Knots are used widely in our

every day life. All the way from

rock-climbing to sailing to

surgery. And empirically over

the many centuries of us tying

knots we have learned how to

relate how some knots are better

than others for specific

applications. But what we lack

is a predictive understanding,

so models that are able to

relate a particular knot

configuration with its

mechanical response, which is

what our study is able to

provide. When you tie your

shoelaces if you do a left-handed

knot followed by another left-

handed knot the result is not

as secure than if you do a left-

handed (knot) followed by a

right-handed knot. Now, the

question is: Why? To address

this question we started with

the simplest possible knot,

which is called the treffle knot

which looks like this, and

change the topology by adding

subsequent turns to the knot.

And then we asked, how much

force does it take to pull the

knot shut? And I can keep

increasing the number of turns

and so as we increase the

number of turns what we are

doing is we are increasing the

force that it takes to close the

knot; that is essentially making

the knot more secure. And we

show that by varying the number

of turns from one to ten, say,

we can increase the pulling

force by a factor of a thousand.

So we can divide this problem

into two parts. We have to be

able to deal with what's

happening in this braid, and

what is happening in this loop.

And the braid is particularly

difficult because we have to

deal with the bending energies

of the rope, the tension, as

well as the friction that comes

from the fact that we have

self-contact in between the rod.

And putting all of this together

into a predictive framework was

the challenge. So in our

experiments we didn't actually

use standard rope we used

nitinol rods and we tied our

treffle knots, changed the

topology by increasing the

number of turns and at some

point the pulling force becomes

so high that I can't actually

close the knot. Because we can

so dramatically change the force

that it takes to slip this knot

we might be able to control

how heavy an object we might be

able to sustain by changing the

topology.

Of course to start somewhere

we had to start with a very

simple example first but what

I believe we have done is set

up the foundations from which

more complex knots configurations

can be studied.