Anisotropic Elastic-Viscoplastic Properties at Finite Strains of Injection-Moulded Low-Density Polyethylene

Injection-moulding is one of the most common manufacturing processes used for polymers. In many applications, the mechanical properties of the product is of great importance. Injection-moulding of thin-walled polymer products tends to leave the polymer structure in a state where the mechanical properties are anisotropic, due to alignment of polymer chains along the melt flow direction. The anisotropic elastic-viscoplastic properties of low-density polyethylene, that has undergone an injection-moulding process, are therefore examined in the present work. Test specimens were punched out from injection-moulded plates and tested in uniaxial tension. Three in-plane material directions were investigated. Because of the small thickness of the plates, only the in-plane properties could be determined. Tensile tests with both monotonic and cyclic loading were performed, and the local strains on the surface of the test specimens were measured using image analysis. True stress vs. true strain diagrams were constructed, and the material response was evaluated using an elastic-viscoplasticity law. The components of the anisotropic compliance matrix were determined together with the direction-specific plastic hardening parameters.     

Quaternions for GUTs

We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyze possible quaternionic groups for GUTs.     

Giant shot-like voltage noise in high current density Nb–AlOx–Nb superconducting tunnel junctions

The flat voltage noise component of current biased, high-transparency Nb/AlO_x/Nb superconducting tunnel junctions has been investigated at frequencies up to 70 kHz. Several aspects of the analyzed phenomena suggest the presence of current noise effects induced by the discreteness of the charge carriers. At subgap voltages, where excess currents occur, a behavior coherent with a multiple Andreev reflection-assisted transport through the tunnel barrier has been found. However, the measured charge values exceed any theoretical prediction.     

Existence of solutions to projected differential equations in Hilbert spaces

We prove existence and uniqueness of integral curves to the (discontinuous) vector field that results when a Lipschitz continuous vector field on a Hilbert space of any dimension is projected on a non-empty, closed and convex subset.

     

The Loewner Equation: Maps and Shapes

An approach called Schramm–Loewner evolution (SLE) provides a new method for dealing with a wide variety of scale-invariant problems in two dimensions. This approach is based upon an older method called Loewner Evolution (LE), which connects analytic and geometrical constructions in the complex plane. In this paper, the bases of LE and SLE are described and some simple applications are discussed in relatively non-technical form. A bibliography of the subject is presented.     

A simple expression for the ADM mass

We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. The result is essentially the same as that given by David Brown and York (Phys. Rev. D 55, 1977–1984 1997; Phys. Rev. D 47, 1407–1419 1993). We will prove this result in two ways, first by direct calculation from the original formula as given by Arnowitt, Deser and Misner and second as a corollary of an earlier result by Brewin for the case of simplicial spaces.     

A Diepoxide Belonging to the Rare C1 Point Group

2,6- and 2,7-Dimethylanthracenes were reduced seriatim with lithium in liquid ammonia and lithium in methylamine to their 1,4,5,8,9,10-hexahydro derivatives. Two-fold epoxidation of these tetraenes provided the cis and trans diepoxides resulting from electrophilic attack at the inner double bonds. Trans diepoxide 1 has the very unusual characteristic of lacking a σ plane of symmetry but possessing an inversion center. As a consequence, the ¹H NMR spectrum of C₁-symmetric 1 is simplified relative to those of its isomers 5, 9, and 10.