1 Implementing 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

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

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

2 Implementating 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 \((v\bigtriangleup t/r << 1)\)

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

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

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