Nonlinear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.Comment: 20 pages, 5 figure

Outlier robust corner-preserving methods for reconstructing noisy images

The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the cost of the other. By combining M-smoothing and least-squares-trimming, the TM-smoother is introduced as a means to unify corner-preserving properties and outlier robustness. To identify edge- and corner-preserving properties, a new theory based on differential geometry is developed. Further, robustness concepts are transferred to image processing. In two examples, the TM-smoother outperforms other corner-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.Comment: Published at http://dx.doi.org/10.1214/009053606000001109 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Nuclear Window to the Extragalactic Universe

We investigate two recent parameterizations of the galactic magnetic field with respect to their impact on cosmic nuclei traversing the field. We present a comprehensive study of the size of angular deflections, dispersion in the arrival probability distributions, multiplicity in the images of arrival on Earth, variance in field transparency, and influence of the turbulent field components. To remain restricted to ballistic deflections, a cosmic nucleus with energy E and charge Z should have a rigidity above E/Z=6 EV. In view of the differences resulting from the two field parameterizations as a measure of current knowledge in the galactic field, this rigidity threshold may have to be increased. For a point source search with E/Z>60 EV, field uncertainties increase the required signal events for discovery moderately for sources in the northern and southern regions, but substantially for sources near the galactic disk.Comment: 15 pages, 30 figures, few additional sentences and references as in accepted publicatio

Modification of the anisotropy and strength differential effect of extruded AZ31 by extrusion-shear

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 1960, 030008 (2018) and may be found at https://doi.org/10.1063/1.5034851.The extrusion of magnesium alloys results in a pronounced fiber texture in which the basal planes are mostly oriented parallel and the c-axes are oriented perpendicular to the extrusion direction. Due to this texture the Strength Differential Effect (SDE), which describes the strength difference between tensile and compression yield strength, and the elastic anisotropy in the sheet plane are obtained during extrusion. The objective of the investigation was to decrease the SDE and anisotropy through specifically influencing the microstructure and texture. To accomplish this objective, the forming processes extrusion (EX) and equal channel angular pressing (ECAP) were combined and integrated into one extrusion die. This combination is called extrusion-shear (ES). With an ES-die, billets of the magnesium alloy AZ31B were formed into a sheet with the thickness of 4 mm and the width of 70 mm. The angles of the used ECAP-applications in the ES-dies were set to 90° and 135°. The results show that the extrusion-shear process is able to decrease the anisotropy and SDE through transformation of the texture compared to conventional extrusion process. Also grain refinement could be observed. However, the outcomes seem to be very sensitive to the process parameters. Only by using the ES-die with an angle of 135° the desired effect could be accomplished