Bifurcation from stable holes to replicating holes in vibrated dense suspensions

Self-replicating segregation patterns in horizontally vibrated binary mixture of granules

Fluidized granular mixtures of various particle sizes exhibit intriguing patterns as different species segregate and condense. However, understanding the segregation dynamics is hindered by the inability to directly observe the time evolution of the internal structure. We discover self-replicating bands within a quasi-2D container subjected to horizontal agitation, resulting in steady surface waves. Through direct observation of surface flow and evolving internal structures, we reveal the crucial role of coupling among segregation, surface flow, and hysteresis in granular fluidity. We develop Bonhoeffer-van der Pol type equations grounded in experimental observations, reproducing complex band dynamics, such as replication, oscillation, and breathing. It suggests the similarity between pattern formation in granular segregation and that in reaction-diffusion systems.

On the influence of additive and multiplicative noise on holes in dissipative systems

We investigate the influence of noise on deterministically stable holes in the cubic-quintic complex Ginzburg-Landau equation. Inspired by experimental possibilities, we specifically study two types of noise: additive noise delta-correlated in space and spatially homogeneous multiplicative noise on the formation of π-holes and 2π-holes. Our results include the following main features. For large enough additive noise, we always find a transition to the noisy version of the spatially homogeneous finite amplitude solution, while for sufficiently large multiplicative noise, a collapse occurs to the zero amplitude solution. The latter type of behavior, while unexpected deterministically, can be traced back to a characteristic feature of multiplicative noise; the zero solution acts as the analogue of an absorbing boundary: once trapped at zero, the system cannot escape. For 2π-holes, which exist deterministically over a fairly small range of values of subcriticality, one can induce a transition to a π-hole (for additive noise) or to a noise-sustained pulse (for multiplicative noise). This observation opens the possibility of noise-induced switching back and forth from and to 2π-holes.

Model of heap formation in vibrated gravitational suspensions

In vertically vibrated dense suspensions, several localized structures have been discovered, such as heaps, stable holes, expanding holes, and replicating holes. Because an inclined free fluid surface is difficult to maintain because of gravitational pressure, the mechanism of those structures is not understood intuitively. In this paper, as a candidate for the driving mechanism, we focus on the boundary condition on a solid wall: the slip-nonslip switching boundary condition in synchronization with vertical vibration. By applying the lubrication approximation, we derived the time evolution equation of the fluid thickness from the Oldroyd-B fluid model. In our model we show that the initially flat fluid layer becomes unstable in a subcritical manner, and heaps and convectional flow appear. The obtained results are consistent with those observed experimentally. We also find that heaps climb a slope when the bottom is slightly inclined. We show that viscoelasticity enhances heap formation and climbing of a heap on the slope.