PHYSICS · Multi-part · Fermi University Physics · Computational Physics · Thermal, Statistical & Complex Systems · Monte Carlo and lattice simulation of physical systems
Many Parts, One Behaviour, Ch Emergence and self-organisation: collective order from local rules
Problem
A ring of L=10 cells, numbered 0 to 9 with cell 9 followed by cell 0, carries three cars moving towards higher numbers under the deterministic Nagel-Schreckenberg rule (ps=0) with vmax=2. At the start car A is in cell 0 with speed 2, car B in cell 3 with speed 0, and car C in cell 4 with speed 1.
((a)) Apply the update by hand, all cars in parallel, for four steps. Give each car's cell and speed after every step, and the total number of cells advanced by all three cars in each step.
((b)) Check that no step's total advance exceeds the number of empty cells on the ring, and compare the flow after the fourth step, total advance divided by L, with J(ρ)=min(ρvmax,1−ρ).