Roulettes: A weak lensing formalism for strong lensing — II. Derivation and analysis —

We present a new extension of the weak lensing formalism capable of describing strongly lensed images. This paper accompanies Paper I, arXiv:1603.04698 where we provided a condensed overview of the approach and illustrated how it works. Here we give all the necessary details, together with some more explicit examples. We solve the non-linear geodesic deviation equation order-by-order, keeping the leading derivatives of the optical tidal matrix, giving rise to a series of maps from which a complete strongly lensed image is formed. The family of maps are decomposed by separating the trace and trace-free parts of each map. Each trace-free tensor represents an independent spin mode, which distort circles into a variety of roulettes in the screen-space. It is shown how summing this series expansion allows us to create large strongly lensed images in regions where convergence, shear and flexion are not sufficient. This paper is a detailed exposition of Paper I which presents the key elements of the subject matter in a wider context.Comment: 25 pages, 9 pages. v3 has minor changes to match published version. Paper I available at arXiv:1603.0469

Effects of Adiabatic Heating on the High Strain Rate Deformation of Polymer Matrix Composites

Polymer matrix composites (PMCs) are increasingly being used in aerospace structures that are expected to experience complex dynamic loading conditions throughout their lifetime. As such, a detailed understanding of the high strain rate behavior of the constituents, particularly the strain rate, temperature, and pressure dependent polymer matrix, is paramount. In this paper, preliminary efforts in modeling experimentally observed temperature rises due to plastic deformation in PMCs subjected to dynamic loading are presented. To this end, an existing isothermal viscoplastic polymer constitutive formulation is extended to model adiabatic conditions by incorporating temperature dependent elastic properties and modifying the components of the inelastic strain rate tensor to explicitly depend on temperature. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The modified constitutive model is then embedded within a strength of materials based micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700Epon 862 (T700E862) unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for the conversion of plastic work to heat in the polymer matrix in the high strain rate analysis of PMC structures

Micromorphology and Site Formation at Hohle Fels Cave, Schwabian Jura, Germany

Die Höhle Hohle Fels liegt auf der Schwäbischen Alb bei Schelklingen und beinhaltet eine stratigraphische Folge, die mindestens 36.000 Jahre zurück geht und Aurignacien-, Gravettien- und Magdalénien-Fundschichten beinhaltet. Die Sedimente vom Hohle Fels wurden mit mikromorphologischen Analysen in Kombination mit Elektronmikroprobe und FTIR-Analysen untersucht. Die Ergebnisse zeigen, dass die Sedimente aus dem inneren Bereich der Höhle stammen und das die feine Matrix in Zusammenhang mit der Nutzung der Höhle durch Bären eine starke Phosphatenanreicherung erlebt hat. Mikrostrukturen belegen kalte und feuchte klimatische Phasen, charakterisiert durch Kryoturbation und Eislinsen. Diese Merkmale sind in den Gravettien- und Magdalénien-Schichten stärker entwickelt und sprechen für kühle Bedingungen während dieser Perioden. Während des letzten Kältemaximums fehlen Hinweise für die Nutzung der Höhle durch Menschen und Höhlenbären. Diese Beobachtungen können als Grundlage dienen, um Hypothesen über das Paläoklima und über menschliches Verhalten im Paläolithikum, die anhand botanischer, faunistischer und archäologischer Daten entwickelt wurden, zu prüfen. Einige der Methoden dieser Untersuchungen wurden zum ersten Mal in den Höhlen der Schwäbischen Alb eingesetzt und lieferten viel versprechende Einblicke in die Archäologie und die naturhistorische Entwicklung der Region.researc