Self-propelled particles with soft-core interactions: patterns, stability, and collapse.

Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones. We model self-propelling biological or artificial individuals interacting through pairwise attractive and repulsive forces. For the first time, we are able to predict stability and morphology of organization starting from the shape of the two-body interaction. We present a coherent theory, based on fundamental statistical mechanics, for all possible phases of collective motion.

[1]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[2]  D. Kaiser,et al.  Fruiting body morphogenesis in submerged cultures of Myxococcus xanthus , 1982, Journal of bacteriology.

[3]  D. Zusman,et al.  Patterns of cellular interactions during fruiting-body formation in Myxococcus xanthus , 1989, Journal of bacteriology.

[4]  D. Kaiser,et al.  Cell alignment required in differentiation of Myxococcus xanthus. , 1990, Science.

[5]  G. Golub,et al.  Scientific Computing and Differential Equations: An Introduction to Numerical Methods , 1991 .

[6]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[7]  Tu,et al.  Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together. , 1995, Physical review letters.

[8]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[9]  Arantxa Etxeverria.  The Origins of Order , 1993 .

[10]  Albano.  Self-Organized Collective Displacements of Self-Driven Individuals. , 1996, Physical review letters.

[11]  Hayakawa,et al.  Collective motion in a system of motile elements. , 1996, Physical review letters.

[12]  D. Ruelle.  Statistical Mechanics: Rigorous Results , 1999 .

[13]  Arthur L. Koch,et al.  The social lifestyle of myxobacteria , 1999 .

[14]  D. Grünbaum,et al.  From individuals to aggregations: the interplay between behavior and physics. , 1999, Journal of theoretical biology.

[15]  Marco Dorigo,et al.  Swarm intelligence: from natural to artificial systems , 1999 .

[16]  L. Edelstein-Keshet,et al.  Complexity, pattern, and evolutionary trade-offs in animal aggregation. , 1999, Science.

[17]  Robert C. Hilborn,et al.  Chaos and Nonlinear Dynamics , 2000 .

[18]  W Ebeling,et al.  Statistical mechanics of canonical-dissipative systems and applications to swarm dynamics. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  W. Rappel,et al.  Self-organization in systems of self-propelled particles. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  I. Couzin,et al.  Collective memory and spatial sorting in animal groups. , 2002, Journal of theoretical biology.

[21]  Lotte Søgaard-Andersen,et al.  Pattern formation by a cell surface-associated morphogen in Myxococcus xanthus , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Werner Ebeling,et al.  Excitation of rotational modes in two-dimensional systems of driven Brownian particles. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Kevin M. Passino,et al.  Stability analysis of swarms , 2003, IEEE Trans. Autom. Control..

[24]  Guy Theraulaz,et al.  Self-Organization in Biological Systems , 2001, Princeton studies in complexity.

[25]  Dale Kaiser,et al.  Coupling cell movement to multicellular development in myxobacteria , 2003, Nature Reviews Microbiology.

[26]  A. Mogilner,et al.  Mathematical Biology Mutual Interactions, Potentials, and Individual Distance in a Social Aggregation , 2003 .

[27]  Roy D. Welch,et al.  Waves and aggregation patterns in myxobacteria , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[28]  H. Chaté,et al.  Onset of collective and cohesive motion. , 2004, Physical review letters.

[29]  Jonathon Howard,et al.  A Self-Organized Vortex Array of Hydrodynamically Entrained Sperm Cells , 2005, Science.

[30]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.