29 January 2015

Zero-lens microscopy

Visible light is good for seeing details down to a fraction of a micron. Below this limit, one uses X-rays, with a wavelength of the order of one Ångström. The problem is that there are no high-quality lenses for X-rays, and so, instead of direct images, one has to settle for scattering or diffraction patterns, much more difficult to interpret (but sometimes more useful).

If the magnifying glass is a one-lens optical instrument and the microscope is (schematically) a two-lens device, then an X-ray scattering setup does zero-lens microscopy!

23 January 2015

Is modern science a by-product of Reformation?

There is a strong connection between Reformation and the birth of modern science, not only in time but also with respect to the number of notable Protestant scientists1. Several explanations were proposed:

20 January 2015

Dielectric sphere in a static field

I'll try to give the simplest solution I can think of to the classical problem of a dielectric sphere in a constant external field, see for instance  Landau & Lifshitz, vol. 8, chapter II, §8.

The sphere radius is \(R\) and its dielectric constant is \(\epsilon_i\), while that of the surrounding medium is \(\epsilon_e\). The electric field at infinity is along the \(z\) axis: \(\mathbf{E}_0 = E_0\, \hat{z}\). Considering the symmetry of the object we will work in spherical coordinates \((r,\theta,\phi)\). Before writing down any equations, let us note the following points:
  1. The system has rotational symmetry about the \(z\) axis. Thus, the field has no component along \(\hat{\phi}\).
  2. The problem is antisymmetric with respect to \(z\) (changing \(E_0\) to \(-E_0\) reverses the sign of the field everywhere).
  3. The field scales by \(E_0\) (doubling the applied field doubles the field at any point in the system).
  4. The only length parameter is the sphere radius \(R\).

18 January 2015

Missing the point on Charlie Hebdo

 A few days ago in the New York Times, David Brooks announced his position very clearly: I am not Charlie Hebdo. I'm responding to his Op-Ed because:
  • similar positions are quite common in the wake of the Paris attack, but at least here
  • the argument is reasoned, carefully presented and respectful of the victims and
  • it is published in a very respected, mainstream journal.
Still, I believe it manages to get the "I am Charlie" response completely wrong.

7 January 2015

Mr K

Yet another story about Khodorkovsky (a little more critical of the man and his past than the usual articles). We learn that he thinks about returning to Russia and that even the even the perspective of replacing Putin is not completely out of the question.

Khodorkovsky's fall does resemble something out of Kafka. All the elements are there: the oppressive state, the lack of a real crime, down to the hero's initial.
However, it also reminds me of an older story: Faust makes a pact with the devil, reaps the benefits, and then complains about the stench of brimstone.
The place does stink, and the publicity for a high-profile victim may be very effective in raising the international awareness, but I cannot bring myself to empathize with Mr K. Not because he is still alive and rich, but because for a long time he has been a part of the problem he now decries. In fact, the only reason he became a cause célèbre is his former belonging to an international elite, and the only reason of this elevated status was the favor of the regime.

Massacre in Paris. We are all Charlie !