Topological mechanics of knots and tangles
Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly under...
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| Published in | Science (American Association for the Advancement of Science) Vol. 367; no. 6473; pp. 71 - 75 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
The American Association for the Advancement of Science
03.01.2020
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| Subjects | |
| Online Access | Get full text |
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| Abstract | Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements. |
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| AbstractList | Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements. It's knot what you know Why is it that some knots seem to hold tight while others readily slip apart? Patil et al. develop a theoretical analysis of the stability of knots and find links between topological parameters (twist charge, crossing numbers, handedness) and mechanical stability. The theory is confirmed using simulations and experiments on color-changing fibers that optically show localized stress differences in different parts of the knot as the two strands are pulled apart. The authors show why some common knots slip easily and untie, whereas others hold tight. Science , this issue p. 71 Simple counting rules predict the relative mechanical stability of knots and tangles. Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements. It's knot what you knowWhy is it that some knots seem to hold tight while others readily slip apart? Patil et al. develop a theoretical analysis of the stability of knots and find links between topological parameters (twist charge, crossing numbers, handedness) and mechanical stability. The theory is confirmed using simulations and experiments on color-changing fibers that optically show localized stress differences in different parts of the knot as the two strands are pulled apart. The authors show why some common knots slip easily and untie, whereas others hold tight.Science, this issue p. 71Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements. |
| Author | Dunkel, Jörn Patil, Vishal P Kolle, Mathias Sandt, Joseph D |
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| Cites_doi | 10.1090/S0002-9947-1990-0958895-7 10.1080/14786446708639836 10.1126/science.aam6897 10.1126/science.1205705 10.1088/1367-2630/17/5/053009 10.1002/adma.201203529 10.1371/journal.pcbi.0020122 10.1073/pnas.1713841115 10.1090/conm/304 10.1038/nphys2560 10.1016/0032-3861(81)90284-6 10.1103/PhysRevLett.33.1139 10.1103/PhysRevLett.115.118302 10.1145/1360612.1360662 10.1103/PhysRevLett.120.158001 10.3390/polym9090444 10.1103/PhysRevLett.99.164301 10.1002/adhm.201800293 10.1137/0147080 10.1142/2940 10.1371/journal.pcbi.0020045 10.1103/PhysRevLett.120.188003 10.1038/nphys3679 10.1007/s100510050145 10.1119/1.10652 10.1142/9789812796189_0006 10.1038/s41598-017-12172-2 10.1006/aama.1996.0511 |
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| Snippet | Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and... It's knot what you know Why is it that some knots seem to hold tight while others readily slip apart? Patil et al. develop a theoretical analysis of the... It's knot what you knowWhy is it that some knots seem to hold tight while others readily slip apart? Patil et al. develop a theoretical analysis of the... |
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| SubjectTerms | Bends Color Deoxyribonucleic acid DNA Experiments Ferromagnetism Fibers Handedness Knots Mechanics (physics) Optical fibers Plasmas (physics) Sailing Simulation Slip Stability analysis Surgery Theoretical analysis Topology |
| Title | Topological mechanics of knots and tangles |
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