A STRUCTURAL ANALYSIS OF THREE-DIMENSIONAL BRAIDS

This paper describes a study of three-dimensional braids produced by a four-step 1 × 1 method. An analytical approach is employed in conjunction with experimental investigations to establish the relationship between the braid structure and braiding parameters. Based on microscopic observations, we divide a three-dimensional braid structure into three representative regions, i.e., the interior, surface and corner, and treat the three regions, respectively. Three types of microstructural unit-cell models are then established. The surface characteristics and the relationship between the interior and surface unit-cells have been derived. Good agreement has been obtained between the calculated and measured values of fiber volume fraction of the braided composite samples.

In Vitro Degradation of Polyglycolide/Chitosan Hybrid Braids

Hybrid braids of polyglycolide （PGA） and chitosan were prepared by the three-yarn braiding method from PGA and chitosan fiber bundles. These braids were in vitro degraded by incubating them in phosphate buffered saline （ PBS ） at pH 7.4 and 37℃ for 5 weeks. Results suggested that PGA/chitosan hybrid braids degraded significantly. Scanning electron micrographs showed that chitosan fibers in the PGA/chitosan hybrid braid with about 75% PGA in weight （ PGA75/chitosan ）were shaped into gel-like after 5 weeks, but those in the hybrid braid with about 25% PGA in weight（PGA25/chitosan） did not change. After 5 weeks, the ultimate tensile loads of PGA and PGA75/chitosan braids lost almost completely, but those of chitosan and PGA25/chitosan braids remained around 14 N. The PGA/chitosan hybrid braids with higher initial ultimate tensile load would have potential applications in tendon/ligament tissue reconstruction.

A Theory of Orbit Braids

In this paper,the authors systematically discuss orbit braids in M×I with regards to orbit configuration space FG(M,n),where M is a connected topological manifold of dimension at least 2 with an effective action of a finite group G.These orbit braids form a group,named orbit braid group,which enriches the theory of ordinary braids.The authors analyze the substantial relations among various braid groups associated to those configuration spaces FG(M,n),F(M/G,n)and F(M,n).They also consider the presentations of orbit braid groups in terms of orbit braids as generators by choosing M=C with typical actions of Zpand(Z_(2))^(2).

Virtual Braids,Virtual Temperley-Lieb Algebra and f-Polynomial

The authors study the properties of virtual Temperley-Lieb algebra and show how the f-polynomial of virtual knot can be derived from a representation of the virtual braid group into the virtual Temperley-Lieb algebra, which is an approach similar to Jones' s original construction.

近三十年沿海发达地区防洪功能变迁研究 ——以粤港澳大湾区为例

沿海发达地区作为中国城镇化进程最为迅猛、经济活力最为旺盛的地区,人口密集、地势低平,其防洪功能的重要性日益凸显。然而,目前对于该区域的防洪功能研究尚显不足,多采用传统的研究方法和服务功能评估,较少结合该区域的生态系统特点以及具备空间可视化优势的防洪功能模型进行深入探讨。鉴于此,文章以高度发达的粤港澳大湾区为例,采用Nature Braid模型,系统评估1990—2020年间的区域防洪功能变迁,并进一步探讨了其供需匹配的现状。研究结果显示,在1990—2020年间,粤港澳大湾区的防洪功能在空间分布上呈现出“四周高、中部低”的特点,而在时间变化上则整体呈现下降趋势。2020年,防洪功能的供需匹配特征总体上表现为空间错位,供需不平衡问题较为突出。因此,在未来的土地利用规划中,为实现区域生态、环境与经济社会的可持续发展,粤港澳大湾区需要加强对现有生态空间的保护,并合理调整土地利用结构。

A forcing relation of braids from Nielsen fixed point theory

In this paper, we focus our attention on the connections between the braid group and Nielsen fixed point theory. A new forcing relation between braids is introduced, and we show that it can be fulfilled by using Nielsen fixed point theory.

Braids with Trivial Simple Centralizer

In this paper, we prove that the n-simple braid divisible by the generators xi for all 2 ≤ i ≤n - 2 has trivial simple centralizer. Consequently, the commuting graph defined on the set of simple braids is disconnected. We also prove that the graph has one major component.

Crossing-changeable braids from chromatic configuration spaces

Motivated by the work in Li et al.(2019),this paper deals with the theory of the braids from chromatic configuration spaces.These kinds of braids possess the property that some strings of each braid may intersect together and can also be untangled,so they are quite different from the ordinary braids in the sense of Artin(1925).This enriches and extends the theory of ordinary braids.

Architectural Model of a Dryland Gravel Braided River,based on 3D UAV Oblique Photogrammetric Data:A Case Study of West Dalongkou River in Eastern Xinjiang,China

Three-dimensional unmanned aerial vehicle(UAV)oblique photogrammetric data were used to infer mountainous gravel braided river lithofacies,lithofacies associations and architectural elements.Hierarchical architecture and lithofacies associations with detailed lithofacies characterizations were comprehensively described to document the architectural model,architectural element scale and gravel particle scale.(1)Nine lithofacies(i.e.,Gmm,Gcm,Gcc,Gci,Gcl,Ss,Sm,Fsm and Fl)were identified and classified as gravel,sand and fine matrix deposits.These are typical depositional features of a mountainous dryland gravel-braided river.(2)Three architectural elements were identified,including channel(CH),gravel bar(GB)and overbank(OB).CH can be further divided into flow channel and abandoned channel,while GB consists of Central Gravel bar(CGB)and Margin Gravel bar(MGB).(3)The gravel bar is the key architectural element of the gravel braided river,with its geological attributes.The dimensions of GBs and their particles are various,but exhibit good relationships with each other.The grain size of GB decreases downstream,but the dimensions of GB do not.The bank erosion affects the GB dimensions,whereas channel incision and water flow velocity influence the grain size of GB.The conclusions can be applied to the dryland gravel braided river studies in tectonically active areas.

Using Digital Twin to Diagnose Faults in Braiding Machinery Based on IoT

The digital twin(DT)includes real-time data analytics based on the actual product or manufacturing processing parameters.Data from digital twins can predict asset maintenance requirements ahead of time.This saves money by decreasing operating expenses and asset downtime,which improves company efficiency.In this paper,a digital twin in braiding machinery based on IoT(DTBM-IoT)used to diagnose faults.When an imbalance fault occurs,the system gathers experimental data.After that,the information is sent into a digital win model of the rotor system to see whether it can quantify and locate imbalance for defect detection.It is possible to anticipate asset maintenance requirements with DT technology by IoT(Internet of Things)sensors,XR(X-Ray)capabilities,and AI-powered analytics.A DT model’s appropriate design and flexibility remain difficult because of the nonlinear dynamics and unpre-dictability inherent in the degrading process of equipment.The results indicate that the DT in braiding machinery developed allows for precise diagnostic and dynamic deterioration analysis.At least there is 37%growth in efficiency over conventional approaches.

An Overview of 3D Thin Shell Textile Preforms

The automobiles, aircraft, and lightweight industries continuously demand thin near-net-shape preforms just out-of-machine as close to the final shape. This study addresses the possibilities of 3D thin shell textile preform as the solution of lightweight reinforcement in various applications. Investigation into the development of 3D thin shells has led to different manufacturing processes. However, 3D thin shell preforms are mostly made by weaving and knitting, but nonwoven, winding, and/or layup techniques have been reported for over a decade. Owing to the complex thin shell manufacturing processes, they are not similar to the conventional methods. The different 3D thin shell preforms can extend the opportunities for new applications in various technical fields. This study presents existing research gaps and a few potential issues to be solved regarding 3D thin shell preforms in the near future.

Study on Geological Genesis and Sedimentary Model of Complex Low Resistivity Reservoir in Offshore Oilfield — A Case of NgIII Formation of X Oilfield in Bohai Sea

In order to study the micro genetic mechanism and main geological controlling factors of low resistivity reservoir in NgIII formation of X oilfield in Bohai sea in China, the clay mineral composition, irreducible water saturation, salinity and conductive minerals of low resistivity reservoir were studied by using the data of core, cast thin section and analysis, and compared with normal resistivity reservoir. At the same time, the control effect of sedimentary environment on low resistivity reservoir was discussed. The results show that the additional conductivity of high bound water content and high montmorillonite content in the reservoir together leads to the significant reduction of reservoir resistivity, which is the main microscopic cause of the formation of low resistance, and is mainly controlled by the sedimentary background such as paleoclimate and sedimentary cycle. During the deposition period of NgIII formation, the paleoclimate was dry and cold, and it was at the end of the water advance of the medium-term sedimentary cycle. The hydrodynamic force of the river channel was weak, the carrying capacity of the riverbed was weak, and the river channel swayed frequently, resulting in fine lithologic particle size, high shale content and complex pore structure of the reservoir, resulting in significant reduction of reservoir resistance. The research conclusion would have strong guiding significance for the development of low resistivity reservoirs in this area.

An Overview of 3D Thin Shell Textile Preforms

The automobiles, aircraft, and lightweight industries continuously demand thin near-net-shape preforms just out-of-machine as close to the final shape. This study addresses the possibilities of 3D thin shell textile preform as the solution of lightweight reinforcement in various applications. Investigation into the development of 3D thin shells has led to different manufacturing processes. However, 3D thin shell preforms are mostly made by weaving and knitting, but nonwoven, winding, and/or layup techniques have been reported for over a decade. Owing to the complex thin shell manufacturing processes, they are not similar to the conventional methods. The different 3D thin shell preforms can extend the opportunities for new applications in various technical fields. This study presents existing research gaps and a few potential issues to be solved regarding 3D thin shell preforms in the near future.

Predicting Financial Contagion and Crisis by Using Jones, Alexander Polynomial and Knot Theory

Topological methods are rapidly developing and are becoming more used in physics, biology and chemistry. One area of topology has showed its immense potential in explaining potential financial contagion and financial crisis in financial markets. The aforementioned method is knot theory. The movement of stock price has been marked and braids and knots have been noted. By analysing the knots and braids using Jones polynomial, it is tried to find if there exists an untrivial knot equal to unknot? After thorough analysis, possible financial contagion and financial crisis prediction are analysed by using instruments of knot theory pertaining in that sense to Jones, Laurent and Alexander polynomial. It is proved that it is possible to predict financial disruptions by observing possible knots in the graphs and finding appropriate polynomials. In order to analyse knot formation, the following approach is used: “Knot formation in three-dimensional space is considered and the equations about knot forming and its disentangling are considered”. After having defined the equations in three-dimensional space, the definition of Brownian bridge concerning formation of knots in three-dimensional space is defined. Using analogy method, the notion of Brownian bridge is translated into 2-dimensional space and the foundations for the application of knot theory in 2-dimensional space have been set up. At the same time, the aforementioned approach is innovative and it could be used in accordance with stochastic analysis and quantum finance.

EXPERIMENTAL STUDY ON OPTIC PERFORMANCES OF OPTIC FIBER BRAIDED IN CARBON FIBER BRAIDED COMPOSITES

D braiding technology has stimulated a great deal of interest in the world at large and been widely used in aerospace, military, civil construction and medical fields. Although 3 D braided composites have many good features, their features are very complicated. Optic fiber sensors can be multi braided into 3 D braided composites to fulfill a new kind of 3 D smart composites to monitor RTM process, study mechanical behaviors and damage states after molding, and monitor its own condition during service life. Since optic performances of optic fibers have direct and important relation to the performances of optic fiber sensors, experimental research is done to devise a method to incorporate the optic fiber into a 3 D structure. The optical performances of the braided optic fibers are tested and compared with the original one to study the optic performances of optic fibers, before their being braided into composites and after the RTM process.

Analysis of mechanical performance of braided esophageal stent structure and its wires

This paper aims to find the relationship between the structural parameters and the radial stiffness of the braided stent and to understand the stress distribution law of the wires. According to the equation of the space spiral curve, a three-dimensional parametrical geometrical model is constructed. The finite element model is built by using the beam-beam contact elements and 3D beam elements. The constituent nitinol wires are assumed to be linear elastic material. The finite element analysis figures out that the radial stiffness of the stent and the stress distribution of the wires are influenced by all the structural parameters. The helix pitch of the wires is the most important factor. Under the condition of the same load and other structural parameters remaining unchanged, when the number of wires is 24, the stress of the wire crosssection is at the minimum. A comparison between the vitro experimental results and the analytical results is conducted, and the data is consistent, which proves that the current finite element model can be used to appropriately predict the mechanical performance of the braided esophageal stents.

INCLINED LAMINAL COMBINATION MODEL OF 3D BRAIDED COMPOSITES

As an advanced composite material, the 3D braided composite has received more and more attention in foreign countries. However, it has received less attention in China. The geometric unit cell which can describe the basic structure and the relationship between the braiding angle and geometric parameters of the fabric and fiber volume ratio are given in this paper based on two 3D braiding processes, namely, the four-step and the twostep ones. Several existing mechanical models to predict groperties of the 3D braided comPOsites are discussed and their shortcomings are pointed out herein. Then a new model called the inclined laminal combination model is proposed, which is based on the classical laminated plate theory and can predict the basic mechanical behavior of the two 3D braided composites with four-step or two-step braid. In the model, each yarn in the unit cell is regarded as an inclined laminate and then a 3D analysis is performed. It is found that the predicted mechanical properties of the 3D braided composites by the proposed model are compared well with the experimental data.

关于Braided双代数的一些注记

本文首先讨论了余半单Ｈｏｐｆ代数的Ｂｒａｉｄｅｄ结构的有限性．其次，对于左Ｈ－模代数Ａ，通过构造新的代数结构Ａ＃σＨ，推广了Ｄｏｉ．Ｙ．在文献［２］中的部分结果．

Making the category of entwined modules into a braided monoidal category

The question of how the category of entwined modules can be made into a braided monoidal category is studied. First, the sufficient and necessary conditions making the category into a monoidal category are obtained by using the fact that if （A, C, ψ） is an entwining structure, then A × C can be made into an entwined module. The conditions are that the algebra and coalgebra in question are both bialgebras with some extra compatibility relations. Then given a monodial category of entwined modules, the braiding is constructed by means of a twisted convolution invertible map Q, and the conditions making the category form into a braided monoidal category are obtained similarly. Finally, the construction is applied to the category of Doi-Hopf modules and （α, β ）-Yetter-Drinfeld modules as examples.

Investigation on the Thermal Conductivity of 3-Dimensional and 4-Directional Braided Composites

It is vital to choose a factual and reasonable micro-structural model of braided composites for improving the calculating precision of thermal property of 3-D braided composites by finite element method （FEM）. On the basis of new microstructure model of braided composites proposed recently, the model of FEM calculation for thermal conductivity of 3-dimennsional and 4-directional braided composites is set up in this paper. The curves of coefficient of effective thermal conductivity versus fiber volume ratio and interior braiding angle are obtained. Furthermore, comparing the results of FEM with the available experimental data, the reasonability and veracity of calculation are confirmed at the same time.