The Rotating Vicsek Model: Pattern Formation and Enhanced Flocking in Chiral Active Matter

We generalize the Vicsek model to describe the collective behaviour of polar circle swimmers with local alignment interactions. While the phase transition leading to collective motion in 2D (flocking) occurs at the same interaction to noise ratio as for linear swimmers, as we show, circular motion enhances the polarization in the ordered phase (enhanced flocking) and induces secondary instabilities leading to structure formation. Slow rotations result in phase separation whereas fast rotations generate patterns which consist of phase synchronized microflocks of controllable self-limited size. Our results defy the viewpoint that monofrequent rotations form a rather trivial extension of the Vicsek model and establish a generic route to pattern formation in chiral active matter with possible applications to control coarsening and to design rotating microflocks.Comment: Contains a Supplementary Materia

Meso-scale turbulence in living fluids

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior amongst the simplest forms of life, and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active non-equilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific, or which generalizations of the Navier-Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.Comment: accepted PNAS version, 6 pages, click doi for Supplementary Informatio

Collective behavior of interacting self-propelled particles

We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the results of large scale simulations and theoretical approaches to the problem

Flocking algorithm for autonomous flying robots

Animal swarms displaying a variety of typical flocking patterns would not exist without underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with agent-based models. If we want to reproduce these patterns with artificial systems, such as autonomous aerial robots, agent-based models can also be used in the control algorithm of the robots. However, finding the proper algorithms and thus understanding the essential characteristics of the emergent collective behaviour of robots requires the thorough and realistic modeling of the robot and the environment as well. In this paper, first, we present an abstract mathematical model of an autonomous flying robot. The model takes into account several realistic features, such as time delay and locality of the communication, inaccuracy of the on-board sensors and inertial effects. We present two decentralized control algorithms. One is based on a simple self-propelled flocking model of animal collective motion, the other is a collective target tracking algorithm. Both algorithms contain a viscous friction-like term, which aligns the velocities of neighbouring agents parallel to each other. We show that this term can be essential for reducing the inherent instabilities of such a noisy and delayed realistic system. We discuss simulation results about the stability of the control algorithms, and perform real experiments to show the applicability of the algorithms on a group of autonomous quadcopters

Topological Sound and Flocking on Curved Surfaces

Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state due to the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow the system additionally supports long-wavelength propagating sound modes which get gapped by the curvature of the underlying substrate. We analytically compute the steady state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry protected topological modes that get localized to special geodesics on the surface (the equator or the neck respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.Comment: 15 pages, 6 figure

Collective behavior of animals: swarming and complex patterns

En esta nota repasamos algunos modelos basados en individuos para describir el movimiento colectivo de agentes, a lo que nos referimos usando la voz inglesa swarming. Estos modelos se basan en EDOs (ecuaciones diferenciales ordinarias) y muestran un comportamiento asintótico complejo y rico en patrones, que mostramos numéricamente. Además, comentamos cómo se conectan estos modelos de partículas con las ecuaciones en derivadas parciales para describir la evolución de densidades de individuos de forma continua. Las cuestiones matemáticas relacionadas con la estabilidad de de estos modelos de EDP's (ecuaciones en derivadas parciales) despiertan gran interés en la investigación en biología matemáticaIn this short note we review some of the individual based models of the collective motion of agents, called swarming. These models based on ODEs (ordinary differential equations) exhibit a complex rich asymptotic behavior in terms of patterns, that we show numerically. Moreover, we comment on how these particle models are connected to partial differential equations to describe the evolution of densities of individuals in a continuum manner. The mathematical questions behind the stability issues of these PDE (partial differential equations) models are questions of actual interest in mathematical biology researc

Rheology and Collective Behavior in Living Tissue

Recent experiments and simulations have indicated that confluent epithelial layers, where there are no gaps or overlaps between the cells, can transition from a soft fluid-like state to a solid-like state, with dynamics that share many features with glass transitions. While a coherent picture has begun to form connecting the microscopic mechanisms that drive this transition with macroscopic observables, much less is known of its consequences in biological processes. Do tissues tune themselves to a fluid state in order to promote collective motion? Has evolution made use of the ability of tissues to tune themselves between fluid and solid states in programming the complex steps leading from the embryo to the organism? Here we describe our recent e↵orts to answer such questions using continuum and mesoscopic models. Employing the biophysical vertex model, active cells in confluent tissue are described as polygons with shape-based energies. Recent work has shown that this class of models yields a solid-liquid transition of tissue with evidence of glassy dynamics near the transition line. Here, we extend one such model to include the influence of cell division and cell death. With careful numerical studies, we refute a recent claim that the presence of such division and death will always fluidify the tissue. In the second part of the thesis, we develop a novel hydrodynamic model of confluent motile tissues that couples a structural order parameter for tissue rigidity to cell polarization. Using this continuum model we identify a new mechanism for pattern formation in confluent tissues via rigidity sensing that we name “morphotaxis”. We find that a single “morphotactic” parameter controls whether a tissue will remain homogeneous or will develop patterns such as asters and bands