Fig.1 shows the arrangement of particles in a snapshot of time for two dimensional simulations of a granular bed driven by a random force. The three images show systems with progressively larger densities of particles. The black particles represent particles which are moving with extreme velocity compared to the bulk. The fast particles are not spread out uniformly in the bed but clustered in localised regions.
In classical systems it is well known that gases in equilibrium can be described by the Maxwell-Boltzmann Equation. The statistical behaviour of the velocity of a gaseous particle is then described by Gaussian of Boltzmann’s distribution of velocities.
Dilute granular systems are often considered to be gaseous when the particles are very energetic or dilute. However the assumption that the velocities obey Boltmann’s Gaussian is not well established. In fact there is strong reported evidence that even for relatively small dissipation Boltzmann Statistics do not true.
Granular systems are examples of non-equilibrium systems; they constantly dissipate energy through collision and require an input of energy to remain in steady state (at constant kinetic energy).
This research project studies the statistical behaviour of one dimensional and two dimensional granular particles that are heated by a random white noise. The system exhibits strong spatial clustering which results in the granular temperature of the system deviating strongly from the homogeneous prediction.
Strongly dissipative systems can be reliably described as a set of isolated particles contained with in fixed width boxes. Such a model allows us to relate the velocity of the particle to space that is available for the particle to move.
