24 January 2014

Lucretius and the depletion interaction

In book 6 of On the Nature of Things, Lucretius explains why magnet attracts iron; the picture he draws is very similar to what we now call depletion interaction (due to smaller particles being removed from the gap between larger ones):

First, stream there must from off the lode-stone seeds
Innumerable, a very tide, which smites
By blows that air asunder lying betwixt
The stone and iron. And when is emptied out
This space, and a large place between the two
Is made a void, forthwith the primal germs
Of iron, headlong slipping, fall conjoined
Into the vacuum, and the ring itself
By reason thereof doth follow after and go
Thuswise with all its body. 
(translated by William Ellery Leonard)

Although this theory did not age very well, there is one particular type of electromagnetic interaction (the Casimir force) that resembles it, being essentially photon depletion.

23 January 2014

Interpretations of the classical electron radius

The classical electron radius:\begin{equation}
r_{\text{e}} = \frac{1}{4 \pi \epsilon _0}\frac{e^2}{m c^2} \simeq 2.82 \, \text{fm}
is usually defined in terms of the electrostatic energy of a charged sphere. The sphere radius is chosen such that, when the total charge equals the elementary one, the energy equals the rest mass of the electron (up to a numerical prefactor).

14 January 2014

Saint-Venant's principle and its relatives - part 1

This venerable principle (published in 1855) and a whole family of analogous results can be explained in a very simple, almost geometrical, manner based on the observation that "the Laplacian is a zero-sum game". Within this class of results (with applications ranging from optical microscopes to the metallic mesh on the door of microwave ovens). Saint-Venant's principle is probably the only one to have an official name, but not the easiest to understand, so we will begin by a simple example from electrostatics.

9 January 2014

No more access to the APS journals in France

Many (most ?) universities and research institutes in France get access to scientific journals through the Couperin consortium. This year, the consortium failed to reach an agreement1 with the American Physical Society (publisher of the Physical Review) who increased their 2014 prices by 7.6% with respect to 20132. As a result, our subscription to the Physical Review will stop as of January 1st 2014.

UPDATE 09/01/2014: For the moment, we do have access to the 2014 papers. Couperin will pursue the negotiations until the end of February.

1. Letter from the APS to the Couperin consortium.
2. Letter from the APS to French researchers. The 7.6% is the overall price increase requested from the consortium. For the Paris-Sud University, for instance, the increase would be 28%.

1 January 2014

Power-law distribution of war magnitudes

While reading Steven Pinker's The better angels of our nature I stumbled upon the following argument for the magnitude of war (number of casualties) following a power-law distribution (page 220):

Recall the mathematical law that a variable will fall into a power-law distribution if it is an exponential function of a second variable that is distributed exponentially. My own guess is that the combination of escalation and attrition is the best explanation for the power-law distribution of war magnitudes.