Wednesday, September 12, 2007


The picture below shows point defects in a film of liquid cristals; the color depends on the thickness of the sample. Note how they come in pairs, the one defect in red and yellow, the other one less colorful in the green-ish.

[Picture Credits: Oleg Lavrentovich from the Liquid Crystal Institute at Kent State University, for more pictures see here. Click to enlarge.]

A liquid crystal like the one pictured above is an anisotropic fluid formed by rod-like or disk-like molecules, typically some nanometers in length, that tend to be parallel to a common direction, similar to the ones used in an LCD screen. The properties of these crystals depend on the temperature, the above one is in the nematic phase, where the molecules have no positional order, but they have long-range orientational order. That is, though the molecules positions are randomly distributed as in a liquid, they all point in the same direction within each domain. This ordering is not perfect on sup domain scales. For more information on the arising defects, see e.g.

and if somebody can tell me why this paper belongs in a 'Philosophical Magazine' (Vol. 86, Nos. 25–26, 1–11 September 2006, 4117–4137), I'd really want to know. Oh well, I can give you my philosophy: defects are interesting, and beauty is not just in simplicity.



  1. Bee - is not just in simplicity...

    Bacon - there is no thing of excellent beauty that hath not some strangeness in the proportion

  2. "...if somebody can tell me why this paper belongs in a 'Philosophical Magazine'..."

    I am not an official scholar, but it seems to me that at one time all of "Natural History" (by which I think they meant "Natural Science" in today's parlance) was dealt=with by Philosophers. See for example "Philosopher's stone" (and yes, I know we don't recognize alchemy as a "science" anymore).

  3. Dear Bee,

    ha, great picture, and great physics! I was lured into theoretical physics by the fascination of topological defects in condensed matter, which was the main interest of my diploma thesis advisor. It's such a beautiful application of deep mathematical concepts...

    By the way - wikipedia knows it all: the Philosophical Magazine, as Larry already has mentioned, originally dealt with "Natural Philosophy". It dates back to 1798, a period when ‘natural philosophy’ embraced all aspects of science: physics, chemistry, astronomy, medicine, botany, biology and geology.

    By some reason, its main topic today is condensed matter physics, so the title sounds odd indeed. I remember also some astonishment when I spotted the journal in the library of the Saarbrücken physics department for the first time.

    Best, stefan

  4. Hi CIP:

    Thanks for that quotation!

    Hi Larry, Stefan

    Thanks for the info. Sounds good to me, why have I never heard of that journal before?

    The picture above I first saw on the APS calender 2007, when I looked up what it shows etc. It was more or less a coincidence that it came into my mind yesterday. Ah forgot, I don't believe in coincidence ;-)



  5. Lovely! There's a similar photo on the cover of Chaikin and Lubinski's textbook. At least on my copy; apparently it's been replaced by a generic paperback edition.

    My favorite bit is how the sum of the defect charges on a closed surface is fixed by the topological genus. On a sphere you always have to have defects!

  6. Hi Bee,

    Thanks for the pretty picture and link to the paper by Kleman and Lavrentovich! Of course those topological defects are a type of singularity. (Where the the light waves have no well-defined phase.) Do they remind you of particles, with their pair creation?

    Sir Michael Berry has done some beautiful work on optical singularities. See this paper by Berry and Dennis, which has some nice images. Also this historical piece. His collected work includes applications to quantum optics.

    More pretty pictures here.

    Cheers, Kris

  7. Hi Rillian,

    There's a similar photo on the cover of Chaikin and Lubinski's textbook.

    Exactly - and that's a great textbook. It's really a pity if they have changed the cover...

    Hi Kris,

    Do they remind you of particles, with their pair creation?

    Maybe you are alluding to this - but if you think about one of the simplest classes of topological defects, vortices in a two-dimensional system with just an angle descrining the rotation of, say, a magnetic moment within the plane, there is an exact mapping of the vortices (and antivortices, as defined by the winding number) to two-dimensional Coulomb charges.

    These charges can indeed be created and annihilated in pairs, and they can form bound neutral "atoms", or charge-anticharge states. As a function of increasing temperature, these bound states can ionise and become unbound, thus triggering what is called the Berezinsky-Kosterlitz-Thouless transition

    Best, stefan

  8. Thanks Stefan! I did have something like that in mind. I think similar phenomena might provide a good model of elementary particles.


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