We study a system of purely repulsive spherical self-propelled particles in the minimal setup inducing motility-induced phase separation (MIPS). We show that, even if explicit alignment interactions are absent, a growing order in the velocities of the clustered particles accompanies MIPS. Particles arrange into aligned or vortexlike domains whose size increases as the persistence of the self-propulsion grows, an effect that is quantified studying the spatial correlation function of the velocities. We explain the velocity alignment by unveiling a hidden alignment interaction of the Vicsek-like form, induced by the interplay between steric interactions and self-propulsion.

We investigate the properties of a model of granular matter consisting of $N$ Brownian particles on a line, subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy, and the energy dissipation. When the typical relaxation time $\tau$ associated with the Brownian process is small compared with the mean collision time ${\tau }_c$ the spatial density is nearly homogeneous and the velocity probability distribution is Gaussian. In the opposite limit $\tau \gg {\tau }_c$ one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the Gaussian one.

Categories provide a coarse-grained description of the world. A fundamental question is whether categories simply mirror an underlying structure of nature or instead come from the complex interactions of human beings among themselves and with the environment. Here, we address this question by modeling a population of individuals who co-evolve their own system of symbols and meanings by playing elementary language games. The central result is the emergence of a hierarchical category structure made of two distinct levels: a basic layer, responsible for fine discrimination of the environment, and a shared linguistic layer that groups together perceptions to guarantee communicative success. Remarkably, the number of linguistic categories turns out to be finite and small, as observed in natural languages.

The empirical evidence that human color categorization exhibits some universal patterns beyond superficial discrepancies across different cultures is a major breakthrough in cognitive science. As observed in the World Color Survey (WCS), indeed, any two groups of individuals develop quite different categorization patterns, but some universal properties can be identified by a statistical analysis over a large number of populations. Here, we reproduce the WCS in a numerical model in which different populations develop independently their own categorization systems by playing elementary language games. We find that a simple perceptual constraint shared by all humans, namely the human Just Noticeable Difference (JND), is sufficient to trigger the emergence of universal patterns that unconstrained cultural interaction fails to produce. We test the results of our experiment against real data by performing the same statistical analysis proposed to quantify the universal tendencies shown in the WCS [Kay P & Regier T. (2003)Proc. Natl. Acad. Sci. USA100: 9085-9089], and obtain an excellent quantitative agreement. This work confirms that synthetic modeling has nowadays reached the maturity to contribute significantly to the ongoing debate in cognitive science.