Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

Statistical physics of social dynamics

This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments. This approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of this review is to integrate several approaches proposed in the literature, from semimicroscopic to phenomenological. In particular, first considered are ``dry'' systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium. The differences and similarities between two types of orientationally ordered states, the nematic and the polar, are clarified. Next, the active hydrodynamics of suspensions or ``wet'' systems is discussed and the relation with and difference from the dry case, as well as various large-scale instabilities of these nonequilibrium states of matter, are highlighted. Further highlighted are various large-scale instabilities of these nonequilibrium states of matter. Various semimicroscopic derivations of the continuum theory are discussed and connected, highlighting the unifying and generic nature of the continuum model. Throughout the review, the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material is discussed. Promising extensions toward greater realism in specific contexts from cell biology to animal behavior are suggested, and remarks are given on some exotic active-matter analogs. Last, the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents, is summarized.

Hydrodynamics of soft active matter

We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities As such, these models allow the establishing of a few fundamental principles of flocking In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences

Collective Motion

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 behavior 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 analogs. Theory and experiment are discussed side by side.

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The Mechanics and Statistics of Active Matter

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.

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Physics of microswimmers--single particle motion and collective behavior: a review.

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.

https://physics.unm.edu/kenkre/papers/Art234.pdf

Phase transitions in systems of self-propelled agents and related network models.

In the context of an extension of Axelrod's model for social influence, we study the interplay and competition between the cultural drift, represented as random perturbations, and mass media, introduced by means of an external homogeneous field. Unlike previous studies [J. C. Gonzalez-Avella et al., Phys. Rev. E72, 065102(R) (2005)], the mass media coupling proposed here is capable of affecting the cultural traits of any individual in the society, including those who do not share any features with the external message. A noise-driven transition is found: for large noise rates, both the ordered (culturally polarized) phase and the disordered (culturally fragmented) phase are observed, while, for lower noise rates, the ordered phase prevails. In the former case, the external field is found to induce cultural ordering, a behavior opposite to that reported in previous studies using a different prescription for the mass media interaction. We compare the predictions of this model to statistical data measuring the impact of a mass media vasectomy promotion campaign in Brazil.

Effects of mass media and cultural drift in a model for social influence

We propose a comprehensive dynamical model for cooperative motion of self-propelled particles, e.g., flocking, by combining well-known elements such as velocity-alignment interactions, spatial interactions, and angular noise into a unified Lagrangian treatment. Noise enters into our model in an especially realistic way: it incorporates correlations, is highly nonlinear, and it leads to a unique collective behavior. Our results show distinct stability regions and an apparent change in the nature of one class of noise-induced phase transitions, with respect to the mean velocity of the group, as the range of the velocity-alignment interaction increases. This phase-transition change comes accompanied with drastic modifications of the microscopic dynamics, from nonintermittent to intermittent. Our results facilitate the understanding of the origin of the phase transitions present in other treatments.

https://physics.unm.edu/kenkre/pdflink/DSK09a-PRE.pdf

Phase transitions induced by complex nonlinear noise in a system of self-propelled agents.

In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters’ fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.

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Fractality à la carte : a general particle aggregation model

Aggregation phenomena are ubiquitous in nature, encompassing out-of-equilibrium processes of fractal pattern formation, important in many areas of science and technology. Despite their simplicity, foundational models such as diffusion-limited aggregation (DLA) or ballistic aggregation (BA), have contributed to reveal the most basic mechanisms that give origin to fractal structures. Hitherto, it has been commonly accepted that, in the absence of long-range particle-cluster interactions, the trajectories of aggregating particles, carrying the entropic information of the growing medium, are the main elements of the aggregation dynamics that determine the fractality and morphology of the aggregates. However, when interactions are not negligible, fractality is enhanced or emerges from the screening effects generated by the aggregated particles, a fact that has led to believe that the main contribution to fractality and morphology is of an energetic character only, turning the entropic one of no special significance, to be considered just as an intrinsic stochastic element. Here we show that, even when long-range attractive interactions are considered, not only screening effects but also, in a very significant manner, particle trajectories themselves are the two fundamental ingredients that give rise to the fractality in aggregates. We found that, while the local morphology of the aggregates is determined by the interactions, their global aspect will exclusively depend on the particle trajectories. Thus, by considering an effective aggregation range, we obtain a wide and versatile generalization of the DLA and BA models. Furthermore, for the first time, we show how to generate a vast richness of natural-looking branching clusters with any prescribed fractal dimension, very precisely controlled.

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V. Dossetti

Papers

Phase transitions in systems of self-propelled agents and related network models.

Effects of mass media and cultural drift in a model for social influence

Phase transitions induced by complex nonlinear noise in a system of self-propelled agents.

Fractality à la carte : a general particle aggregation model

Fractality \`a la carte: a general particle-cluster aggregation model