An intruder to a group of identical small beads enclosed in a rectangular plate will gradually migrate to either the center or one side of the plate when the plate is subjected to a horizontal vibration. By considering probabilities for a bead to move into and off the space between the intruder and the near side of the plate, we predict that the size ratio and the mass ratio of the intruder to small bead have equal but opposite effects in determining the direction of migration. The prediction is confirmed by a molecular dynamics simulation

The study focuses on the average energy of a monolayer of granular particles confined in a rectangular container. The container is shaken sinusoidally in a horizontal plane. The motion of every particle is recorded by a CCD camera so that the kinetic energy of the system can be analyzed by tracking the trajectory of each particle. It is found that the average energy changes abruptly at a certain critical filling fraction while the configuration of the particles makes a transition from a disordered to a solid-like state. We determine the critical value of the filling fraction and the energy of the solid-like state using a resonant condition

This study theoretically considers the motion of N identical inelastic particles between two oscillating walls. The particles' average energy increases abruptly at certain critical filling fractions, wherein the system changes into a solid-like phase with particles clustered in their compact form. Molecular dynamics simulations of the system show that the critical filling fraction is a decreasing function of vibration amplitude independent of vibration frequency, which is consistent with previous experimental results. This study considers the entire group of particles as a giant pseudo-particle with an effective size and an effective coefficient of restitution. The N-particles system is then analytically treated as a one-particle problem. The critical filling fraction's dependence on vibration amplitude can be explained as a necessary condition for a stable resonant solution. The fluctuation to the system's mean flow energy is also studied to show the relation between the granular temperature and the system phase

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Previous computer simulations of the Minority Game (MG)1 have shown that the average agent number in the winning group (i.e., the minority group) had a maximal value such that the global gain was also maximal when an optimal amount of information was available to all agents 2 . This property was further examined 8 3and its connection to financial markets has also been discussed 9 .Here