Friday, February 1, 2008

On the Torus

What is it ?
In layman’s terms the inner tube of a tire or if you prefer, a doughnut or a vadai. Technically, it is the surface of revolution of a circle about a coplanar axis outside itself (to put that in context, a sphere is a surface of revolution of a circle about one of its diameters, i.e., a coplanar axis through its center).

Why am I talking about it?
I always thought that a torus is a strange object, almost like a mobius strip or something. Mathematically it is a weird compact manifold. And so I imagined that a torus is as likely to occur in nature as a cube. But then, I found out today that certain dumbbell shaped surfactants self assemble into nanoscale tori [1]! Further digging and googling told me something I should have known, that people who make Carbon nanotubes have actually seen Carbon nanorings that form at the same time, that are essentially tori.

What does this mean?
So, the above facts tell us that self assembly can lead to tori. If it is easy to form and stays stable, then more likely than not, we will find it in nature. And indeed we do. They call it (rather unimaginatively) the torovirus.

Goes to show that one has to modify and augment one’s intuition with each new fact learnt!

[1] A Primer on self assembly of surfactants available here.


Anonymous said...

Interesting! I wonder what other self assembled shapes can be found in nature. Is it possible to predict various possible shapes based on some simple energy considerations?

CuriousCat said...

Well yes. Do you remember the earlier discussion about how cone shaped surfactants form spherical miscelles while cylinder shaped surfactants form lipid bilayers? This is determined by how to maximize the netropy of the polymer chain that forms the lypophillic tail of the surfactant molecule.

Same considerations will imply that a dumbbell shaped surfactant will form a cylinderical miscelle. And all the cyliner has to do is fold back on itself to form a torus!

It is kind of obvious after the fact is n't it? I was just surprised that it never occurred to me.

Anonymous said...

oh yes, that was easy!