2014/06/26 by Maksym Romenskyy, Romenskyy, Maksym, Vladimir Lobaskin +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Biological Physics (physics.bio-ph) #Chemical and Physical Properties of Materials #FOS: Physical sciences #Insect and Arachnid Ecology and Behavior #Micro and Nano Robotics #Scientific Research and Discoveries #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1406.6921
openalex publication_date 2014/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the orientational ordering in systems of self-propelled particles\nwith selective interactions. To introduce the selectivity we augment the\nstandard Vicsek model with a bounded-confidence collision rule: a given\nparticle only aligns to neighbors who have directions quite similar to its own.\nNeighbors whose directions deviate more than a fixed restriction angle \α\nare ignored. The collective dynamics of this systems is studied by agent-based\nsimulations and kinetic mean field theory. We demonstrate that the reduction of\nthe restriction angle leads to a critical noise amplitude decreasing\nmonotonically with that angle, turning into a power law with exponent 3/2 for\nsmall angles. Moreover, for small system sizes we show that upon decreasing the\nrestriction angle, the kind of the transition to polar collective motion\nchanges from continuous to discontinuous. Thus, an apparent tricritical point\nis identified and calculated analytically. We also find that at very small\ninteraction angles the polar ordered phase becomes unstable with respect to the\napolar phase. We show that the mean-field kinetic theory permits stationary\nnematic states below a restriction angle of 0.681 \π. We calculate the\ncritical noise, at which the disordered state bifurcates to a nematic state,\nand find that it is always smaller than the threshold noise for the transition\nfrom disorder to polar order. The disordered-nematic transition features two\ntricritical points: At low and high restriction angle the transition is\ndiscontinuous but continuous at intermediate \α. We generalize our\nresults to systems that show fragmentation into more than two groups and obtain\nscaling laws for the transition lines and the corresponding tricritical points.\nA novel numerical method to evaluate the nonlinear Fredholm integral equation\nfor the stationary distribution function is also presented.\n