Friday, March 16, 2012


Thanks to JAHC we have some first simulations in a smoothed-particle hydrodynamics (SPH) bath, that seems to indicate that the 8 spins around and that there is a lift-off. These tests are very delicate and small changes can make a lot of difference, as you can see in the 3th and 4th clip below of the a thinner figure 8 knot, which only spins around without moving upwards. Note: the driving force is the spiraled profile that spins round the knotted string at a constant speed.

In this simulation the SPH particles are set to transparent,
so the behavior of the 8 knot's is clearly visible.

This is a cross-section view of the SPH particle bath to visualize the motion within the fluid. The four 180° arches that make up the 8 are given 4 colors: blue, green, magenta and red to visualize how the object crawls round through the medium.  

A slightly thinner 8 knot:

A cross-section view of the thinner 8-knot, that shows a balanced rotation of the 8-knot.

The thinner 8-knot only spins around but does not lift-off.

The basic idea of how the 8 whould spiral upwards like a helicopter:

Extra: A Free moving Torus with spiraled profile

This more refined simulation shows nicely how the torus with spiraled profile, moves forward at an even velocity through the medium, while it spins round. Look at how the 4 colors: red, green, blue and magenta (90° parts of the circle) change periodically, as one quarter fades into the cross-section view, while the other fades out.