riemann-nonconvex

Simulation of a totally asymmetric attractive interacting particle system

This is a supplemental material to the article Márton Balázs, Attila László Nagy, Bálint Tóth, István Tóth: Coexistence of Shocks and Rarefaction Fans: Complex Phase Diagram of a Simple Hyperbolic Particle System (2016). The article was published in the Journal of Statistical Physics, Volume 165, Issue 1, October 2016. The official abstract page is available here. A read-only shared PDF version of the full text can be found here.

Microscopic model

Markov jump process on a 1-dim discrete N-torus with rates c between neighbouring lattice points.

Initial data

Step-function (Riemann problem)

Files

• runsim.sh: script to run a bunch of simulations and create movies
• sim/sim.c: source code of the simulation

View the comments in sim.c to adjust parameters. Feel free to customize runsim.sh to run the simulations needed.

Examples

Here are some result videos from example runs using common parameters and different initial densities.

The common paramaters are:

• number of lattice points on torus: N=5000
• parameters in rates: A=0, B=0.0176654
• time elapsed between shots taken: DT_SHOT=5000
• total number of shots: SHOTS=5000
• number of independent simulations to calc the average: SUM=10000

The following examples illustrate the different phenomenons due to the initial densities on the left (vl) and right (vr):

vl	vr	center	edge	video link
0.7	0.5	R	S
0.8	-0.65	RSR	S
-0.74	-0.4	S	R
0.15	-0.55	SR	SR
-0.4	0.5	SRS	RS
0.75	0	RS	S

(abbrevations: S=shock wave, R=rarefaction fan)