A Topological Study of Textile Structures. Part II: Topological Invariants in Application to Textile Structures

Grishanov, S. A.; Meshkov, Vadim R.; Omelchenko, Alexander

doi:10.1177/0040517508096221

Cited by 24 publications

(32 citation statements)

References 5 publications

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“…The main problem that Grishanov et al attack with topological methods is the classification of textile structures, i.e., deciding whether two given structures are equivalent [13]. Applying knot theory allows them to re-use results for determining knot equivalence.…”

Section: Discussionmentioning

confidence: 99%

“…In summary, this leaves us with inefficient algorithms of knot equivalence and a comprehensive overview by Grishanov et al of invariants that can be used to classify doubly-periodic textile structures [13]. However, it is not clear how these techniques can be used for textile pattern retrieval, as no similarity measures between textile structures or invariants are defined.…”

Section: Discussionmentioning

confidence: 99%

“…Additionally, due to the huge diversity of textile structures, it is impractical to come up with a complete natural language classification of every possible structure. Consequently, there have been • • • ⊂ several attempts to define textile structures in a formal and mathematical way [12,13].…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

A Similarity Measure for Weaving Patterns in Textiles

Helmer

Ngo

2015

Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval

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We propose a novel approach for measuring the similarity between weaving patterns that can provide similarity-based search functionality for textile archives. We represent textile structures using hypergraphs and extract multisets of k-neighborhoods from these graphs. The resulting multisets are then compared using Jaccard coefficients, Hamming distances, and cosine measures. We evaluate the different variants of our similarity measure experimentally, showing that it can be implemented efficiently and illustrating its quality using it to cluster and query a data set containing more than a thousand textile samples.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

A Similarity Measure for Weaving Patterns in Textiles

Helmer

Ngo

2015

Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval

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“…The topological rules correct errors without ambiguity. Topological algebras appeared in textile science a quarter of a century ago and recently became a key part of generating textile models (94,(102)(103)(104)(105). Correcting ordering errors during virtual-specimen generation by invoking formally tabulated topological ordering rules leads to very robust methods that can deal with arbitrary errors.…”

Section: Solid Tow Representationsmentioning

confidence: 99%

Stochastic Virtual Tests for High-Temperature Ceramic Matrix Composites

Cox

Bale

Begley

et al. 2014

Annu. Rev. Mater. Res.

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We review the development of virtual tests for high-temperature ceramic matrix composites with textile reinforcement. Success hinges on understanding the relationship between the microstructure of continuous-fiber composites, including its stochastic variability, and the evolution of damage events leading to failure. The virtual tests combine advanced experiments and theories to address physical, mathematical, and engineering aspects of material definition and failure prediction. Key new experiments include surface image correlation methods and synchrotron-based, micrometer-resolution 3D imaging, both executed at temperatures exceeding 1,500• C. Computational methods include new probabilistic algorithms for generating stochastic virtual specimens, as well as a new augmented finite element method that deals efficiently with arbitrary systems of crack initiation, bifurcation, and coalescence in heterogeneous materials. Conceptual advances include the use of topology to characterize stochastic microstructures. We discuss the challenge of predicting the probability of an extreme failure event in a computationally tractable manner while retaining the necessary physical detail. 17.1

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“…Topological rules correct such errors without ambiguity, since they embody the essential patterning that defines any single textile architecture. Topological algebras have a long history in textile science and have recently become a key part of generating textile models (Miyazaki et al, 1995;Grishanov et al, 2009aGrishanov et al, , 2009bXiao and Geng, 2010;Lomov et al, 2011).…”

mentioning

confidence: 99%