Dispersion processes

We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step, each of these particles moves to a neighbour of $v$ chosen independently and uniformly at random. The dispersion process ends once the particles have all stopped moving, i.e. at the first step at which each vertex is occupied by at most one particle. For the complete graph $K_n$ and star graph $S_n$, we show that for any constant $\delta>1$, with high probability, if $M \le n/2(1-\delta)$, then the process finishes in $O(\log n)$ steps, whereas if $M \ge n/2(1+\delta)$, then the process needs $e^{\Omega(n)}$ steps to complete (if ever). We also show that an analogous lazy variant of the process exhibits the same behaviour but for higher thresholds, allowing faster dispersion of more particles. For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes (in terms of $M$) we give bounds on the time to finish and the maximum distance traveled from the origin as a function of the number of particles $M$

Collective Lévy walk for efficient exploration in unknown environments

One of the key tasks of autonomous mobile robots is to explore the unknown environment under limited energy and deadline conditions. In this paper, we focus on one of the most efficient random walks found in the natural and biological system, i.e., Lévy walk. We show how Lévy properties disappear in larger robot swarm sizes because of spatial interferences and propose a novel behavioral algorithm to preserve Lévy properties at the collective level. Our initial findings hold potential to accelerate target search processes in large unknown environments by parallelizing Lévy exploration using a group of robots

Swimmers at Interfaces Enhance Interfacial Transport

The behavior of fluid interfaces far from equilibrium plays central roles in nature and in industry. Active swimmers trapped at interfaces can alter transport at fluid boundaries with far reaching implications. Swimmers can become trapped at interfaces in diverse configurations and swim persistently in these surface adhered states. The self-propelled motion of bacteria makes them ideal model swimmers to understand such effects. We have recently characterized the swimming of interfacially-trapped Pseudomonas aeruginosa PA01 moving in pusher mode. The swimmers adsorb at the interface with pinned contact lines, which fix the angle of the cell body at the interface and constrain their motion. Thus, most interfacially-trapped bacteria swim along circular paths. Fluid interfaces form incompressible two-dimensional layers, altering leading order interfacial flows generated by the swimmers from those in bulk. In our previous work, we have visualized the interfacial flow around a pusher bacterium and described the flow field using two dipolar hydrodynamic modes; one stresslet mode whose symmetries differ from those in bulk, and another bulk mode unique to incompressible fluid interfaces. Based on this understanding, swimmers-induced tracer displacements and swimmer-swimmer pair interactions are explored using analysis and experiment. The settings in which multiple interfacial swimmers with circular motion can significantly enhance interfacial transport of tracers or promotemixing of other swimmers on the interface are identified through simulations and compared to experiment. This study identifies important factors of general interest regarding swimmers on or near fluid boundaries, and in the design of biomimetic swimmers to enhance transport at interfacesComment: arXiv admin note: substantial text overlap with arXiv:2204.0230

Enhanced foraging in robot swarms using collective Lévy walks

A key aspect of foraging in robot swarms is optimizing the search efficiency when both the environment and target density are unknown. Hence, designing optimal exploration strategies is desirable. This paper proposes a novel approach that extends the individual Lévy walk to a collective one. To achieve this, we adjust the individual motion through applying an artificial potential field method originating from local communication. We demonstrate the effectiveness of the enhanced foraging by confirming that the collective trajectory follows a heavy-tailed distribution over a wide range of swarm sizes. Additionally, we study target search efficiency of the proposed algorithm in comparison with the individual Lévy walk for two different types of target distributions: homogeneous and heterogeneous. Our results highlight the advantages of the proposed approach for both target distributions, while increasing the scalability to large swarm sizes. Finally, we further extend the individual exploration algorithm by adapting the Lévy walk parameter α, altering the motion pattern based on a local estimation of the target density. This adaptive behavior is particularly useful when targets are distributed in patches

Methodological Guidelines for Engineering Self-organization and Emergence

The ASCENS project deals with the design and development of complex self-adaptive systems, where self-organization is one of the possible means by which to achieve self-adaptation. However, to support the development of self-organising systems, one has to extensively re-situate their engineering from a software architectures and requirements point of view. In particular, in this chapter, we highlight the importance of the decomposition in components to go from the problem to the engineered solution. This leads us to explain and rationalise the following architectural strategy: designing by following the problem organisation. We discuss architectural advantages for development and documentation, and its coherence with existing methodological approaches to self-organisation, and we illustrate the approach with an example on the area of swarm robotics

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte