Saddle-Node Bifurcation to Jammed State for Quasi-One-Dimensional Counter Chemotactic Flow

The transition of a counter chemotactic particle flow from a free-flow state to a jammed state in a quasi-one-dimensional path is investigated. One of the characteristic features of such a flow is that the constituent particles spontaneously form a cluster that blocks the path, called a path-blocking cluster (PBC), and causes a jammed state when the particle density is greater than a threshold value. Near the threshold value, the PBC occasionally desolve itself to recover the free flow. In other words, the time evolution of the size of the PBC governs the flux of a counter chemotactic flow. In this paper, on the basis of numerical results of a stochastic cellular automata (SCA) model, we introduce a Langevin equation model for the size evolution of the PBC that reproduces the qualitative characteristics of the SCA model. The results suggest that the emergence of the jammed state in a quasi-one-dimensional counter flow is caused by a saddle-node bifurcation.Comment: 5pages, 8figure

Segregation pattern reorientation of granular mixture on horizontally oscillating tray

Reorientation of the segregation pattern of a binary granular mixture on a two-dimensional hor- izontally oscillating tray is numerically realized. The mixture consists of large-and-heavy particles and small-and-light particles, the segregation pattern of which shows a transition between a striped pattern perpendicular to the oscillation and that parallel to the oscillating direction according to the change of area-fractions of two types of particles. The transition mechanism is discussed on the basis of a simplified 1-dimensional dynamics.Comment: 10 pages, 6 figure

Stability of transverse dunes against perturbations; a theoretical study using dune skeleton model

The dune skeleton model is a reduced model to describe the formation process and dynamics of characteristic types of dunes emerging under unidirectional steady wind. Using this model, we study the dependency of the morphodynamics of transverse dunes on the initial random perturbations and the lateral field size. It was found that i) an increase of the lateral field size destabilizes the transverse dune to cause deformation of a barchan, ii) the initial random perturbations decay with time by the power function until a certain time; thereafter, the dune shapes change into three phases according to the amount of sand and sand diffusion coefficient, iii) the duration time, until the transverse dune is broken, increases exponentially with increasing the amount of sand and sand diffusion coefficient. Moreover, under the condition without the sand supply from windward ground, the destabilization of transverse dune in this model qualitatively corresponds to the subaqueous dunes in water tank experiments.Comment: 7pages, 8figure

Swarming of Self-Propelled Camphor Boats

When an ensemble of self-propelled camphor boats move in a one-dimensional channel, they exhibit a variety of collective behaviors. Under certain conditions, the boats tend to cluster together and move in a relatively tight formation. This type of behavior, referred to as clustering or swarming here, is one of three types recently observed in experiment. Similar clustering behavior is also reproduced in simulations based on a simple theoretical model. Here we examine this model to determine the clustering mechanism and the conditions under which clustering occurs. We also propose a method of quantifying the behavior that may be used in future experimental work.Comment: 4 pages, 5 figure