https://aurora.auburn.edu/handle/11200/44139 Sat, 04 Apr 2026 21:54:22 GMT 2026-04-04T21:54:22Z https://aurora.auburn.edu/handle/11200/49907 Noble gas abundance and isotope ratios in the atmosphere of Jupiter from the Galileo Probe Mass Spectrometer The Galileo Probe Mass Spectrometer provided the first data on the noble gas mixing and isotope ratios in the Jovian atmosphere. These measurements and the comparison with solar values constrain models of Jupiter's formation. Significant refinements to the initially reported abundances of argon, krypton, and xenon have been enabled through post‐encounter laboratory calibrations using a refurbished engineering unit mass spectrometer nearly identical to the flight unit. The abundances relative to hydrogen for argon, krypton, and xenon are respectively 2.5±0.5, 2.7±0.5, and 2.6±0.5 times the solar ratios. The mixing ratios of He and Ne found in these studies are consistent with previously reported values of 0.8 and 0.1 times solar respectively. The Jovian 36Ar/38Ar ratio is 5.6±0.25 and the 20Ne/22Ne ratio is 13±2, consistent with the solar values of 5.77 and 13.81, respectively, that are derived from lunar mineral grain analysis. The distribution of xenon isotopes at Jupiter also resembles the solar distribution. https://aurora.auburn.edu/handle/11200/49907 https://aurora.auburn.edu/handle/11200/48505 An efficient auxiliary variable method for quantification of spin density, R2* decay and field inhomogeneity maps in magnetic resonance imaging Quantification of spin density, $R_2^*$ decay and off-resonance frequency maps is very important in some applications of magnetic resonance imaging (MRI). To reconstruct these parameter maps, a time-varying model such as mono-exponentials must be used to represent the signal from each voxel. When only a single-shot trajectory is adopted, the underlying reconstruction problem is significantly nonlinear and therefore requires an iterative algorithm. The regularized trust region method previously proposed to address this problem is stable but lacks speed. In this paper, we propose a novel auxiliary variable method that is very efficient in solving the underlying optimization problem. This method introduces an auxiliary variable in the spatial-temporal domain that separates the data fidelity term and the structure fidelity term. The algorithm then alternately optimizes the data fidelity and the structure fidelity to reach the solution. The data fidelity optimization has a closed-form solution and can be solved very efficiently. The structure fidelity optimization fits the exponential model with the auxiliary variable and can also be rapidly computed. Some preliminary comparisons between the auxiliary variable method and the trust region method show that the new method is 10 times faster than the trust region method at a reasonable reconstruction precision. Tue, 07 Apr 2015 00:00:00 GMT https://aurora.auburn.edu/handle/11200/48505 2015-04-07T00:00:00Z