ArticleNature communications2023
Spontaneous vortex formation by microswimmers with retarded attractions.
Article in Nature communications, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
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Who cites it
16 citing papers in PubMed, 37 citations in OpenAlex.
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- Automated decision-making by chemical echolocation in active droplets.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Reservoir computing from collective dynamics of active colloidal oscillators.Communications AI & computing · 2026Article
- Tunable colloidal swarmalators with hydrodynamic coupling.Nature communications · 2025Article
- Morphology, Polarization Patterns, Compression, and Entropy Production in Phase-Separating Active Dumbbell Systems.Entropy (Basel, Switzerland) · 2025Article
- Lane formation in criss-crossing crowds.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- The 2025 motile active matter roadmap.Journal of physics. Condensed matter : an Institute of Physics journal · 2025Review
- Understanding collective behavior in biological systems through potential field mechanisms.Scientific reports · 2025Article
- Microrobotic Swarms for Cancer Therapy.Research (Washington, D.C.) · 2025Review
- Swarm Autonomy: From Agent Functionalization to Machine Intelligence.Advanced materials (Deerfield Beach, Fla.) · 2025Review
- Long-Distance Autonomous Navigation of Optical Microrobotic Swarms in Complex Environments.Advanced intelligent systems (Weinheim an der Bergstrasse, Germany) · 2024Article
- Persistent and responsive collective motion with adaptive time delay.Science advances · 2024Article
- Synchronous and Fully Steerable Active Particle Systems for Enhanced Mimicking of Collective Motion in Nature.Advanced materials (Deerfield Beach, Fla.) · 2024Article
- Harnessing synthetic active particles for physical reservoir computing.Nature communications · 2024Article
Corrections and comments
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Authors and funding
5 authors at 2 institutions in 2 countries.
Funding
No grant is acknowledged in the PubMed record.
Abstract
Collective states of inanimate particles self-assemble through physical interactions and thermal motion. Despite some phenomenological resemblance, including signatures of criticality, the autonomous dynamics that binds motile agents into flocks, herds, or swarms allows for much richer behavior. Low-dimensional models have hinted at the crucial role played in this respect by perceived information, decision-making, and feedback, implying that the corresponding interactions are inevitably retarded. Here we present experiments on spherical Brownian microswimmers with delayed self-propulsion toward a spatially fixed target. We observe a spontaneous symmetry breaking to a transiently chiral dynamical state and concomitant critical behavior that do not rely on many-particle cooperativity. By comparison with the stochastic delay differential equation of motion of a single swimmer, we pinpoint the delay-induced effective synchronization of the swimmers with their own past as the key mechanism. Increasing numbers of swimmers self-organize into layers with pro- and retrograde orbital motion, synchronized and stabilized by steric, phoretic, and hydrodynamic interactions. Our results demonstrate how even most simple retarded interactions can foster emergent complex adaptive behavior in small active-particle ensembles.
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