Computational analysis of liquid crystalline elastomer membranes: Changing Gaussian curvature without stretch energy

Liquid crystalline elastomers (LCEs) can undergo extremely large reversible shape changes when exposed to external stimuli, such as mechanical deformations, heating or illumination. The deformation of LCEs result from a combination of directional reorientation of the nematic director and entropic elasticity. In this paper, we study the energetics of initially flat, thin LCE membranes by stress driven reorientation of the nematic director. The energy functional used in the variational formulation includes contributions depending on the deformation gradient and the second gradient of the deformation. The deformation gradient models the in-plane stretching of the membrane. The second gradient regularises the non-convex membrane energy functional so that infinitely fine in-plane microstructures and infinitely fine out-of-plane membrane wrinkling are penalised. For a specific example, our computational results show that a non-developable surface can be generated from an initially flat sheet at cost of only energy terms resulting from the second gradients. That is, Gaussian curvature can be generated in LCE membranes without the cost of stretch energy in contrast to conventional materials. © 2013 Elsevier Ltd. All rights reserved.

Modeling the carbon nanofiber addressed liquid crystal microlens array from experimentally observed optical phenomena

This paper presents a novel method of using experimentally observed optical phenomena to reverse-engineer a model of the carbon nanofiber-addressed liquid crystal microlens array (C-MLA) using Zemax. It presents the first images of the optical profile for the C-MLA along the optic axis. The first working optical models of the C-MLA have been developed by matching the simulation results to the experimental results. This approach bypasses the need to know the exact carbon nanofiber-liquid crystal interaction and can be easily adapted to other systems where the nature of an optical device is unknown. Results show that the C-MLA behaves like a simple lensing system at 0.060-0.276 V/μm. In this lensing mode the C-MLA is successfully modeled as a reflective convex lens array intersecting with a flat reflective plane. The C-MLA at these field strengths exhibits characteristics of mostly spherical or low order aspheric arrays, with some aspects of high power aspherics. It also exhibits properties associated with varying lens apertures and strengths, which concur with previously theorized models based on E-field patterns. This work uniquely provides evidence demonstrating an apparent "rippling" of the liquid crystal texture at low field strengths, which were successfully reproduced using rippled Gaussian-like lens profiles. © 2014 Published by Elsevier B.V.

Refining sparse principal components

In this paper, we discuss methods to refine locally optimal solutions of sparse PCA. Starting from a local solution obtained by existing algorithms, these methods take advantage of convex relaxations of the sparse PCA problem to propose a refined solution that is still locally optimal but with a higher objective value. © 2010 Springer -Verlag Berlin Heidelberg.

Twin plane re-entrant mechanism for catalytic nanowire growth.

A twin-plane based nanowire growth mechanism is established using Au catalyzed Ge nanowire growth as a model system. Video-rate lattice-resolved environmental transmission electron microscopy shows a convex, V-shaped liquid catalyst-nanowire growth interface for a ⟨112⟩ growth direction that is composed of two Ge {111} planes that meet at a twin boundary. Unlike bulk crystals, the nanowire geometry allows steady-state growth with a single twin boundary at the nanowire center. We suggest that the nucleation barrier at the twin-plane re-entrant groove is effectively reduced by the line energy, and hence the twin acts as a preferential nucleation site that dictates the lateral step flow cycle which constitutes nanowire growth.

Surface contact and design of fibrillar 'friction pads' in stick insects (Carausius morosus): mechanisms for large friction coefficients and negligible adhesion.

Many stick insects and mantophasmids possess tarsal 'heel pads' (euplantulae) covered by arrays of conical, micrometre-sized hairs (acanthae). These pads are used mainly under compression; they respond to load with increasing shear resistance, and show negligible adhesion. Reflected-light microscopy in stick insects (Carausius morosus) revealed that the contact area of 'heel pads' changes with normal load on three hierarchical levels. First, loading brought larger areas of the convex pads into contact. Second, loading increased the density of acanthae in contact. Third, higher loads changed the shape of individual hair contacts gradually from circular (tip contact) to elongated (side contact). The resulting increase in real contact area can explain the load dependence of friction, indicating a constant shear stress between acanthae and substrate. As the euplantula contact area is negligible for small loads (similar to hard materials), but increases sharply with load (resembling soft materials), these pads show high friction coefficients despite little adhesion. This property appears essential for the pads' use in locomotion. Several morphological characteristics of hairy friction pads are in apparent contrast to hairy pads used for adhesion, highlighting key adaptations for both pad types. Our results are relevant for the design of fibrillar structures with high friction coefficients but small adhesion.