Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

we give the concept of ‘braiding’ for 2-groupoids, and we show that this structure is equivalent tobraided regular, crossed modules.

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

A micromechanical model for 2-D triaxial braided composites is presented. The tow arrangement in the representative unit cell is modeled by solving the packing problem using analytical optimization, avoiding the need to measure the geometric properties experimentally. These results are used in the development of a closed-form micromechanical model predicting the full 3-D stiffness matrix of the...

This paper presents the design of a single module composing a modular soft variable stiffness manipulator for minimal access surgery. The module exploits flexible fluidic actuation for obtaining multi directional bending and elongation capabilities. A novel flexible crimped braided sheath is introduced in order to increase the performances of the flexible actuator. Granular jamming based stiffe...

Let (H, σ) be a coquasitriangular Hopf algebra, not necessarily finite dimensional. Following methods of Doi and Takeuchi, which parallel the constructions of Radford in the case of finite dimensional quasitriangular Hopf algebras, we define Hσ , a sub-Hopf algebra of H, the finite dual of H. Using the generalized quantum double construction and the theory of Hopf algebras with a projection, we...