. The fast shocks ($> 3000$ km s$^{-1}$) observed in the NE are propagating in the low-density bubble, where the shock is just beginning to encounter the shell, while the slower shocks elsewhere have already encountered the bubble wall. The diffuse nature of the synchrotron emission in the SW and NW is due to electrons that were accelerated early in the lifetime of the remnant, when the shock was still in the bubble. Electrons in a bubble could produce gamma-rays by inverse-Compton scattering. The wind-blown bubble scenario requires a single-degenerate progenitor, which should leave behind a companion star.Comment: Accepted for publication in ApJ. 50 pages, 9 figure