Large Braid Research Articles

Connected components of affine primitive permutation groups

For a finite group G, the Hurwitz space Hr,gin(G) is the space of genus g covers of the Riemann sphere with r branch points and the monodromy group G.In this paper, we give a complete list of primitive genus one systems of affine type. That is, we assume that G is a primitive group of affine type. Under this assumption we determine the braid orbits on the suitable Nielsen classes, which is equivalent to finding connected components in Hr,1in(G). Furthermore, we give a new algorithm for computing large braid orbits on Nielsen classes. This algorithm utilizes a correspondence between the components of Hr,1in(G) and Hr,1in(M), where M is the point stabilizer in G.

The Dinosaurian Ichnofauna of the Lower Cretaceous (Valanginian–Barremian) Broome Sandstone of the Walmadany Area (James Price Point), Dampier Peninsula, Western Australia

ABSTRACTExtensive and well-preserved tracksites in the coastally exposed Lower Cretaceous (Valanginian–Barremian) Broome Sandstone of the Dampier Peninsula provide almost the entire fossil record of dinosaurs from the western half of the Australian continent. Tracks near the town of Broome were described in the late 1960s as Megalosauropus broomensis and attributed to a medium-sized theropod trackmaker. Brief reports in the early 1990s suggested the occurrence of at least another nine types of tracks, referable to theropod, sauropod, ornithopod, and thyreophoran trackmakers, at scattered tracksites spread over more than 80 km of coastline north of Broome, potentially representing one of the world's most diverse dinosaurian ichnofaunas. More recently, it has been proposed that this number could be as high as 16 and that the sites are spread over more than 200 km. However, the only substantial research that has been published on these more recent discoveries is a preliminary study of the sauropod tracks and...

Volume bounds for generalized twisted torus links

Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their hyperbolic volumes that depend only on the number of strands being twisted. We exhibit a family of twisted torus knots for which this upper bound is sharp, and another family with volumes approaching infinity. Consequently, we show there exist twisted torus knots with arbitrarily large braid index and yet bounded volume.

Effect of Interface Properties on Mechanical Behavior of 3D Four-Directional Braided Composites with Large Braid Angle Subjected to Uniaxial Tension

A Representative Volume Cell (RVC) chosen to epitomize the entire three dimensional four-directional braided composites is investigated to evaluate the mechanical behavior of the material by computational micromechanics. In addition to including several damage modes of braid yarn and matrix within the braided composites, the numerical model also takes into account interface damage mode by using a Cohesive Zone Model (CZM). A parametrical study is conducted to evaluate the influence of interface properties on the macro stress-strain curve and the interaction of different failure modes of the braided composites under uniaxial tensile loading. The interface damage evolution of the braided composites with large braid angle is also provided further. Preliminary results indicate that the interface damage, which is one of the key factors to cause the nonlinearity of the stress-strain relationship, can decrease the elastic modulus but not obviously control the ultimate strength of the braided composites with large braid angle.

Vortex braids in the head wave formed as a dam breaks

The formation of flow-backing large vortex braids in a head dam-break wave running over the washed-out soil is revealed experimentally. Vortex dipoles braiding together with the captured soil are formed in the viscous near-bottom layer. Ascending and descending dipoles twist, forming a large near-bottom braid which rises to the water surface and forms a wall consisting of water and soil. The braids hold large soil particles if the flow velocity exceeds the critical value.

Morphology, flow structure, and suspended bed sediment transport at two large braid‐bar confluences

Mid‐channel bars and their associated confluences are key morphodynamic nodes within braided rivers, with past studies having investigated the morphodynamics of small natural channels or laboratory models with relatively low width/depth (W/D) ratios, typically at <10. This paper investigates the morphology, suspended bed sediment distribution, and flow structure at two large braid bar confluences in the Río Paraná (Argentina), wherein W/D ratios are much higher (approaching 100) than in smaller channels. The results highlight the significant control of the cross‐sectional distribution of downstream flow velocity on confluence flow, suspended bed sediment concentration, and morphodynamics and indicate that this factor may become progressively more significant with increasing channel scale and W/D ratio, particularly when simple discharge (or momentum) ratios between the incoming flows are used to explain the flow dynamics. Additionally, secondary flow cells, often proposed to occupy a large part of the channel width in small river channel confluences, are only identified in relatively small portions of the channel width at these larger spatial scales. Such a restriction seems related to the generative mechanisms of secondary flows at these higher W/D ratios, which are likely to be dominated by turbulence generated along the mixing layer between the two flows and topographic influences that limit the spatial extent of these effects. This paper highlights the importance of these findings with respect to the flow and sediment dynamics of large channel confluences.

Progressive damage and nonlinear analysis of 3D four-directional braided composites under unidirectional tension

A representative volume cell (RVC) is chosen to analyze the progressive damage behavior of 3D four-directional braided composites with large braid angle subjected to uniaxial tension. An anisotropic damage model is established by Murakami-Ohno damage theory. A new damage evolvement model is proposed, which is controlled by material fracture energy of braided composites constituents and equivalence displacements. According to the different damage modes (yarn transverse tension, compression and shear; yarn longitudinal tension and compression; matrix cracking), the different damage states and progressive damage of the braided composite are obtained. The numerical results show that the main failure modes of the braided composites are transverse tension, shear breakage of yarns and matrix cracking, which are in good agreement with the relevant experimental results in some literatures.

Topological Entropy of Braids on the Torus

A fast method is presented for computing the topological entropy of braids on the torus. This work is motivated by the need to analyze large braids when studying two-dimensional flows via the braiding of a large number of particle trajectories. Our approach is a generalization of Moussafir's technique for braids on the sphere. Previous methods for computing topological entropies include the Bestvina--Handel train-track algorithm and matrix representations of the braid group. However, the Bestvina--Handel algorithm quickly becomes computationally intractable for large braid words, and matrix methods give only lower bounds, which are often poor for large braids. Our method is computationally fast and appears to give exponential convergence towards the exact entropy. As an illustration we apply our approach to the braiding of both periodic and aperiodic trajectories in the sine flow. The efficiency of the method allows us to explore how much extra information about flow entropy is encoded in the braid as the number of trajectories becomes large.

Fluvial evolution of the lower Mississippi River valley during the last 100 k.y. glacial cycle: Response to glaciation and sea-level change

The lower Mississippi valley contains multiple large braid belts for which age control has been limited. Application of the optically stimulated luminescence technique has produced a new chronology of lower Mississippi valley channel-belt formation and insight into the valley9s evolution during the last glacial cycle. Fluvial deposits range from last interglacial meander belts (85 ± 7 to 83 ± 7 ka) to multiple braid belts (64 ± 5 to 11 ± 1 ka) and record large-amplitude responses of the Mississippi River to glacially induced changes in discharge and sediment supply during the last glacial cycle. Slackwater deposits in buried tributary valleys from the middle Mississippi valley and northern lower Mississippi valley suggest that the river was flowing at a position 8–21 m below the present flood plain during the last interglacial, then rapidly aggraded and switched to a braided regime to form the highest and oldest braid belt by 64 ± 5 to 50 ± 4 ka, coincident with initial glaciation of the upper drainage basin. The Mississippi River remained braided until final meltwater withdrawal from its headwaters in the earliest Holocene. Braid-belt formation and incision was controlled by fluctuations in meltwater and sediment discharge, while glacio-eustatic sea level controlled the elevation to which the river was graded, causing late glacial braid belts to dip below the Holocene flood plain in the southern lower Mississippi valley. Moreover, avulsions in the middle Mississippi valley and northern lower Mississippi valley during the last glaciation have pinned the river over regions of shallow bedrock, preventing the modern river from incising to its last interglacial profile. The new chronology and longitudinal profiles presented here provide insight into the response of this continental-scale river system to climatic (glacial) and base-level forcing during the last 100 k.y. glacial cycle.

Topological Entropy of Braids on the Torus

We present a fast method for computing the topological entropy of braids on the torus. This work is motivated by the need to analyze large braids when studying two‐dimensional flows via the braiding of a large number of particle trajectories. Our approach is a generalization of Moussafir’s technique for braids on the disk. Previous methods for computing topological entropy include the Bestvina–Handel train‐track algorithm and matrix representations of the braid group. However, the Bestvina–Handel algorithm is computationally intractable for large braid words, and matrix methods give only lower bounds, which are often poor for large braids. Our method is computationally fast and gives exponential convergence towards the exact entropy. As an illustration we apply our approach to the braiding of both periodic and aperiodic trajectories in the sine flow.

In search of minimal random braid configurations

A geometric braid consists of n curves stretching between two parallel planes. A group structure may be defined on a geometric braid yielding an algebraic braid. Braids provide information on the structure of knots and links, and have many practical applications, for example in fluid mechanics and astrophysics. A well-known problem in braid theory consists of finding minimal crossing number braids. No efficient algorithm which solves this problem using group theory seems to be possible for n>3. Here we investigate several different approaches to obtaining minimal configurations: we employ three different relaxation techniques and compare them with each other and with an algebraic heuristic algorithm, in terms of minimization (of energy and crossing number) and time efficiency. By energy we mean total string length of the braid. It is found that more than half of the crossings of a sufficiently large braid (in terms of crossing number and number of strings) are redundant. We analyse the different methods and say in what circumstances which method is to be favoured and conclude that minimum braid energy and minimum braid crossing number are substantially different measures of topological complexity for braids.

Topological defects in the Abrikosov lattice of vortices in type-II superconductors.

The free energy costs for various defects within an Abrikosov lattice of vortices are calculated using the lowest Landau level approximation (LLL). Defect solutions with boundary conditions for lines to meet at a point (crossing defect) and for lines to twist around each other (braid defect) are sought for 2, 3, 6, and 12 lines. Many results have been unexpected, including the nonexistence of a stable two- or three-line braid. This, and the high energy cost found for a six-line braid lead us to propose that the equilibrium vortex state is not entangled below the irreversibility line of the high-$T_c$ superconductors or in a large part of the vortex-liquid phase above this line. Also, the solution for an infinite straight screw dislocation is found, and used to give a limiting form for the free energy cost of very large braids. This depends on the area enclosed by the braid as well as its perimeter length.

Facies relationships in Pleistocene outwash gravels, southern Ontario: a model for bar growth in braided rivers

ABSTRACTFacies relationships in Pleistocene braided outwash deposits in southern Ontario demonstrate the presence of a large braid bar with adjacent side channel. The core of the bar is up to 6 m high, and consists of crudely horizontally stratified gravels. Downstream from the core is the bar front facies, consisting of large gravelly foresets up to 4 m high, rounded off in many places by reactivation surfaces. Upstream from the core is the bar stoss side facies consisting of several sets (individually up to 35 cm thick) of tabular cross‐bedding, arranged in coarsening‐upward sequences. The stoss side—core—bar front relationships are continuously exposed in one 400 m long quarry face which is cut almost parallel to the palaeoflow direction. A transverse quarry face shows the side channel facies, which consists of trough cross‐bedded sands. Gravel layers can be seen to finger from the main gravelly bar into the sandy side channel, but they do not reach the base of the channel. This surprising relationship indicates that gravel moved only in the topographically higher parts of the system. After deposition in the side channel, and growth upstream and downstream from the bar core, the entire system aggraded. Crudely horizontally stratified, and imbricated gravel sheets were laid down as a bar top facies.Grain size analyses indicate strongly bimodal distributions, implying that much of the sand in the spaces between pebbles and boulders filtered in after the gravel had been deposited. This interpretation is strengthened by velocity calculations—mean velocities in excess of 300 cm/s would be needed to roll the gravel as bed load, but at such a velocity, a large amount of sand would be transported entirely in suspension.In a final section of the paper, our results are combined with other work on braided systems in an attempt to formulate a more general facies model.