Bistability Phenomena In Granular Materials

This thesis reviews the recent advances in the field of granular matter, focusing on the bistability in granular systems, mainly from the angle of nonlinear dynamics and non-equilibrium phase change. Anita et al used two coupled variables to set up dynamic model, which we find this model have a few of flaws, couldn't describe the bistability in granular systems, whose potential curve is a parabola, only one stability state. When we considering on the random fluctuations, we could according to the generalized langevin equation to set up nonlinear dynamical model, using computer imitate the potential curve of potential function verse the angel of sand-pile, we find this model exactly exist bistability state. We find the problem that sand-pile have self-organized critical (SOC) nature don't perfect on theories, BTW think sand-pile only have one angle of repose, that is the only one critical point in phase change, which belonging to the second order phase change, but our model proving that the angle of repose have a certain region, belonging to the first order phase change. Only the sand-pile is small enough that we couldn't distinguish the angle of θ_r and θ_m which is the effect of finite size, in this case, sand-pile happen second order phase change. Using computer to imitate this model, the angle of repose θ_r and the maximum angle (moving angle) θ_m are agree with the result of experimental perfectly.Our innovation in this model: on the basis of analysis and modify others model, according to generalized langevin equation to set up a dynamical model which describe the bistability phenomenon in granular systems. And imitate this model, the result is agree with the experimental result perfectly.In fact, many natural phenomenon and disasters, such as mud-rock flow, snow-slide, mountain-slid, earthquake and so on, all of them have a close relation to the bistability nature of granular material. So use our model to study the bistability behavior in granular system have an important meaning both on theory and practical applying.