Existence of sign-changing solutions for the p-Laplacian equation from linking type theorem

In this paper, the existence of sign-changing solutions for p-Laplacian equation is obtained via a new linking theorem.     

Glass-forming Photoconductive Organic Compounds II1: Glass-forming Properties of 1,3,5-Triaryl-2-pyrazolines

Glass-forming properties of 2-pyrazoline derivatives were examined and discussed in terms of the molecular structure. The results show that the molecular shape of 1,3,5-triaryl-2-pyrazolines is responsible for the glass-forming properties of these compounds. Glass transition points of several 1,3,5-triaryl-2-pyrazoline derivatives were measured.     

Asymptotic analysis for an extended discrete Lotka–Volterra system related to matrix eigenvalues

The integrable discrete hungry Lotka–Volterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.     

The Augmentation Quotients of the Groups of Order 25, II

We have described the structure of Q _n (G) = Δ ⁿ (G)/Δ ⁿ⁺¹(G) for 35 particular classes of groups G with order 2⁵ in the previous article. In this article, the structure of Q _n (G) for all the remaining classes of groups G with order 2⁵ are presented.     

Berkovich nanoindentation study of monocrystalline tungsten: a crystal plasticity study of surface pile-up deformation

Abstract

In this paper, it was investigated whether Berkovich indentation test with a triangular-based pyramidal imprint would exhibit the same surface pile-up deformation behaviour as in Vickers or spherical indentation tests. The characteristic correlation between the pile-up patterns of monocrystalline tungsten and the geometry of slip systems was examined both experimentally and computationally. Surface pile-up patterns for three different crystallographic orientations of specimens with corresponding rotational crystal symmetry were characterised. In addition, the effect of the varying azimuthal orientation of the indenter on the pile-up patterns was also discussed. Predictions from finite element simulation based on the crystal plasticity theory are also presented and compared with the measured results. It was found that the surface pile-up patterns of Berkovich indentation did not necessarily reflect the rotational crystal symmetry of tungsten single crystal specimens. The pile-up patterns were affected by the variation of the indenter’s azimuthal orientation. The height of the pile-up hillocks was often highly non-uniform even on the same surface plane indicating strong influence of slip geometry leading to the plastic anisotropy.     

Nanoconfined heliconical structure of twist-bend nematic liquid crystal phase

We produced controlled heliconical structures of a twist-bend nematic (N_TB) liquid-crystal (LC) phase in nanoconfinement in a porous anodic aluminium oxide (AAO) film. The structural parameters of the N_TB phase such as conical angle and helical pitch can be modulated by varying the surface energy of the inner surface of the porous AAO film, done by using different self-assembled monolayers (SAMs). The LC molecules tend to be more freely packed, thus forming a larger conical angle, when placed on the tri-deca-fluoro-1,1,2,2-tetrahydrooctyl-trichlorosilane (FOTS)-treated substrate, which has a relatively low surface energy. In contrast, the molecules form a more tightly packed structure, and thus a smaller conical angle, when placed on the 2-(methoxy(polyethyleneoxy)-propyl)trimethoxysilane (PEG 6/9)-treated substrate, which has higher surface energy. This work improves our collective understanding of self-assembled heliconical structures in the N_TB phase.     

Real-time focus control in broad flat field laser material processing

Broad flat field laser scanning is critical to the success of laser material processing, used in techniques such as rapid prototyping & manufacturing (RP&M) and micro-machining. For these techniques it is necessary to produce high-performance optical systems that can fulfill the need for a smaller focused spot size over broad, flat field scanning areas. This paper concentrates on the issues of defocus error compensation. A dynamic focusing system is designed, intended primarily for broad flat field galvanometric laser scanning applications. Key technologies are described in detail; corresponding solutions have been used to design and produce a CO₂ infrared optical focusing system, which is capable of scanning a focused spot size of 120 μm or less over areas up to 500 mm².