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The HoneyComb Paradigm for Research on Collective Human Behavior

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Published on: January 19, 2019

Topological-distance-dependent transition in flocks with binary interactions.

Biplab Bhattacherjee¹, Shradha Mishra¹, S S Manna¹

¹Satyendra Nath Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata-700098, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 15, 2016

Summary

This summary is machine-generated.

This study reveals unique phase transitions in binary flocking models. For n=1, a novel transition occurs, while n=2 shows a standard discontinuous transition, and n≥3 exhibit continuous transitions.

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Area of Science:

Complex Systems
Statistical Physics
Agent-Based Modeling

Background:

Flocking models simulate collective behavior in systems with many interacting agents.
Binary flock models simplify interactions to focus on pairwise dynamics and topological neighbors.
Understanding phase transitions in these models is crucial for explaining emergent order.

Purpose of the Study:

To investigate phase transitions in a binary flocking model with varying topological neighbor parameters (n).
To characterize the nature of transitions (discontinuous, continuous) based on the value of n.
To analyze the stability of flocking states using hydrodynamic equations.

Main Methods:

Extensive numerical simulations of the binary flocking model.
Analysis of order parameter behavior across different topological neighbor values (n=1, 2, ≥3).
Linear stability analysis of hydrodynamic equations for the polarized state.

Main Results:

A novel discontinuous transition observed for n=1, characterized by a delayed switch to an ordered state.
A standard discontinuous transition between two metastable states identified for n=2.
Continuous transitions observed for n≥3.
Hydrodynamic analysis confirms instability of the polarized state near critical points, with critical speed increasing with n.

Conclusions:

The topological neighbor parameter (n) significantly influences the type of phase transition in binary flocking models.
The n=1 transition represents a unique dynamic where order emerges after an initial delay.
Hydrodynamic stability analysis supports simulation findings and provides insights into critical phenomena.