There has been quite an amount of work done using simulation techniques to attempt to describe the critical phenomenon of the dipolar hard sphere model. But a critical liquid gas transition has remained elusive.

Granular materials have been shown to closely mimic the behavior of ideal classical particles when externally driven. We have chosen a granular fluid as our model system to study the dipolar hard sphere model. In order to do this we first have to has a grasp on the statistical mechanics involved in driven granular materials. Velocity measurements have been preformed on collections of very precise macroscopic particles. The distribution of the velocities for these particles does in fact deviate from the Maxwell-Boltzmann form. Although, in the very low density limit the distribution is very close to a Gaussian. This allows us to define a kinetic temperature as the width, or second moment, of the velocity distribution function. Knowing that there exists a well defined kinetic temperature, we can utilize granular materials to study the behavior of ideal thermal systems.

This is a cartoon of two dipolar hard spheres. The colors represent the poles of each particle, for example if these particles were magnetic the colors would represent (N-S)(N-S). This is the lowest energy configuration for two dipolar spheres. As you add particles to this chain eventually the energy loss due to bending is compensated by the energy gained due to joining the ends. The critical number for this is 4 dipoles. This is quite remarkable, since it says that energetically it is better to form rings than chains. This does not take into account the entropy.

Well, here it goes... We utilize an apparatus that looks something like the picture below. We put our magnetic particles inside of the dish on top, and briskly shake the dish up and down (in a very precise way). This gives the particles some energy. Due to the fact that there are minor imperfections in the particles and the plate, the particles can pick up some tangential kicks from each other and the bottom surface. These tangential kicks allow the particles move around and not just bounce up and down. Then we use a CCD camera to visualize the particles, as shown in the picture. Now you have an idea how we do thing and sort-of an idea of why we do them, so lets see what we get after we do it.

In a nutshell, what we find are clusters and patterns that spontaneously form. The look of these clusters is determined by two important parameters. The images to the right are a few snapshots of the types of structures that form. First the number of particles in the system, or more specifically the density; (the number of particles contained in a particular space). Second, and somewhat obvious, the Granular Temperature (T), or like we said above, the width of the distribution of velocities. This last parameter is somewhat of a subtle point. I will explain more below.

The picture to the left is known as the Phase Diagram, it serves as road map for the parameters discussed above. On the vertical axis is the Temperature (T) of the system and on the horizontal is the number of particles, or the density since the volume is fixed. What this means is that if you pick a particular density say 0.05 and a particular temperature, say 40.0 you would find that the system is acting like a gas. That means that all of the particles are moving about quite wildly and there is no "clumpyness". But, if for example you moved down in temperature across the line labeled Ts you would start to find that that gas had changed a bit and has now become a combination of clumps of particles and individual particles that are shaking about.