hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form

Presented as Invited Lecture at the International Symposium on Discontinuous Galerkin Methods: Theory, Computation and Applications, in Newport, RI, USA.\ud \ud We develop the error analysis for the hp-version of a discontinuous finite element approximation to second-order partial differential equations with nonnegative characteristic form. This class of equations includes classical examples of second-order elliptic and parabolic equations, first-order hyperbolic equations, as well as equations of mixed type. We establish an a priori error bound for the method which is of optimal order in the mesh size h and 1 order less than optimal in the polynomial degree p. In the particular case of a first-order hyperbolic equation the error bound is optimal in h and 1/2 an order less than optimal in p

Modeling the Martian dust cycle 2. Multiannual radiatively active dust transport simulations

Multiannual dust transport simulations have been performed using a Mars general circulation model containing a dust transport scheme which responds to changes in the atmospheric state. If the dust transport is 'radiatively active,� the atmospheric state also responds to changes in the dust distribution. This paper examines the suspended dust distribution obtained using different lifting parameterizations, including an analysis of dust storms produced spontaneously during these simulations. The lifting mechanisms selected are lifting by (1) near-surface wind stress and (2) convective vortices known as dust devils. Each mechanism is separated into two types of parameterization: threshold-sensitive and -insensitive. The latter produce largely unrealistic annual dust cycles and storms, and no significant interannual variability. The threshold-sensitive parameterizations produce more realistic annual and interannual behavior, as well as storms with similarities to observed events, thus providing insight into how real Martian dust storms may develop. Simulations for which dust devil lifting dominates are too dusty during northern summer. This suggests either that a removal mechanism (such as dust scavenging by water ice) reduces opacities at this time or that dust devils are not the primary mechanism for storm production. Simulations for which near-surface wind stress lifting dominates produce the observed low opacities during northern spring/summer, yet appear unable to produce realistic global storms without storm decay being prevented by the occurrence of large-scale positive feedbacks on further lifting. Simulated dust levels are generally linked closely to the seasonal state of the atmosphere, and no simulation produces the observed amount of interannual variability

Pressure observations by the curiosity rover : Initial results

The authors would like to express their gratitude to the MSL and REMS instrument teams in making this wonderful Mars mission come true. Ari-Matti Harri and Hannu Savijarvi are thankful for the Finnish Academy grants 132825 and 131723.Peer reviewedPublisher PD

Volatile and Organic Compositions of Sedimentary Rocks in Yellowknife Bay, Gale crater, Mars

H₂O, CO₂, SO₂, O₂, H₂, H₂S, HCl, chlorinated hydrocarbons, NO and other trace gases were evolved during pyrolysis of two mudstone samples acquired by the Curiosity rover at Yellowknife Bay within Gale crater, Mars. H₂O/OH-bearing phases included 2:1 phyllosilicate(s), bassanite, akaganeite, and amorphous materials. Thermal decomposition of carbonates and combustion of organic materials are candidate sources for the CO₂. Concurrent evolution of O₂ and chlorinated hydrocarbons suggest the presence of oxychlorine phase(s). Sulfides are likely sources for S-bearing species. Higher abundances of chlorinated hydrocarbons in the mudstone compared with Rocknest windblown materials previously analyzed by Curiosity suggest that indigenous martian or meteoritic organic C sources may be preserved in the mudstone; however, the C source for the chlorinated hydrocarbons is not definitively of martian origin

The Petrochemistry of Jake_M: A Martian Mugearite

“Jake_M,” the first rock analyzed by the Alpha Particle X-ray Spectrometer instrument on the Curiosity rover, differs substantially in chemical composition from other known martian igneous rocks: It is alkaline (>15% normative nepheline) and relatively fractionated. Jake_M is compositionally similar to terrestrial mugearites, a rock type typically found at ocean islands and continental rifts. By analogy with these comparable terrestrial rocks, Jake_M could have been produced by extensive fractional crystallization of a primary alkaline or transitional magma at elevated pressure, with or without elevated water contents. The discovery of Jake_M suggests that alkaline magmas may be more abundant on Mars than on Earth and that Curiosity could encounter even more fractionated alkaline rocks (for example, phonolites and trachytes)

Elemental Geochemistry of Sedimentary Rocks at Yellowknife Bay, Gale Crater, Mars

Sedimentary rocks examined by the Curiosity rover at Yellowknife Bay, Mars, were derived from sources that evolved from approximately average Martian crustal composition to one influenced by alkaline basalts. No evidence of chemical weathering is preserved indicating arid, possibly cold, paleoclimates and rapid erosion/deposition. Absence of predicted geochemical variations indicates that magnetite and phyllosilicates formed by diagenesis under low temperature, circum-neutral pH, rock-dominated aqueous conditions. High spatial resolution analyses of diagenetic features, including concretions, raised ridges and fractures, indicate they are composed of iron- and halogen-rich components, magnesium-iron-chlorine-rich components and hydrated calcium-sulfates, respectively. Composition of a cross-cutting dike-like feature is consistent with sedimentary intrusion. Geochemistry of these sedimentary rocks provides further evidence for diverse depositional and diagenetic sedimentary environments during the early history of Mars

Mineralogy of a Mudstone at Yellowknife Bay, Gale Crater, Mars

Sedimentary rocks at Yellowknife Bay (Gale Crater) on Mars include mudstone sampled by the Curiosity rover. The samples, John Klein and Cumberland, contain detrital basaltic minerals, Ca-sulfates, Fe oxide/hydroxides, Fe-sulfides, amorphous material, and trioctahedral smectites. The John Klein smectite has basal spacing of ~10 Å indicating little interlayer hydration. The Cumberland smectite has basal spacing at ~13.2 Å as well as ~10 Å. The ~13.2 Å spacing suggests a partially chloritized interlayer or interlayer Mg or Ca facilitating H_2O retention. Basaltic minerals in the mudstone are similar to those in nearby eolian deposits. However, the mudstone has far less Fe-forsterite, possibly lost with formation of smectite plus magnetite. Late Noachian/Early Hesperian or younger age indicates that clay mineral formation on Mars extended beyond Noachian time

X-ray Diffraction Results from Mars Science Laboratory: Mineralogy of Rocknest at Gale Crater

The Mars Science Laboratory rover Curiosity scooped samples of soil from the Rocknest aeolian bedform in Gale crater. Analysis of the soil with the Chemistry and Mineralogy (CheMin) x-ray diffraction (XRD) instrument revealed plagioclase (~An57), forsteritic olivine (~Fo62), augite, and pigeonite, with minor K-feldspar, magnetite, quartz, anhydrite, hematite, and ilmenite. The minor phases are present at, or near, detection limits. The soil also contains 27 ± 14 weight percent x-ray amorphous material, likely containing multiple Fe^(3+)- and volatile-bearing phases, including possibly a substance resembling hisingerite. The crystalline component is similar to the normative mineralogy of certain basaltic rocks from Gusev crater on Mars and of martian basaltic meteorites. The amorphous component is similar to that found on Earth in places such as soils on the Mauna Kea volcano, Hawaii

A Habitable Fluvio-Lacustrine Environment at Yellowknife Bay, Gale Crater, Mars

The Curiosity rover discovered fine-grained sedimentary rocks, inferred to represent an ancient lake, preserve evidence of an environment that would have been suited to support a Martian biosphere founded on chemolithoautotrophy. This aqueous environment was characterized by neutral pH, low salinity, and variable redox states of both iron and sulfur species. C, H, O, S, N, and P were measured directly as key biogenic elements, and by inference N and P are assumed to have been available. The environment likely had a minimum duration of hundreds to tens of thousands of years. These results highlight the biological viability of fluvial-lacustrine environments in the post-Noachian history of Mars

The martian planetary boundary layer

The Martian planetary boundary layer (PBL) consists of the layers of the atmosphere closest to the surface, within which interactions between the atmosphere and the surface itself are dominant. In general, this represents the lowest 1-10 km of the atmosphere, within which surface-driven intense convection may take place, with convective plumes and vortices rising to heights in excess of 5-10 km during the day (Thomas and Gierasch, 1985; Haberle et al., 1993b; Larsen et al., 2002; Balme and Greeley, 2006; Hinson et al., 2008). At night, convection is inhibited and radiative cooling produces a stably-stratified layer at the surface, and the PBL reduces to a shallow layer forced by mechanical turbulence at the bottom of the stable layer. It is therefore a highly dynamic and variable region of the atmosphere at virtually all locations on Mars, with additional variability induced by interactions with local surface topography