hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Evidence of direct detection of interstellar deuterium in the local interstellar medium by IBEX

We report the first in situ measurements of neutral deuterium originating in the local interstellar medium (LISM) in Earth’s orbit. These measurements were performed with the IBEX-Lo camera on NASA’s interstellar boundary explorer (IBEX) satellite. All data from the spring observation periods of 2009 through 2011 have been analysed. In the three years of the IBEX mission time, the observation geometry and orbit allowed for a total observation time of 115.3 days for the LISM. However, the effects of the spinning spacecraft and the stepping through 8 energy channels mean that we are only observing the interstellar wind for a total time of 1.44 days, in which 2 counts for interstellar deuterium were collected. We report here a conservative number, because a possibility of systematic error or additional noise, though eliminated in our analysis to the best of our knowledge, only supports detection at a 1-sigma level. From these observations, we derive a ratio D/H = (5.8 ± 4.4) × 10-4 at 1 AU. After modelling the transport and loss of D and H from the termination shock to Earth’s orbit, we find that our result of D/HLISM = (1.6 ± 1.2) × 10-5 agrees with D/HLIC = (1.6 ± 0.4) × 10-5 for the local interstellar cloud. This weak interstellar signal is extracted from a strong terrestrial background signal consisting of sputter products from the sensor’s conversion surface. As reference, we accurately measure the terrestrial D/H ratio in these sputtered products and then discriminate this terrestrial background source. Because of the diminishing D and H signal at Earth’s orbit during the rising solar activity due to photoionisation losses and increased photon pressure, our result demonstrates that in situ measurements of interstellar deuterium in the inner heliosphere are only possible during solar minimum conditions.

The trouble with quality filtering based on relative Cramér-Rao lower bounds.

Cramér Rao Lower Bounds (CRLB) have become the standard for expression of uncertainties in quantitative MR spectroscopy. If properly interpreted as a lower threshold of the error associated with model fitting, and if the limits of its estimation are respected, CRLB are certainly a very valuable tool to give an idea of minimal uncertainties in magnetic resonance spectroscopy (MRS), although other sources of error may be larger. Unfortunately, it has also become standard practice to use relative CRLB expressed as a percentage of the presently estimated area or concentration value as unsupervised exclusion criterion for bad quality spectra. It is shown that such quality filtering with widely used threshold levels of 20% to 50% CRLB readily causes bias in the estimated mean concentrations of cohort data, leading to wrong or missed statistical findings-and if applied rigorously-to the failure of using MRS as a clinical instrument to diagnose disease characterized by low levels of metabolites. Instead, absolute CRLB in comparison to those of the normal group or CRLB in relation to normal metabolite levels may be more useful as quality criteria. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.

Local Interstellar Medium: Six Years of Direct Sampling by IBEX

The Interstellar Boundary Explorer (IBEX) has been directly observing neutral atoms from the local interstellar medium for the last six years (2009–2014). This paper ties together the 14 studies in this Astrophysical Journal Supplement Series Special Issue, which collectively describe the IBEX interstellar neutral results from this epoch and provide a number of other relevant theoretical and observational results. Interstellar neutrals interact with each other and with the ionized portion of the interstellar population in the “pristine” interstellar medium ahead of the heliosphere. Then, in the heliosphereʼs close vicinity, the interstellar medium begins to interact with escaping heliospheric neutrals. In this study, we compare the results from two major analysis approaches led by IBEX groups in New Hampshire and Warsaw. We also directly address the question of the distance upstream to the pristine interstellar medium and adjust both sets of results to a common distance of ~1000 AU. The two analysis approaches are quite different, but yield fully consistent measurements of the interstellar He flow properties, further validating our findings. While detailed error bars are given for both approaches, we recommend that for most purposes, the community use “working values” of ~25.4 km s⁻¹, ~75°7 ecliptic inflow longitude, ~−5°1 ecliptic inflow latitude, and ~7500 K temperature at ~1000 AU upstream. Finally, we briefly address future opportunities for even better interstellar neutral observations to be provided by the Interstellar Mapping and Acceleration Probe mission, which was recommended as the next major Heliophysics mission by the NRCʼs 2013 Decadal Survey.