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Boltzmann-Ginzburg-Landau Approach to Simple Models of Active Matter

出版	2013
URL	http://books.google.com.hk/books?id=ewjVoAEACAAJ&hl=&source=gbs_api

註釋The phenomenon of collective motion is present among many different biological systems like bird flocks or fish schools. In these systems, the collective motion arises without any leader or external force, and is only due to interaction among individuals and the out of equilibrium nature of the whole system. We want to study simple models of collective motion in order to establish universality classes among dry active matter, i.e. individuals that interact without the help of a fluid medium. Many of such systems have already been studied microscopically. We want to obtain coarse-grained equations of such models to confirm the microscopical results and to predict new properties. We perform a derivation of hydrodynamic equations using the introduced Boltzmann-Ginzburg-Landau approach. The equations are derived for four different Vicsek type models. A simple polar model, a mixed case of polar particles with nematic interactions, a model of nematic particles with nematic interactions and finally a model for polar particles with metric free interactions. In each case, the obtained equations are studied analytically and numerically. We find out that the hydrodynamic equations reproduce faithfully the qualitative properties of underlying microscopical models, like the different observed phases and the nature of phase transition between them. Some new phases not previously observed in microscopical models are found. Most of them where a posteriori confirmed in simulations of microscopical models.