Mean curvatures and Gauss maps of a pair of isometric helicoidal and rotation surfaces in Minkowski 3-space

It is proved that, in Minkowski 3-space, a CSM-helicoidal surface, i.e., a helicoidal surface under cubic screw motion is isometric to a rotation surface so that helices on the helicoidal surface correspond to parallel circles on the rotation surface. By distinguishing a CSM-helicoidal surface as three cases, that is, the case of type I, the case of type II with negative and positive pitch, the relations are discussed between the mean curvatures or Gauss maps of a pair of isometric helicoidal and rotation surface. A CSM-helicoidal surface of Case 1 or 2 and its isometric rotation surface with null axis have same mean curvatures (resp. Gauss maps) if and only if they are minimal. But each pair of isometric CSM-helicoidal surface of Case 3 and rotation surface with spacelike axis have different Gauss maps.     

Mechanical Behavior of Bulk Poly(Ethylene Terephthalate) Subjected to Simple Shear

Abstract

Mechanical behavior of bulk semicrystalline poly(ethylene terephthalate) (PET) processed through simple shear is investigated. The equal channel angular extrusion (ECAE) process was used to achieve the simple shear condition. The PET samples were processed in one and two ECAE passes in the same direction, with the sample rotated 180° about the extrusion axis for the second pass. Microstructural features at the nanometer and micrometer scales were studied by small‐angle x‐ray scattering (SAXS) and scanning electron microscopy (SEM). SAXS results showed that at the nanometer scale, two types of lamellar orientations are induced in both samples, but with different extents of orientation. In the ECAE‐oriented PET structures on the micrometer scale, as revealed by SEM, are well‐defined macrofibrils. However, the fibrillar structures in the sample extruded once are more oriented than those in the sample extruded twice. Fractography investigations suggest that the ECAE‐induced fibrillar structure and stretched amorphous chains are responsible for the change in mechanical properties.     

Nanoparticle‐Loaded Cylindrical Micelles from Nanopore Extrusion of Block Copolymer Spherical Micelles

Hybrid cylindrical micelles loaded with nanoparticles are fabricated via extrusion of spherical micelles in solution phase through small long cylindrical pores. Small gold nanoparticles (AuNPs) are pre‐coated with thiol‐terminated polystyrene and then further encapsulated in the core part of block copolymer spherical micelles by a precipitation method. By varying the starting mass ratio of AuNPs and the diblock copolymers polystyrene‐b‐polyisoprene (PS‐b‐PI) during the encapsulation, the AuNPs loading density along the cylindrical micelles can be controlled. The mechanism for this sphere‐to‐cylinder transition induced by extruding hybrid spherical micelles through small cylindrical nanopores is discussed. These findings provide a novel way to manufacture high‐quality and functional polymeric nano­wires, which may open the door to new applications such as in plasmonic waveguides.

     

Study of Metallocene-Catalyzed Linear Low-Density Polyethylene Solid-State Extrusion: Processing and Mechanical Properties

The effect of extrusion temperature and extrusion drawing ratio (EDR) on the die swell ratio (DSR) and mechanical properties of metallocene-catalyzed linear low-density polyethylene (m-LLDPE) was examined with the application of solid-state extrusion (SSE). Scanning electron microscopy (SEM) was employed to characterize the microstructure and morphology of the extrudates. Extruded from a convergence-divergence die, compared with samples obtained by melt-state extrusion (MSE), the DSR decreases for SSE samples prepared at low extrusion temperature and high EDR. Mechanically strong SSE samples were also obtained at low extrusion temperatures and high EDR. Mechanically strong SSE samples were also obtained at low extrusion temperatures and high EDR. SEM indicates that the microstructures of the MSE samples consist primarily of ring-banded spherulites; the microstructure of the SSE samples was microfibers oriented along the direction of extrusion. The highly oriented microfibers contribute to the improved mechanical strength of the SSE samples.     

Extrusions and intrusions in fatigued metals. Part 1. State of the art and history†

Current state and historical progress in experimental and theoretical studies of surface relief appertaining to persistent slip bands (PSBs) and leading to fatigue crack initiation in cyclically deformed metals is presented as a thorough critical overview. A comprehensive inventory of microscopic techniques used for this study is tabulated chronologically with emphasis to their applicability to polycrystals. The most relevant experimental characteristics concerning surface relief evolution, namely the form of extrusions and intrusions in single- and polycrystalline materials, are surveyed. Theoretical models and computational simulations of extrusion and intrusion formation and fatigue crack initiation are critically reviewed.     

Lüders deformation and superplastic flow of metals extruded by KOBO method

The work brings the results of the study on mechanical properties of some metallic materials subjected to very large plastic deformation by KOBO extrusion. The unexpected features of the KOBO products like Lüders deformation in pure metals and superplastic flow in coarse grain materials are discussed in terms of micro- and nano-scale elements of their structure. The choice to the experiment materials having different crystallographic and phase structure (commercial purity aluminium, multiphase aluminium 7075 alloy, pure zinc and multiphase magnesium AZ91 alloy) and different history (extrusion, casting) allowed to identify the common nano-size elements of the structure generated during the KOBO deformation which seems to be responsible for the mechanical behaviour of these materials. In particular, clusters of point defects (self-interstitials) formed under the KOBO extrusion conditions (cyclic change in the deformation path, high hydrostatic pressure) were found in these materials regardless of grain size and material early history. They correlate with appearance of unstable Lüders-like or even Portevin–LeChatelier deformation at ambient and superplastic flow at elevated temperatures.     

Effect of the shear layer on the etching behavior of 6060 aluminum extrusion alloys

The occurrence of preferential grain etching (PGE) during alkaline etching of aluminum extrusion alloys from the 6XXX series is often linked to the presence of certain impurity elements such as zinc, causing an undesired etching appearance. In the presented work, an additional culprit in this context is identified, which has not been investigated yet. A clear relation between PGE and the presence of a subsurface shear layer is identified for extruded Al 6060 alloys containing 0.02 and 0.06 wt% Zn. This shear layer can be distinguished from the bulk of the metal by its difference in crystallographic texture as visualized by electron backscatter diffraction (EBSD). For the Zn enriched alloy, the <111>//ND grains are etched away faster than grains with other orientations, resulting in the grainy appearance typical for PGE. Independent of the Zn content in the alloy, once the shear layer is removed and <111>//ND grains are practically absent on the new surface, the depths variations caused by preferential etching disappear. Instead, the surface of the alloy is attacked uniformly by the caustic etch bath.     

Continuous separation of maslinic and oleanolic acids from olive pulp by high‐speed countercurrent chromatography with elution‐extrusion mode

In this work, a continuous high‐speed countercurrent chromatography method has been developed on the basis of elution‐extrusion mode and this method was successfully applied to the separation of maslinic and oleanolic acid from the extract of olive pulp. In the process of ‘elution’, the sample solution was continuously loaded into the column and the maslinic acid was steadily eluted out in this step while highly retained oleanlic acid always stayed in the column. In the process of ‘extrusion’, the oleanlic acid was pushed out of the column with the stationary phase. In this way, we achieved a large sample loading. A total of 120 mL sample solution (about 89.55% of the column volume) which contains 600 mg olive pulp extract was pumped in the apparatus by a constant‐flow pump and the maslinic and oleanolic acids were largely separated within 120 min. Both of these two compounds presented high yields and high purities (271.6 mg for maslinic acid with 86.7% and 83.9 mg oleanolic acids with 83.4%).     

Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.