Spatio-temporal patterns driven by autocatalytic internal reaction noise

The influence that intrinsic local density fluctuations can have on solutions of mean-field reaction-diffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the presence of strong internal reaction noise. The dynamics of the Gray-Scott (GS) model with constant external source is first cast in terms of a continuum field theory representing the corresponding master equation. We then derive a Langevin description of the field theory and use these stochastic differential equations in our simulations. The nature of the multiplicative noise is specified exactly without recourse to assumptions and turns out to be of the same order as the reaction itself, and thus cannot be treated as a small perturbation. Many of the complex patterns obtained in the absence of noise for the GS model are completely obliterated by these strong internal fluctuations, but we find novel spatial patterns induced by this reaction noise in regions of parameter space that otherwise correspond to homogeneous solutions when fluctuations are not included.Comment: 12 pages, 18 figure

Continuum limit of self-driven particles with orientation interaction

We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the interactions of individuals among animal societies such as fish schools. In this article, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non conservative equation for the director of the mean velocity and is proved to be hyperbolic. The derivation is based on the introduction of a non-conventional concept of a collisional invariant of a collision operator

Autonomous Motility of Active Filaments due to Spontaneous Flow-Symmetry Breaking

We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which is active due a permanent distribution of stresslets along its contour. A bending instability of an initially straight filament spontaneously breaks flow symmetry and leads to autonomous filament motion which, depending on conformational symmetry, can be translational or rotational. At high ratios of activity to elasticity, the linear instability develops into nonlinear fluctuating states with large amplitude deformations. The dynamics of these states can be qualitatively understood as a superposition of translational and rotational motion associated with filament conformational modes of opposite symmetry. Our results can be tested in molecular-motor filament mixtures, synthetic chains of autocatalytic particles, or other linearly connected systems where chemical energy is converted to mechanical energy in a fluid environment.Comment: 7 pages, 3 figures; contains supplemental text; movies at http://proofideas.org/rjoy/gallery; published in Physical Review Letter

Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions

The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer simulations. In this paper, we study the model following an alternative approach based on the analogy with the zero range process, which is one of the few known exactly solvable stochastic dynamical models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the model exhibits a continuous phase transition at the critial density only in a limiting case. Furthermore, we investigate the phase diagram of the model by replacing the periodic boundary conditions by open boundary conditions.Comment: 8 pages, 6 figure

A Stochastic Approach to Shortcut Bridging in Programmable Matter

In a self-organizing particle system, an abstraction of programmable matter, simple computational elements called particles with limited memory and communication self-organize to solve system-wide problems of movement, coordination, and configuration. In this paper, we consider a stochastic, distributed, local, asynchronous algorithm for "shortcut bridging", in which particles self-assemble bridges over gaps that simultaneously balance minimizing the length and cost of the bridge. Army ants of the genus Eciton have been observed exhibiting a similar behavior in their foraging trails, dynamically adjusting their bridges to satisfy an efficiency trade-off using local interactions. Using techniques from Markov chain analysis, we rigorously analyze our algorithm, show it achieves a near-optimal balance between the competing factors of path length and bridge cost, and prove that it exhibits a dependence on the angle of the gap being "shortcut" similar to that of the ant bridges. We also present simulation results that qualitatively compare our algorithm with the army ant bridging behavior. Our work gives a plausible explanation of how convergence to globally optimal configurations can be achieved via local interactions by simple organisms (e.g., ants) with some limited computational power and access to random bits. The proposed algorithm also demonstrates the robustness of the stochastic approach to algorithms for programmable matter, as it is a surprisingly simple extension of our previous stochastic algorithm for compression.Comment: Published in Proc. of DNA23: DNA Computing and Molecular Programming - 23rd International Conference, 2017. An updated journal version will appear in the DNA23 Special Issue of Natural Computin

Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system's behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages, and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively), and provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv requirements; write first author for higher-resolution version

Swarming in shallow waters

A swarm is a collection of separate objects that move autonomously in the same direction in a concerted fashion. This type of behavior is observed in ensembles of various organisms but has proven inherently difficult to realize in artificial chemical systems, where the components have to self-assemble dynamically and, at the same time, propel themselves. This paper describes a class of systems in which millimeter-sized components interact hydrodynamically and organize into dissipative structures that swarm in thin fluid layers. Depending on the geometry of the particles, various types of swarms can be engineered, including ensembles that rotate, follow a "leader", or are pushed in front of a larger particle

Vitellogenin Underwent Subfunctionalization to Acquire Caste and Behavioral Specific Expression in the Harvester Ant Pogonomyrmex barbatus

PMCID: PMC3744404This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication

Traffic Instabilities in Self-Organized Pedestrian Crowds

In human crowds as well as in many animal societies, local interactions among individuals often give rise to self-organized collective organizations that offer functional benefits to the group. For instance, flows of pedestrians moving in opposite directions spontaneously segregate into lanes of uniform walking directions. This phenomenon is often referred to as a smart collective pattern, as it increases the traffic efficiency with no need of external control. However, the functional benefits of this emergent organization have never been experimentally measured, and the underlying behavioral mechanisms are poorly understood. In this work, we have studied this phenomenon under controlled laboratory conditions. We found that the traffic segregation exhibits structural instabilities characterized by the alternation of organized and disorganized states, where the lifetime of well-organized clusters of pedestrians follow a stretched exponential relaxation process. Further analysis show that the inter-pedestrian variability of comfortable walking speeds is a key variable at the origin of the observed traffic perturbations. We show that the collective benefit of the emerging pattern is maximized when all pedestrians walk at the average speed of the group. In practice, however, local interactions between slow- and fast-walking pedestrians trigger global breakdowns of organization, which reduce the collective and the individual payoff provided by the traffic segregation. This work is a step ahead toward the understanding of traffic self-organization in crowds, which turns out to be modulated by complex behavioral mechanisms that do not always maximize the group's benefits. The quantitative understanding of crowd behaviors opens the way for designing bottom-up management strategies bound to promote the emergence of efficient collective behaviors in crowds.Comment: Article published in PLoS Computational biology. Freely available here: http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.100244