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A classical theorem of braid theory, dating back to Artin's work, says that two closed braids in a solid torus are ambient isotopic if and only if they represent the same conjugacy class of the braid group. This theorem can be reformulated in the framework of link theory without referring to the group structure. A link in a surface bundle over the circle is transversal whenever it covers the circle. In this terminology, Artin's theorem states that in a solid torus trivially fibered over the circle transversal links are ambient isotopic if and only if they are isotopic in the class of transversal links. We generalize this result by proving that (in the piecewise linear category) transversal links in an arbitrary compact orientable -manifold fibered over the circle with a compact fiber are ambient isotopic if and only if they are isotopic in the class of transversal links. [ABSTRACT FROM AUTHOR]

Let n, m ∈ ℕ, n ≥ 3 and n ≥ m ≥ 2. In this paper, we study some properties of the unrestricted virtual singular braid of braid monoid UVSBmn and group UVSGmn. These properties emerged by studying the analogous properties of the unrestricted virtual singular pseudosymmetric braid of braid monoid and group. These mathematical objects are submonoids and subgroups of the virtual singular braid group VSGn. For many of these quotients, we have obtained reduced presentations. [ABSTRACT FROM AUTHOR]

Representations of braid group B n on n ≥ 2 strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group V B n on n ≥ 2 strands is an extension of the classical braid group B n by the symmetric group S n . In this paper, we consider flat virtual braid groups F V B n on n ≥ 2 strands and construct a family of representations of F V B n by automorphisms of free groups of rank 2 n . It has been established that these representations do not preserve the forbidden relations between classical and virtual generators. We investigated some algebraic properties of the constructed representations. In particular, we established conditions of faithfulness in case n = 2 and proved that the kernel contains a free group of rank two for n ≥ 3 . [ABSTRACT FROM AUTHOR]

This study investigated the effects of different braid materials (polyethylene terephthalate, nylon 6, and their hybrid), weaving frequencies of the braids (7, 9, 11, 13 Hz), and concentrations of polyether sulfone solution (15% and 18 wt%) on braid angles, braid thickness, and bursting resistance. The results showed that for all types of single and hybrid braids, the braid angle decreases with increasing spinning frequency. When spinning frequency was increased from 7 to 13 Hz, the average wall thickness of polyethylene terephthalate, nylon 6, and the hybrid braids increased by approximately 50%, 65%, and 60%, respectively. The bursting pressure results were obtained in the range of 9.3 to 20.2 bars. The Fourier transform infrared spectroscopy results revealed no chemical bond between the braids and the polyether sulfone layer. Optical and electron microscope analyses revealed formation of uniform thickness of the polyether sulfone layers on the surface of the braids, as well as the penetration of polyether sulfone into the gaps between the filaments. The analyses also showed macroscopic adhesion of polyether sulfone to the braids and provided information on the amount and size of the pores in the polymer layers. The results showed that the selection of appropriate weaving frequency, braid materials, and polyether sulfone layer concentration are important as controllable parameters for producing polymeric hollow fiber composites with excellent burst pressure resistance. [ABSTRACT FROM AUTHOR]

In this paper, we show that every finite spatial graph is a connected sum of a planar graph, which is a forest, and a tangle. As a consequence, we get that any finite spatial graph is a connected sum of a planar graph and a braid. Using these decompositions it is not difficult to find a set of generators and defining relations for the fundamental group of compliment of a spatial graph in 3-space ℝ 3 . [ABSTRACT FROM AUTHOR]

The behavior of dry fibers is a key component in modeling composite materials. However, it can become very expensive in computation time to model each individual filament. We propose here a new multi-scale method featuring beam elements embedded in truss elements. Truss elements are used to model contact responses and traction while beams elements are used to characterize flexion. This approach is compared to three different models using truss elements only, beam elements only, and a reference case. The reference case is also validated by experimental results of a glass braid being extended to drape over a square mandrel. The embedded element cumulative error on estimation of the deformed braid angle, thickness and length compared to the reference case is lower than their pure truss and pure beam models, while being 8 times faster than the reference case. • Textile are modelled at the fiber level using chains of finite elements. • Fiber behavior is modelled using beam elements embedded in truss elements. • A biaxial braid conforming to a square mandrel is modelled. • Accuracy of textile modelling is improved while being 8 times faster. [ABSTRACT FROM AUTHOR]

The application of braided composite materials in the automotive industry requires an in-depth understanding of the mechanical properties. To date, the intralaminar fracture toughness of braided composite materials, typically used for describing post-failure behavior, has not been well-characterized experimentally. In this paper, a modified compact tension test, utilizing a relatively large specimen and a metallic loading frame, is used to measure the transverse intralaminar fracture toughness of a tri-axial braided composite. During testing, a relatively long fracture process zone ahead of the crack tip was observed. Crack propagation could be correlated to the failure of individual unit cells, which required failure of bias-yarns. The transverse interlaminar fracture toughness was found to be two orders of magnitude higher than the reference interlaminar fracture toughness of the same material. This is due to the fact, that intralaminar crack propagation requires breaking of fibers, which is not the case for interlaminar testing. [ABSTRACT FROM AUTHOR]