## 29 May 2015

### Global cooling: is the paper really claiming it?

A recent paper in Nature finds a strong correlation between ocean circulation and oscillations in Atlantic surface temperatures which could be moving to a negative phase. According to the authors, "[t]his may offer a brief respite from the persistent rise of global temperatures."

This claim has been taken up by various sites, along a much stronger prediction: decades of global cooling by up to 0.5°C. However, I cannot find this second item anywhere in the original paper. Where does it come from?!

## 25 May 2015

### The structure factor of a liquid - part IV

#### Sum rule for impenetrable systems

The hard sphere liquid is an idealized model, but some of its properties hold for a very large class of systems, those that have an impenetrable core of size $$R_c$$ ($$g(r< 2 R_c = 0$$). Let us write the Fourier relation between $$g(r) -1$$ and $$S(q) -1$$ (the inverse of Eq. (4) in post II):

### The structure factor of a liquid - part III

This is the third part in a series. In part I and part II we defined the basic concepts used in the theory of liquids, in particular the radial distribution function $$g(r)$$ and the structure factor $$S(q)$$.

The simplest system one can imagine is the ideal gas. There is no interaction between particles: $$u(r) = 0$$, leading to $$g(r) = 1$$ (the particle at the origin does not affect the position of its neighbors) and $$S(q) = 1$$. The ideal gas is a trivial case, but it can be seen as the reference state for other systems. In particular, one could say that the functions $$g(r) - 1$$ and $$S(q) - 1$$ that appear in Equation (4) of part II quantify the difference with respect to the ideal gas (due to the interaction potential $$u(r) \neq 0$$.)

## 23 May 2015

### Nîmes

 The Maison Carrée reflected by the façade of the Carré d'Art.

## 16 May 2015

### The structure factor of a liquid - part II

[Continuing the preliminary discussion started in part I.]
We are now interested in an explicit form for $$g(\mathbf{r})$$ (we return here to the general case —where $$g$$ depends on the full vector $$\mathbf{r}$$, and not only on its modulus— simply to avoid the radial integrals). Taking particle 0 as fixed in $$\mathbf{r}_0$$, $$\rho g(\mathbf{r}) {\text{d}}^D \mathbf{r} = \text{d} n (\mathbf{r} - \mathbf{r}_0)$$ is the number of particles (among the remaining $$N-1$$) found in the volume $${\text{d}}^D \mathbf{r}$$ positioned at $$\mathbf{r}$$ with respect to the reference particle. One can formally count these particles by writing:

### The structure factor of a liquid - part I

This post only summarizes some basic concepts and results that will help understand the discussion in the following posts. For a detailed introduction to liquid theory, see one of the many books and review papers [1].