1 / 16

New Perspectives in the Study of Swarming Systems

New Perspectives in the Study of Swarming Systems. Cristi á n Huepe Unaffiliated NSF Grantee - Chicago, IL. USA. Collaborators: Maximino Aldana, Paul Umbanhowar, Hernan Larralde, V. M. Kenkre, V. Dossetti. This work was supported by the National Science Foundation under Grant No. DMS-0507745.

zahi
Download Presentation

New Perspectives in the Study of Swarming Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. New Perspectives in the Study of Swarming Systems Cristián Huepe Unaffiliated NSF Grantee - Chicago, IL. USA. Collaborators: Maximino Aldana, Paul Umbanhowar, Hernan Larralde,V. M. Kenkre, V. Dossetti. This work was supported by the National Science Foundation under Grant No. DMS-0507745.

  2. Talk Outline • Overview of Swarming Systems Research • Biological and technological motivation • Various theoretical approaches • Agent-Based Modeling • Minimal agent-based models • Order parameters and phase transition • Intermittency and Clustering • Experimental and numerical results • The two-particles case • The N-particle case • The Network Approach • Motivation: “small-world” effect • Analytic solution • Future Challenges and Experiments

  3. Biological & technological motivation Biological agents From Iain Couzin’s group: http://www.princeton.edu/~icouzin Decentralized robots From James McLurkin’s group: http://people.csail.mit.edu/jamesm/swarm.php

  4. Various approaches • Biology:Iain Couzin (Oxford/Princeton), Stephen Simpson (U of Sidney), Julia Parrish, Daniel Grünbaum (U of Washington), Steven Viscido (U of South Carolina), Leah Edelstein-Keshet (U of British Columbia), Charlotte Hemelrijk (U of Groningen) • Engineering:Naomi Leonard (Princeton), Richard Murray (CALTECH), Reza Olfati-Saber (Dartmouth College), Ali Jadbabaie (U of Pennsylvania), Stephen Morse (Yale U), Kevin Lynch, Randy Freeman (Northwestern U), Francesco Bullo (UCSB), Vijay Kumar (U of Pennsylvania) • Applied math / Non-equilibrium Physics: Chad Topaz, Andrea Bertozzi, Maria D’Orsogna (UCLA), Herbert Levine (UCSD), Tamás Vicsek (Eötvös Loránd U), Hugues Chaté (CEA-Saclay), Maximino Aldana (UNAM), Udo Erdmann (Helmholtz Association), Bruno Eckhardt (Philipps-U Marburg), Edward Ott (U of Maryland)

  5. Minimal agent-based models (10) • Vicsek et al. noise • Original Vicsek Algorithm (OVA) • Standard Vicsek Algorithm (SVA) • Guillaume-Chaté Algorithm (GCA)

  6. Order parameters & phase transition • Degree of alignment(magnetization): • Local density: • Distance to nearest neighbor:

  7. Degree of alignment vs. amount of noise • Local density vs. amount of noise

  8. (Grégoire & Chaté: PRL 90(2)025702) • GCA: 1st order phase transition? • Observations: • Apparent 2nd order phase transition for large N • SVA appears to have larger finite-size effect • GCA appears to present similar transition • SVA and GCA: Unrealistic local densities

  9. Intermittency and Clustering • Experiments • Simulations

  10. The two-particle case • 1st passage problem in a 1D random walk. • We compute the continuous approximation • Diffusion equation with • Analytic solution in Laplace space for: • Distribution of laminar intervals

  11. The N-particle case • Alignment vs. time • N=5000 agents • N=500 agents • N=2 agents • Probability distribution of the degree of alignment

  12. Clustering Analysis • Power-law cluster size (agent number) distribution • No characteristic cluster size • Power-law cluster size transition prob. • Of belonging to cluster of size ‘n’ at ‘t’ and ‘n+n’ at ‘t+1’

  13. The Network Approach • Motivation: We replace • Moving agents by fixed nodes. • Effective long-range interactions by a few long-range connections. • Each node linked with probability 1-p to one of its K neighbors and p to any other node. • Small-world effect: • 1% of long range connections • Phase with long-range order appears p = 0.1

  14. Analytic Solution • Mean-field approximation • Vicsek time-step and order parameter: • Order parameter: • The calculation requires: • Expressing PDFs in terms of moments • A random-walk analogy • Central limit theorem • Expansion about the phase transition point

  15. Results • SVA: 2nd order phase transition with critical behavior: • GCA: 1st order phase transition Vicsek AlgorithmGuillaume-Chate Algorithm

  16. Future Challenges & Experiments • Examine a more rigorous connection between the network model and the self-propelled system • Understand the effects of intermittency in the swarm’s non-equilibrium dynamics • Consider new order parameters • New quantitative experiments • (With Paul Umbanhowar)

More Related