This paper describes dynamic transitions of convection motions of granules under vertical vibrations. The granule motion of one convection mode, which has been studied by many authors, is downward along the vertical side walls and upward in the middle forming a heap. The present study focuses on the granule motion of the other convection mode that occurs in rectangular containers: granules move upward along the vertical side walls, and downwards in the middle forming a valley. This latter convection mode is stable enough to yield multiple pairs of convection rolls. The number of convection rolls is strongly dependent on the vibrational acceleration, granular size, and to a lesser extent on frequency, given the bed height and width. The critical vibrational acceleration, where a transition occurs between the two convection modes, is dependent on the bed height but not on the bed width in the range investigated (100–200 mm). In the case of large granules (mean diameter d¯≥0.78 mm) a chaotic state (where convective motion of granules ceases to exist) is found to appear in between the two convection modes mentioned above. © 1996 The American Physical Society.

In order to investigate thermodynamic properties and microscopic structure around the crystal-smectic transition, we present constant-pressure molecular-dynamics simulations for soft parallel spherocylinders as a model for liquid crystals. The method of Andersen [J. Chem. Phys. 72, 2384 (1980)] as well as the method of Parrinello and Rahman [Phys. Rev. Lett. 45, 1196 (1980)] are applied to a right parallelepiped simulation box, and the equation of state for this model is evaluated. Thermodynamic properties such as enthalpy and volume as functions of reduced density ${\mathrm{\rho }}^{\mathrm{*}}$ or of temperature show a clear first-order transition. The dependence of ${\mathit{l}}_{\mathrm{\perp }}$ the square root of the specific area of the plane perpendicular to the molecular axis, on ${\mathrm{\rho }}^{\mathrm{*}}$ shows a feature characteristic of two-dimensional melting. We calculate the specific length ${\mathit{l}}_{\mathit{z}}$ in the direction of the molecular axis, which corresponds to the thickness of a smectic layer in the liquid-crystal region. From the ${\mathrm{\rho }}^{\mathrm{*}}$ dependence of ${\mathit{l}}_{\mathit{z}}$ and ${\mathit{l}}_{\mathit{z}}$/${\mathit{l}}_{\mathrm{\perp }}$, we show that the anisotropy of the molecular volume plays an important role in the crystal-smectic transition. We also observe a clear change in both diffusion and structural properties before and after this transition. The mean-square displacements in directions perpendicular to the alignment show that in the smectic phase the moleules diffuse freely within the layers, although the density wave in the direction perpendicular to layers does exist even after the transition.

This paper presents two-dimensional particle dynamics simulations of a vertically vibrated layer of granules, wherein a spontaneous formation of parametric surface waves appears. The investigation of the dynamic process and mechanism that leads to the formation of the granular surface waves has revealed that the dissipation coefficient in shear direction plays a crucial role in the formation of wave patterns. Scaling relations between the units in simulations and experiments are evaluated. Simulation results are shown to compare well with experimental ones.

This paper presents molecular dynamics simulations of two-dimensional vertically vibrated beds of granules. We have succeeded in observing pressure and density wave propagations that arise from the collective motion of granules. In addition, investigation is made of the variation in kinetic energy per particle along the bed height.

We investigate how the interaction of particles mediated by an elastic deformation of a nematic liquid crystal is influenced by the initial deformation of the director field. To this end, we calculate the interaction energy between particles in a nematic cell with hybrid boundary conditions, homeotropic on the surface of one confining plate and planar on the other. We find an analytic form of the interaction energy in the case of weak anchoring on the surface of the particle. This interaction energy sensitively depends on the position of the two particles as well as the interparticle distance and can be nonmonotonic with a minimum in its landscape. This nontrivial energy landscape might lead to a chainlike superstructure of particles.