RESUMO
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.
RESUMO
Medical textiles are widely used to exert pressure on human tissues during treatment of post-surgical hematoma, burn-related wounds, chronic venous ulceration, and other maladies. However, the inability to dynamically sense and adjust the applied pressure often leads to suboptimal pressure application, prolonging treatment or resulting in poor patient outcomes. Here, a simple strategy for measuring sub-bandage pressure by integrating stretchable optomechanical fibers into elastic bandages is demonstrated. Specifically, these fibers possess an elastomeric photonic multilayer cladding that surrounds an extruded stretchable core filament. They can sustain repetitive strains of over 100%, and respond to deformation with a predictable and reversible color variation. Integrated into elastic textiles, which apply pressure as a function of their strain, these fibers can provide instantaneous and localized pressure feedback. These colorimetric fiber sensors are well suited for medical textiles, athletic apparel, and other smart wearable technologies, especially when repetitive, large deformations are required.