Modulus method and radial stretch map in the Heisenberg group

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.

Ligament origins are preserved in distal radial intraarticular two-part fractures: a computed tomography-based study

Background Operative fixation of intraarticular distal radius fractures is increasingly common. A greater understanding of fracture patterns will aid surgical fixation strategy. Previous studies have suggested that ligamentous insertions may less commonly be involved, but these have included heterogeneous groups of fractures and have not addressed Lister's tubercle. Purpose We hypothesize that fracture lines of distal radial intraarticular 2-part fractures have reproducible patterns. They propagate through the cortical bone between ligament origins and do not involve Lister's tubercle. Methods Axial CT scans of two-part intraarticular distal radius fractures were assessed independently by two examiners. The fractures were mapped onto a grid and the cortical breaches expressed as a percentile of the total radial width or length. The cortical breaches were compared with the ligamentous insertions on the distal and Lister's tubercle. Associated injuries were also documented. Results The cortical breaches occurred between the ligamentous insertions in 85%. Lister's tubercle was not involved in 95% of the fractures. Three major fracture patterns emerged: radial styloid, dorsal, and volar. Each major pattern had two subtypes. Associated injuries were common. Scapholunate dissociation was associated with all types, not just the radial styloid fracture pattern. Conclusions The fracture patterns of two-part intraarticular fractures mostly involved the interligamentous zones. Three major groups were identified: dorsal, volar, and radial styloid. Lister's tubercle was preserved with fractures tending to propagate radial or ulnar to this structure. We suggest conceptualizing fracture fragments as osseo-ligamentous units to aid prediction of fracture patterns and associated injury. Study Design Diagnostic III Level of Evidence 3.

THE SOLAR WIND AS A POSSIBLE SOURCE OF FAST TEMPORAL VARIATIONS OF THE HELIOSPHERIC RIBBON

We present a possible source of pickup ions (PUIs) the ribbon observed by the Interstellar Boundary EXplorer (IBEX). We suggest that a gyrating solar wind and PUIs in the ramp and in the near downstream region of the termination shock (TS) could provide a significant source of energetic neutral atoms (ENAs) in the ribbon. A fraction of the solar wind and PUIs are reflected and energized during the first contact with the TS. Some of the solar wind may be reflected propagating toward the Sun but most of the solar wind ions form a gyrating beam-like distribution that persists until it is fully thermalized further downstream. Depending on the strength of the shock, these gyrating distributions can exist for many gyration periods until they are scattered/thermalized due to wave-particle interactions at the TS and downstream in the heliosheath. During this time, ENAs can be produced by charge exchange of interstellar neutral atoms with the gyrating ions. In order to determine the flux of energetic ions, we estimate the solar wind flux at the TS using pressure estimates inferred from in situ measurements. Assuming an average path length in the radial direction of the order of a few AU before the distribution of gyrating ions is thermalized, one can explain a significant fraction of the intensity of ENAs in the ribbon observed by IBEX. With a localized source and such a short integration path, this model would also allow fast time variations of the ENA flux.

Estimating Annual CO2 Flux for Lutjewad Station Using Three Different Gap-Filling Techniques

Long-term measurements of CO2 flux can be obtained using the eddy covariance technique, but these datasets are affected by gaps which hinder the estimation of robust long-term means and annual ecosystem exchanges. We compare results obtained using three gap-fill techniques: multiple regression (MR), multiple imputation (MI), and artificial neural networks (ANNs), applied to a one-year dataset of hourly CO2 flux measurements collected in Lutjewad, over a flat agriculture area near the Wadden Sea dike in the north of the Netherlands. The dataset was separated in two subsets: a learning and a validation set. The performances of gap-filling techniques were analysed by calculating statistical criteria: coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), maximum absolute error (MaxAE), and mean square bias (MSB). The gap-fill accuracy is seasonally dependent, with better results in cold seasons. The highest accuracy is obtained using ANN technique which is also less sensitive to environmental/seasonal conditions. We argue that filling gaps directly on measured CO2 fluxes is more advantageous than the common method of filling gaps on calculated net ecosystem change, because ANN is an empirical method and smaller scatter is expected when gap filling is applied directly to measurements.