Clusters of biological organisms often show diverse collective motions. Considering the physical properties of active elements with mutual interactions, we propose a mathematical model of collective motion. Several kinds of cluster motion seen in nature, including collective rotation, chaos, and wandering, occur in computer simulations of our deterministic model. By introducing a set of dimensionless parameters, we categorize the collective motions and obtain their phase diagram. We analyze the collective motions with a disorder parameter and Lyapunov spectra to characterize their transitions. [S0031-9007(96)00218-9]

Pattern dynamics of directional crack propagation phenomena observed in drying process of starch-water mixture is investigated. To visualize the three-dimensional structure of the drying-fracture process two kinds of experiments are performed, i.e., resin solidification planing method and real-time measurement of water content distribution with MR instruments. A cross section with polygonal structure is visualized in both experiments. The depth dependency of cell size is measured. The phenomenological model for water transportation is also discussed.

We analysed pigeon flock flights using GPS trajectory data to reveal the most important kinematic aspects of flocking behaviour. We quantitatively investigated the internal motion of the flock based on pairwise statistics and found the following general relationships in all datasets: i) the temporal order of decisions characterised by the delay between directional changes is strictly related to the spatial order characterised by the longitudinal relative position within the flock; ii) during circling motion, pigeons use a mixture of two idealised and fundamentally different turning strategies, namely, parallel-path and equal-radius type turning. While pigeons tend to maintain their relative position within the flock on average, as in the parallel-path approximation, those who turn later also get behind as in the equal-radius case. Equal-radius type turning also tends to be expressed more during smaller radius turns.

The formation of three-dimensional prismatic cracks in the drying process of starch-water mixtures is investigated numerically. We assume that the mixture is an elastic porous medium which possesses a stress field and a water content field. The evolution of both fields are represented by a spring network and a phenomenological model with the water potential, respectively. We find that the water content distribution has a propagating front which is not explained by a simple diffusion process. The prismatic structure of cracks driven by the water content field is observed. The depth dependence and the coarsening process of the columnar structure are also studied. The particle diameter dependence of the scale of the columns and the effect of the crack networks on the dynamics of the water content field are also discussed.

As a model of proportion regulation in differentiation process of biological system, globally coupled activator-inhibitor systems are studied. Formation and destabilization of one and two cluster state are predicted analytically.Numerical simulations show that the proportion of units of clusters is chosen within a finite range and it is selected depend on the initial condition.