Cyclic and coherent states in flocks with topological distance

Frontiers in Physics

Bhattacharya, Kunal¹  Manna, Subhrangshu Sekhar²  Bhattacherjee, Biplab² 

[1] Birla Institute of Technology and Science, Pilani, Department of Physics, Pilani - 333031, Pilani, Rajasthan, India;Satyendra Nath Bose National Centre for Basic Sciences, Department of Theoretical Sciences, Block-JD, Sector-III, Salt Lake, Kolkata, 700098, West Bengal, India

关键词: collective behavior;    Flocking;    Cyclic states;    Phase Transition;    spin model;   

DOI  :  10.3389/fphy.2013.00035

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

A simple model of the two dimensional collective motion of a group of mobile agents have been studied.Like birds, these agents travel in open free space where each of them interacts with the first $n$neighbors determined by the topological distance with a free boundary condition. Using the same prescriptionfor interactions used in the Vicsek model with scalar noise it has been observed that the flock,in absence of the noise, arrives at a number of interesting stationary states. One of the two most prominentstates is the `single sink state' where the entire flock travels along the same direction maintaining perfectcohesion and coherence. The other state is the `cyclic state' where every individual agent executes a uniformcircular motion, and the correlation among the agents guarantees that the entire flock executes a pulsatingdynamics i.e., expands and contracts periodically between a minimum and a maximum size of the flock. We have studied another limiting situation when refreshing rate of the interaction zone is the fastest. In this case the entire flock gets fragmented into smaller clusters of different sizes.On introduction of scalar noise a crossover is observed when the agents cross over from a ballisticmotion to a diffusive motion. Expectedly the crossover time is dependent on the strength of thenoise $\eta$ and diverges as $\eta \to 0$.An even more simpler version of this model has been studied by suppressing the translationaldegrees of freedom of the agents but retaining their angular motion. Here agents are the spins,placed at the sites of a square lattice with periodic boundary condition. Every spin interacts withits $n$ = 2, 3 or 4 nearest neighbors. In the stationary state the entire spin pattern moves as a whole when interactions are anisotropic with $n$ = 2 and 3; but it is completely frozen when the interaction is isotropic with $n=4$. These spin configu.

【 授权许可】

CC BY