Transitions in vertically oscillated granular media: molecular dynamics simulations
Kreft, Jennifer Katherine
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Transitions in equilibrium systems are somewhat well understood, however similar transitions in nonequilibrium systems such as oscillated grains have not been extensively studied. One example is sublimation: the transition of a solid into a gas. This transition is studied in a granular monolayer subjected to circular forcing. We find that the solid and fluid phases coexist during the transition and that, unlike in equilibrium systems, they have granular temperatures that differ by two orders of magnitude. Another transition studied was the emergence of surface wave patterns in granular layers. It has been found that in Rayleigh-Benard convection in a molecular fluid, thermal noise plays a significant role in the onset of patterns. The type of transition is noise induced first order. Similarly, it is found that noise in granular media also significantly alters the transition to a patterned state. The system was modeled using the Swift-Hohenberg equation and a noise strength much higher (1.2 × 10−2 for a pattern of wavelength 21 times the particle diameter) than an average molecular fluid (≈ 10−8 ) was needed to reproduce simulation results. The transition to the patterned state in the MD simulation was compared with that in a simulation based on continuum equations for granular media.62 It was found that the dispersion relation for the patterns in both simulations agreed well with experiment. However, since fluctuations were also not included in the continuum equations, the onset of patterns in the continuum simulation was markedly different from the MD simulations due to the absence of noise in the system. These continuum equations were based on the assumption that the velocity distribution function in grains is Gaussian. Theoretical predictions of the shape of this function as well as some experiments have indicated that the universal shape might be P(v) ∝ exp(−Bv 1.5 ). The velocity distribution function in a quasi-2D granular gas was measured in experiment and simulation. The shape of the curve for this geometry was found to be highly dependent on the frictional properties of the container and particles. The segregation of a granular layer based on size of the particles was also studied. We compared molecular dynamics simulations to experiments to investigate what of the proposed mechanisms are relevant in this system. In conclusion, the molecular dynamics simulations of oscillated granular media has shown that this nonequilibrium system exhibits many behaviors not found in corresponding equilibrium situations.