Fitting the curve in Excel®:Systematic curve fitting of laboratory and remotely sensed planetary spectra

Spectroscopy in planetary science often provides the only information regarding the compositional and mineralogical make up of planetary surfaces. The methods employed when curve fitting and modelling spectra can be confusing and difficult to visualize and comprehend. Researchers who are new to working with spectra may find inadequate help or documentation in the scientific literature or in the software packages available for curve fitting. This problem also extends to the parameterization of spectra and the dissemination of derived metrics. Often, when derived metrics are reported, such as band centres, the discussion of exactly how the metrics were derived, or if there was any systematic curve fitting performed, is not included. Herein we provide both recommendations and methods for curve fitting and explanations of the terms and methods used. Techniques to curve fit spectral data of various types are demonstrated using simple-to-understand mathematics and equations written to be used in Microsoft Excel® software, free of macros, in a cut-and-paste fashion that allows one to curve fit spectra in a reasonably user-friendly manner. The procedures use empirical curve fitting, include visualizations, and ameliorates many of the unknowns one may encounter when using black-box commercial software. The provided framework is a comprehensive record of the curve fitting parameters used, the derived metrics, and is intended to be an example of a format for dissemination when curve fitting data

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Radiolytic H2 production on Noachian Mars: Implications for habitability and atmospheric warming

Protected from harmful radiation, subfreezing temperatures, and low pressures, subsurface rock-hosted habitats provide potentially sustainable refugia for microbial ecosystems inside small rocky planets, such as Mars. For many chemolithotrophic communities on Earth, water–rock alteration reactions have been shown to produce the key electron donors and acceptors necessary to sustain microbial life on geologic timescales. Here we quantitatively demonstrate that radiolysis likely generated concentrations of dissolved H2 capable of sustaining microbial communities in the subsurface of Noachian Mars (3.7–4.1 Gyr ago). When considering an environment with H2O groundwater, dissolved H2 concentrations reach up to ∼55 mM in a cold early Mars climate scenario and ∼35 mM in a warm early Mars climate scenario; whereas when considering an environment with eutectic NaCl brine groundwater, dissolved H2 concentrations reach up to ∼85 mM in a cold early Mars climate scenario and ∼45 mM in a warm early Mars climate scenario. Specifically within the subsurface habitable zone, dissolved H2 concentrations range from ∼50–55 mM for a cold climate scenario with H2O groundwater. For a warm climate scenario with H2O groundwater, dissolved H2 concentrations within the subsurface habitable zone range from ∼1–30 mM. For a cold climate scenario with eutectic NaCl brine groundwater, dissolved H2 concentrations within the subsurface habitable zone range from ∼65–85 mM. For a warm climate scenario with eutectic NaCl brine groundwater, dissolved H2 concentrations within the subsurface habitable zone range from ∼1-40 mM. Radiolysis likely produced [1.3–4.8] × 1010 moles H2 per year globally during the Noachian depending on the assumed porosity and groundwater composition. Radiolytic H2, and CH4 derived from radiolytic H2, can be locked in hybrid clathrate hydrates within the cryosphere and released by large impacts, volcanism, or obliquity variations. This process could warm the Noachian climate to above-freezing temperatures, and we predict that ∼1–8 warming events would be possible during the Noachian and Hesperian solely from radiolytically produced H2. We demonstrate that the region immediately beneath the cryosphere, termed the subcryospheric highly-fractured zone (SHZ), likely contained dissolved H2 concentrations and temperatures suitable for life regardless of the background climate scenario, making it the most consistently habitable environment on ancient Mars in terms of reductant availability. Material from this zone can be exposed by faulting and in the ejecta and uplifts of impacts, making the SHZ a crucial astrobiological target for testing the subsurface biosphere hypothesis

Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order Accuracy

Smoothness-increasing accuracy-conserving (SIAC) filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order k + 12 to order 2k + 1 for specific types of translation invariant meshes (Cockburn et al. in Math. Comput. 72:577–606, 2003; Curtis et al. in SIAM J. Sci. Comput. 30(1):272–289, 2007; Mirzaee et al. in SIAM J. Numer. Anal. 49:1899–1920, 2011). Additionally, it improves the weak continuity in the discontinuous Galerkin method to k ? 1 continuity. Typically this improvement has a positive impact on the error quantity in the sense that it also reduces the absolute errors. However, not enough emphasis has been placed on the difference between superconvergent accuracy and improved errors. This distinction is particularly important when it comes to understanding the interplay introduced through meshing, between geometry and filtering. The underlying mesh over which the DG solution is built is important because the tool used in SIAC filtering—convolution—is scaled by the geometric mesh size. This heavily contributes to the effectiveness of the post-processor. In this paper, we present a study of this mesh scaling and how it factors into the theoretical errors. To accomplish the large volume of post-processing necessary for this study, commodity streaming multiprocessors were used; we demonstrate for structured meshes up to a 50× speed up in the computational time over traditional CPU implementations of the SIAC filter.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Science-Driven Preparations for Landing on Europa

No abstract available