http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and 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

For animals that forage or travel in groups, making movement decisions often depends on social interactions among group members. However, in many cases, few individuals have pertinent information, such as knowledge about the location of a food source, or of a migration route. Using a simple model we show how information can be transferred within groups both without signalling and when group members do not know which individuals, if any, have information. We reveal that the larger the group the smaller the proportion of informed individuals needed to guide the group, and that only a very small proportion of informed individuals is required to achieve great accuracy. We also demonstrate how groups can make consensus decisions, even though informed individuals do not know whether they are in a majority or minority, how the quality of their information compares with that of others, or even whether there are any other informed individuals. Our model provides new insights into the mechanisms of effective leadership and decision-making in biological systems.

/pdf/effective-leadership-and-decision-making-in-animal-groups-on-2gjkbk8yrp.pdf

Effective leadership and decision-making in animal groups on the move

Differently from passive Brownian particles, active particles, also known as self-propelled Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy from their environment and converting it into directed motion. Because of this constant flow of energy, their behavior can be explained and understood only within the framework of nonequilibrium physics. In the biological realm, many cells perform directed motion, for example, as a way to browse for nutrients or to avoid toxins. Inspired by these motile microorganisms, researchers have been developing artificial particles that feature similar swimming behaviors based on different mechanisms. These man-made micromachines and nanomachines hold a great potential as autonomous agents for health care, sustainability, and security applications. With a focus on the basic physical features of the interactions of self-propelled Brownian particles with a crowded and complex environment, this comprehensive review will provide a guided tour through its basic principles, the development of artificial self-propelling microparticles and nanoparticles, and their application to the study of nonequilibrium phenomena, as well as the open challenges that the field is currently facing.

/pdf/active-particles-in-complex-and-crowded-environments-4pyirdi1aj.pdf

Active Particles in Complex and Crowded Environments

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

We study the onset of collective motion, with and without cohesion, of groups of noisy self-propelled particles interacting locally. We find that this phase transition, in two space dimensions, is always discontinuous, including for the minimal model of Vicsek et al. [Phys. Rev. Lett. 75,1226 (1995)] for which a nontrivial critical point was previously advocated. We also show that cohesion is always lost near onset, as a result of the interplay of density, velocity, and shape fluctuations.

https://hal.archives-ouvertes.fr/hal-00001019/document

Onset of collective and cohesive motion.

We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order-like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on the other hand, these objects are not present. A statistically homogeneous ordered phase is then observed, which is characterized by anomalously strong density fluctuations, superdiffusion, and strong intermittency.

/pdf/collective-motion-of-self-propelled-particles-interacting-52fku5am3k.pdf

Collective motion of self-propelled particles interacting without cohesion.

We argue that the model introduced by Vicsek et al. in which self-propelled particles align locally with neighbors is, because of its simplicity, central to most studies of collective motion or "active" matter. After reviewing brieﬂy its main properties, we show how it can be expanded into three main directions: changing the symmetry of the particles and/or of their interactions, adding local cohesion, and taking into account the ﬂuid in which the particles move.

Modeling collective motion: variations on the Vicsek model

We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result, we derive from the individual dynamics the hydrodynamic equations for the density and velocity fields, thus giving a microscopic foundation to the phenomenological equations used in previous approaches. A homogeneous spontaneous motion emerges below a transition line in the noise-density plane. Yet, this state is shown to be unstable against spatial perturbations, suggesting that more complicated structures should eventually appear.

https://arxiv.org/pdf/cond-mat/0601038.pdf

Boltzmann and hydrodynamic description for self-propelled particles.

Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation. Explicit expressions for the transport coefficients are given, as a function of the microscopic parameters of the model. We show that the homogeneous state with zero hydrodynamic velocity is unstable above a critical density (which depends on the microscopic parameters), signalling the onset of a collective motion. Comparison with numerical simulations on a standard model of self-propelled particles shows that the phase diagram we obtain is robust, in the sense that it depends only slightly on the precise definition of the model. While the homogeneous flow is found to be stable far from the transition line, it becomes unstable with respect to finite-wavelength perturbations close to the transition, implying a non-trivial spatio-temporal structure for the resulting flow. We find solitary wave solutions of the hydrodynamic equations, quite similar to the stripes reported in direct numerical simulations of self-propelled particles.

https://iopscience.iop.org/article/10.1088/1751-8113/42/44/445001/pdf

Guillaume Grégoire

Papers

Onset of collective and cohesive motion.

Collective motion of self-propelled particles interacting without cohesion.

Modeling collective motion: variations on the Vicsek model

Boltzmann and hydrodynamic description for self-propelled particles.

Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis