PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems
Many Parts, One Behaviour, Ch Emergence and self-organisation: collective order from local rules
Problem
To estimate how ordered a swarm of N=6 drones is, an engineer reads off their headings (measured anticlockwise from east): 355∘, 5∘, 350∘, 8∘, 2∘, 358∘. He takes the arithmetic mean of the six angle values and reports a mean heading of 179.7∘ (almost due west), concluding: "The mean heading is nearly opposite to most of the individual headings, so the swarm is not flying together at all; it is disordered."
((a)) Find the error in this method.
((b)) Compute the correct order parameter va=∣∑ie^i∣/N for these six headings, treating all drones as moving at the same speed, and state whether the swarm is in fact ordered.