Dynamics of a Rotating Sphere on Free Surface of Vibrated Granular Materials

We investigate the rotational dynamics of a low-density sphere on the free surface of a vertically vibrated granular material（VGM）. The dynamical behavior of the sphere is influenced by the external energy input from an electromagnetic shaker which is proportional to ε,where ε is equal to the ratio between the square of the dimensionless acceleration Γ and the square of the vibration frequency f of the container. Empirical results reveal that as the VGM transits from local-to-global convection,an increase in ε generally corresponds to an increase in the magnitudes of the rotational ω（RS） and translational v（CM） velocities of the sphere, an increase in the observed tilting angle θ（bed） of the VGM bed, and a decrease in the time t（wall） it takes the sphere to roll down the tilted VGM bed and hit the container wall. During unstable convection, an increase in ε results in a sharp decrease in the sphere＇s peak and mean ω（RS）,and a slight increase in t（wall）.For the range of ε values covered in this study, the sphere may execute persistent rotation, wobbling or jamming, depending on the vibration parameters and the resulting convective flow in the system.

Dynamics of 2×2 matrix non-Hermitian quantum systems on Bloch sphere

By casting evolution to the Bloch sphere, the dynamics of 2 × 2 matrix non-Hermitian systems are investigated in detail. This investigation reveals that there are four kinds of dynamical modes for such systems. The different modes are classified by different kinds of fixed points, namely,the elliptic point, spiral point, critical node, and degenerate point. The Hermitian systems and the unbroken PT non-Hermitian cases belong to the category with elliptic points. The degenerate point just corresponds to the systems with exceptional point(EP). The topological properties of the fixed point are also discussed. It is interesting that the topological charge for the degenerate point is two, while the others are one.

Influence of wall motion on particle sedimentation using hybrid LB-IBM scheme

We integrate the lattice Boltzmann method(LBM) and immersed boundary method(IBM) to capture the coupling between a rigid boundary surface and the hydrodynamic response of an enclosed particle laden fluid. We focus on a rigid box filled with a Newtonian fluid where the drag force based on the slip velocity at the wall and settling particles induces the interaction. We impose an external harmonic oscillation on the system boundary and found interesting results in the sedimentation behavior. Our results reveal that the sedimentation and particle locations are sensitive to the boundary walls oscillation amplitude and the subsequent changes on the enclosed flow field. Two different particle distribution analyses were performed and showed the presence of an agglomerate structure of particles. Despite the increase in the amplitude of wall motion, the turbulence level of the flow field and distribution of particles are found to be less in quantity compared to the stationary walls. The integrated LBM-IBM methodology promised the prospect of an efficient and accurate dynamic coupling between a non-compliant bounding surface and flow field in a wide-range of systems. Understanding the dynamics of the fluid-filled box can be particularly important in a simulation of particle deposition within biological systems and other engineering applications.