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Cristian Micheletti
SISSA
Via Beirut 2A
I-34014 Trieste
ITALY

FAX: +39 040 3787528
e-mail: michelet@sissa.it

Optimal packing of a uniform tube.

The helix in the decoration of my Home page corresponds to the optimally-packed arrangement of a tube with uniform cross-section. More precisely, the helical shape allows to pack a tube so that each tube portion (of given arclength) is as tightly packed as possible. You can find a detailed account of this result in Nature 406, p. 287-290 (2000). This special helix has a pitch to radius ratio equal to 2.512...

The following intuitive argument can explain why this particular helical aspect ratio is the best one for packing. When the pitch (distance of successive turns) is small compared to the helix radius, there is unused space along the helix axis, as in Fig. (a). In the opposite regime, when the pitch is large compared to the radius there is unused space between the helix turns (see Fig. c). Only the helix with the pitch to radius ratio equal to 2.512... makes the most efficient use of space both along the helix axis and between helix turns (see Fig. b).

(a)__ (b)__ (c)__

GIF MOVIE. Watch the GIF animation (800 Kbytes) where the helical packing changes as the pitch to radius ratio is modified (courtesy of Piotr Pieranski).

Additional related material is avaliable from Piotr Pieranski homepage.

An amazing fact, is that helices commonly found in proteins (see figure below) have precisely this "magic" aspect ratio.


The backbone of helical motifs found in proteins has the same aspect ratio of the optimal helix of Fig. b!

Optimal UNpacking.

So far we have seen examples of optimal packing.
What about optimal unpacking?
Well... my daughter seems to have a lot to teach about it!

(2001)

Last updated Mon Dec 17 10:58:37 GMT+1 2001