The Mechanics and Statistics of Active Matter

Active particles contain internal degrees of freedom with the ability to take in and dissipate energy and, in the process, execute systematic movement. Examples include all living organisms and their motile constituents such as molecular motors. This article reviews recent progress in applying the principles of nonequilibrium statistical mechanics and hydrodynamics to form a systematic theory of the behaviour of collections of active particles -- active matter -- with only minimal regard to microscopic details. A unified view of the many kinds of active matter is presented, encompassing not only living systems but inanimate analogues. Theory and experiment are discussed side by side.Comment: This review is to appear in volume 1 of the Annual Review of Condensed Matter Physics in July 2010 and is posted here with permission from that journa

Effect of the orientational relaxation on the collective motion of patterns formed by self-propelled particles

We investigate the collective behavior of self-propelled particles (SPPs) undergoing competitive processes of pattern formation and rotational relaxation of their self-propulsion velocities. In full accordance with previous work, we observe transitions between different steady states of the SPPs caused by the intricate interplay among the involved effects of pattern formation, orientational order, and coupling between the SPP density and orientation fields. Based on rigorous analytical and numerical calculations, we prove that the rate of the orientational relaxation of the SPP velocity field is the main factor determining the steady states of the SPP system. Further, we determine the boundaries between domains in the parameter plane that delineate qualitatively different resting and moving states. In addition, we analytically calculate the collective velocity $\vec{v}$ of the SPPs and show that it perfectly agrees with our numerical results. We quantitatively demonstrate that $\vec{v}$ does not vanish upon approaching the transition boundary between the moving pattern and homogeneous steady states.Comment: 3 Figure

Entropy evaluation sheds light on ecosystem complexity

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem on a lattice in which two species struggle for survival. The method quantitatively reproduces the scale-free law of the prey shoals size, where the simpler mean-field approach fails: the direct near neighbor correlations are found to be the fundamental ingredient describing the system self-organized behavior. Furthermore, entropy allows the measurement of structural ordering, that is found to be a key ingredient in characterizing two different coexistence behaviors, one where predators form localized patches in a sea of preys and another where species display more complex patterns. The general nature of the introduced method paves the way for its application in many other systems of interest.Comment: 13 pages, 5 figure

Universality in Bacterial Colonies

The emergent spatial patterns generated by growing bacterial colonies have been the focus of intense study in physics during the last twenty years. Both experimental and theoretical investigations have made possible a clear qualitative picture of the different structures that such colonies can exhibit, depending on the medium on which they are growing. However, there are relatively few quantitative descriptions of these patterns. In this paper, we use a mechanistically detailed simulation framework to measure the scaling exponents associated with the advancing fronts of bacterial colonies on hard agar substrata, aiming to discern the universality class to which the system belongs. We show that the universal behavior exhibited by the colonies can be much richer than previously reported, and we propose the possibility of up to four different sub-phases within the medium-to-high nutrient concentration regime. We hypothesize that the quenched disorder that characterizes one of these sub-phases is an emergent property of the growth and division of bacteria competing for limited space and nutrients.Comment: 12 pages, 5 figure

Effects of anisotropic interactions on the structure of animal groups

This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each animal deploys itself depending on the position of a limited number of close group mates. The proposed model is shown to produce clustered formations, as well as lines and V-like formations. The key factors which trigger the onset of different patterns are argued to be the relative strength of attraction and repulsion forces and, most important, the anisotropy in their application.Comment: 22 pages, 9 figures. Submitted. v1-v4: revised presentation; extended simulations; included technical results. v5: added a few clarification