Lab 5 : Self Propelled Particles

1 Viscek Model : Polarization

• Polarisation based on the paper of Vicsek et al. (1995)
• How to form polarized groups of free particles
• Vsicel Model in polar coordinate system
• Motions of Equations:
• \(\left \langle \theta_{j}(t) \right \rangle_{r}\) is the average orientiation of particles at distance smaller than \(r\) with respect to particel \(i\)
• \(\bigtriangleup \theta_{i}\) is the rotational nosie

1.1 Case I : video

particle_no = 400
boxsize = 300
speed0 = 3.5
radius0 = 10
noise_intensity = 0.2
noise_mode = "polarisation"
sim_run = 700

• links : https://www.youtube.com/watch?v=4HJ-ZxhU-go&t=47s
• please copy and paste the link to your brower if Rpub blocked youtube

1.2 Case II : video

particle_no = 400
boxsize = 300
speed0 = 3.5
radius0 = 10
noise_intensity = 0.5
noise_mode = "polarisation"
sim_run = 700

• links : https://www.youtube.com/watch?v=EKDCEoaDUjs
• please copy and paste the link to your brower if Rpub blocked youtube

1.3 Polarisation (Order Parameter) Vs noise intensity

2 Modified Viscek Model : Attraction

• The following attraction Model and equations chosen from the paper of Costanzo and Hemelrijk (2018).

• To perform attraction, the following parameters have to modfiy

• Maximal angular velocity

  

• \(\omega = [0/\bigtriangleup t, +\pi/\bigtriangleup t]\)

• \(\bigtriangleup \Theta_{i} = [-\pi, +\pi]\)

• when \(v = 0\), particles do not move and mill

• when \(v => \infty\), particles get complete mixing without milling

• For milling (attraction) when \(v > 0\) and \((v\bigtriangleup t/r << 1)\)

2.1 Case I : video

particle_no = 400
boxsize = 1000
speed0 = 20
radius0 = 15
noise_intensity = 0.1
noise_mode = "attraction"
sim_run = 600

• links : https://youtu.be/nMgTDm25o6A
• please copy and paste the link to your brower if Rpub blocked youtube

2.2 Case II : video

particle_no = 400
boxsize = 1000
speed0 = 20
radius0 = 15
noise_intensity = 0.5
noise_mode = "attraction"
sim_run = 600

• links : https://youtu.be/9M4Uxpo5qEs
• please copy and paste the link to your brower if Rpub blocked youtube

2.3 Case III : video

particle_no = 400
boxsize = 1000
speed0 = 20
radius0 = 15
noise_intensity = 0.9
noise_mode = "attraction"
sim_run = 600

• links : https://youtu.be/oedk4t6l4Vs
• please copy and paste the link to your brower if Rpub blocked youtube

2.4 Attraction (Order Parameter) Vs noise intensity

2.5 Phase diagram : Attraction (OP) Vs Noisy Intensity

• with the attraction Model the paper of Costanzo and Hemelrijk (2018), it found that the phase transition diagram is at noise intensity = 0.5, where the order of parameter for Attraction is minmium.

Reference

Costanzo, A, and CK Hemelrijk. 2018. “Spontaneous Emergence of Milling (Vortex State) in a Vicsek-Like Model.” Journal of Physics D: Applied Physics 51 (13): 134004.

Vicsek, Tamás, András Czirók, Eshel Ben-Jacob, Inon Cohen, and Ofer Shochet. 1995. “Novel Type of Phase Transition in a System of Self-Driven Particles.” PRL 75 (6): 1226–9. https://link.aps.org/doi/10.1103/PhysRevLett.75.1226.