The internal strain of three-dimensional braided composites with co-braided FBG sensors

The performance analysis of three-dimensional (3-D) braided composites is made difficult by their complex and interlacing structure, and is still under development. To get complete first-hand data on the material parameters of these composites, co-braided optical fiber sensors (OFS) can be used to measure the internal strain. This information is helpful for subsequent stiffness predictions and failure analysis. This paper introduces a method of incorporating OFS into braided composites, and establishes a constitutive theoretical model for the hybrid material. Experiments are conducted to measure the internal strain of specimens under tension, and the results are compared to theoretical predictions.     

Braided Fiber Current Collectors for High-Energy-Density Fiber Lithium-Ion Batteries

Fiber lithium-ion batteries represent a promising power strategy for the rising wearable electronics. However, most fiber current collectors are solid with vastly increased weights of inactive materials and sluggish charge transport, thus resulting in low energy densities which have hindered the development of fiber lithium-ion batteries in the past decade. Here, a braided fiber current collector with multiple channels was prepared by multi-axial winding method to not only increase the mass fraction of active materials, but also to promote ion transport along fiber electrodes. In comparison to typical solid copper wires, the braided fiber current collector hosted 139 % graphite with only 1/3 mass. The fiber graphite anode with braided current collector delivered high specific capacity of 170 mAh g⁻¹ based on the overall electrode weight, which was 2 times higher than that of its counterpart solid copper wire. The resulting fiber battery showed high energy density of 62 Wh kg⁻¹.     

THE GENERALIZED SMASH PRODUCT AND COPRODUCT

91. PreliminariesThroughout the paper all spaces are over a fixed ground field K. If C is a coalgebra,then we always denote the comultiplication and counit by b and E respectively. Set b(c) Z of @ cd for c E C. If M is a right (left) C -comodule, then we use p for the structure mapof M, and set p(m) = ac(o) @ m(1) (p(m) ~ ac(--1) @ m(o)) for m E M. Let H be abialgebra. Denote left H-module category by HM and left H-comodule category by HM.If M and N are in HM, then M @ N is also a l…     

Topology and Geometry of Smectic Order on Compact Curved Substrates

Smectic order on arbitrary curved substrate can be described by a differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. We use the formalism of differential forms to systematically classify and characterize all low energy smectic states on torus as well as on sphere. A two dimensional smectic order confined on either manifold exhibits many topologically distinct low energy states. Different states are not accessible from each other by local fluctuations. The total number of low energy states scales as the square root of the system area. We also address the energetics of 2D smectic on a curved substrate and calculate the mean field phase diagram of smectic on a thin torus. Finally, we discuss the motion of disclinations for spherical smectics as low energy excitations, and illustrate the interesting connection between spherical smectic and the theory of elliptic functions.     

Generalized Lie Algebras and Cocycle Twists

We use the results of Etingof and Gelaki on the classification of (co)triangular Hopf algebras to extend Scheunert's “discoloration” technique to Lie algebras in the category of (co)modules. As an application, we prove a PBW-type theorem for such Lie algebras. We also discuss the relationship between Lie algebras in the category of (co)modules and symmetric braided Lie algebras introduced by Gurevich. Finally, we construct examples of symmetric braided Lie algebras that are essentially different from Lie coloralgebras.