The Vicsek model encompasses the paradigm of active dry matter. Motivated by collective behavior of insects in swarms, we have studied finite-size effects and criticality in the three-dimensional, harmonically confined Vicsek model. We have discovered a phase transition that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Scale-free chaotic swarms occupy a compact region of space and comprise a recognizable “condensed” nucleus and particles leaving and entering it. Susceptibility, correlation length, dynamic correlation function, and largest Lyapunov exponent obey power laws. The critical line and a narrow criticality region close to it move simultaneously to zero confinement strength for infinitely many particles. At the end of the first chaotic window of confinement, there is another phase transition to infinitely dense clusters of finite size that may be termed flocking black holes.

The harmonically confined Vicsek model displays qualitative and quantitative features observed in natural insect swarms. It exhibits a scale-free transition between single and multicluster chaotic phases. Finite-size scaling indicates that this unusual phase transition occurs at zero confinement [ Phys. Rev. E 107, 014209 (2023)]. While the evidence of the scale-free-chaos phase transition comes from numerical simulations, here we present its mean-field theory. Analytically determined critical exponents are those of the Landau theory of equilibrium phase transitions plus dynamical critical exponent $z=1$ and a new critical exponent $\phi =0.5$ for the largest Lyapunov exponent. The phase transition occurs at zero confinement and noise in the mean-field theory. The noise line of zero largest Lyapunov exponents informs observed behavior: (i) the qualitative shape of the swarm (on average, the center of mass rotates slowly at the rate marked by the winding number and its trajectory fills compactly the space, similarly to the observed condensed nucleus surrounded by vapor) and (ii) the critical exponents resemble those observed in natural swarms. Our predictions include power laws for the frequency of the maximal spectral amplitude and the winding number.

Collective biological systems display power laws for macroscopic quantities and are fertile probing grounds for statistical physics. Besides power laws, natural insect swarms present strong scale-free correlations, suggesting closeness to phase transitions. Swarms exhibit imperfect dynamic scaling: their dynamical correlation functions collapse into single curves when written as functions of the scaled time $t{\xi }^{-z}$ ($\xi$: correlation length, $z$: dynamic exponent), but only for short times. Triggered by markers, natural swarms are not invariant under space translations. Measured static and dynamic critical exponents differ from those of equilibrium and many nonequilibrium phase transitions. Here we show the following: (i) The recently discovered scale-free-chaos phase transition of the harmonically confined Vicsek model has a novel extended critical region for $N$ (finite) insects that contains several critical lines. (ii) As alignment noise vanishes, there are power laws connecting critical confinement and noise that allow calculating static critical exponents for fixed $N$. These power laws imply that the unmeasurable confinement strength is proportional to the perception range measured in natural swarms. (iii) Observations of natural swarms occur at different times and under different atmospheric conditions, which we mimic by considering mixtures of data on different critical lines and $N$. Unlike results of other theoretical approaches, our numerical simulations reproduce the previously described features of natural swarms and yield static and dynamic critical exponents that agree with observations.

Animal motion and flocking are ubiquitous nonequilibrium phenomena that are often studied within active matter. In examples such as insect swarms, macroscopic quantities exhibit power laws with measurable critical exponents and ideas from phase transitions and statistical mechanics have been explored to explain them. The widely used Vicsek model with periodic boundary conditions has an ordering phase transition but the corresponding homogeneous ordered or disordered phases are different from observations of natural swarms. If a harmonic potential (instead of a periodic box) is used to confine particles, then the numerical simulations of the Vicsek model display periodic, quasiperiodic, and chaotic attractors. The latter are scale-free on critical curves that produce power laws and critical exponents. Here, we investigate the scale-free chaos phase transition in two space dimensions. We show that the shape of the chaotic swarm on the critical curve reflects the split between the core and the vapor of insects observed in midge swarms and that the dynamic correlation function collapses only for a finite interval of small scaled times. We explain the algorithms used to calculate the largest Lyapunov exponents, the static and dynamic critical exponents, and compare them to those of the three-dimensional model.

We propose a computational model to study the growth and spread of bacterial biofilms on interfaces, as well as the action of antibiotics on them. Bacterial membranes are represented by boundaries immersed in a fluid matrix and subject to interaction forces. Growth, division and death of bacterial cells follow dynamic energy budget rules, in response to variations in environmental concentrations of nutrients, toxicants and substances released by the cells. In this way, we create, destroy and enlarge boundaries, either spherical or rod-like. Appropriate forces represent details of the interaction between cells, and the interaction with the environment. We can investigate geometrical arrangements and the formation of porous structures. Numerical simulations illustrate the evolution of top views and diametral slices of small biofilm seeds, as well as the action of antibiotics. We show that cocktails of antibiotics targeting active and dormant cells can entirely eradicate a biofilm. Hybrid multiscale models, immersed boundary methods, dynamic energy budget models, bacterial biofilm, antibiotic resistance. 87.18.Fx, 87.17.Aa, 87.18.Hf, 87.64.Aa COPYRIGHT: © Global Science Press ana carpio@mat.ucm.es ( Ana Carpio)