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The square knot and the granny knot. 

The square knot and the granny knot. 

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Motivated by recent advances in single molecule manipulation techniques that enabled several groups to tie knots in individual polymer strands and to monitor their dynamics, we have used computer simulations to study "friction knots" joining a pair of polymer strands. The key property of a friction knot splicing two ropes is that it becomes jammed...

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Context 1
... experimental advances, this paper dis- cusses the dynamics of a friction knot formed by a pair of polymer molecules. Although mathematically knots are only well-defined in closed loops, 1 friction knots and other "physical knots" in open strings can be and have been stud- ied in various contexts. Friction knots, such as the square knot shown in Fig. 1, are commonly used by sailors and climbers to join a pair of ropes. Pulling at the ends of the ropes in Fig. 1 jams the knot so that the ropes remain con- nected regardless of the applied force. An elegant theory pro- posed in Ref. 9 shows that if the friction coefficient between the ropes exceeds a certain knot dependent critical ...
Context 2
... Although mathematically knots are only well-defined in closed loops, 1 friction knots and other "physical knots" in open strings can be and have been stud- ied in various contexts. Friction knots, such as the square knot shown in Fig. 1, are commonly used by sailors and climbers to join a pair of ropes. Pulling at the ends of the ropes in Fig. 1 jams the knot so that the ropes remain con- nected regardless of the applied force. An elegant theory pro- posed in Ref. 9 shows that if the friction coefficient between the ropes exceeds a certain knot dependent critical value, then the knot will hold no matter how hard one pulls on the ropes. This theory also explains why the ...
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... regardless of the applied force. An elegant theory pro- posed in Ref. 9 shows that if the friction coefficient between the ropes exceeds a certain knot dependent critical value, then the knot will hold no matter how hard one pulls on the ropes. This theory also explains why the modification of the square knot known as granny knot also shown in Fig. 1 is a poor way of splicing two ropes that fails at a low force. In view of Ref. 7, an analogous microscopic arrangement in- volving a pair of interwoven polymer strands that are being separated by a mechanical force can be devised experimen- tally. This type of scenario has also been suggested as a possible mechanism for slow relaxation ...
Context 4
... At the beginning of each simula- tion, the two strands are connected by the square or the granny knot positioned such that the contour length of the polymer chain between the knot and the end of each strand is the same. The first monomer of one strand and the last mono- mer of the other are subjected to forces F and −F, respec- tively cf. Fig. 1, and the knot is monitored as a function of time until the two strands become separated. To describe the knot's response to the pulling force, we measure the mean time before the knot disappears and monitor the distance R between the monomers at which the forces are applied. The observed trajectories Rt typically display an initial ...