Physicists often describe nature in two opposing ways, which I characterize as particle and continuum approaches. In the particle approach, we try to understand the properties and dynamics of isolated objects and their interactions. In the continuum approach, on the other hand, we ignore discreteness, use conservation principles to formulate continuum equations, and then solve or simulate those equations to explain complex phenomena.
Here, I illustrate those contrasting methods by describing phenomena that occur in the physics of granular materials and particles immersed in fluids. These phenomena have a host of applications in engineering, geophysics, and astrophysics, and are of considerable intrinsic interest. Although the complementarity of particle and continuum or field approaches also has a long history in our understanding of physics on subatomic scales, it will be interesting to see how that issue plays out in a macroscopic, yet still controversial, context.
In fluid dynamics, a continuum description...
