simulate_particle: Simulate particle trajectories

Description

Simulates particle trajectories using either the standard Vicsek model or a two-interaction variation of the Vicsek model.

Usage

simulate_particle(v_abs, n_t = 100, T_sim = 5, h = 0.1,
    cut_r = 0.5, sigma_0 = 0.1,
    noise_type = "Gaussian", model = "Vicsek")

Value

Returns an S4 object of class particle.data. See particle.data-class for details of the returned object structure.

Arguments

v_abs: Absolute velocity magnitude for all particles.
n_t: Number of particles (default: 100).
T_sim: Total simulation time steps (default: 5).
h: Time step size for numerical integration (default: 0.1).
cut_r: Radius of interaction between particles (default: 0.5).
sigma_0: Standard deviation of noise (default: 0.1).
noise_type: Distribution of noise: "Gaussian" or "Uniform" (default: "Gaussian").
model: Type of interaction model: "Vicsek" or "two_interactions_Vicsek" (default: "Vicsek").

References

Vicsek, T., Czirok, A., Ben-Jacob, E., Cohen, I., & Shochet, O. (1995). Novel type of phase transition in a system of self-driven particles, Physical Review Letters, 75(6), 1226.

Chat'e, H., Ginelli, F., Gr'egoire, G., Peruani, F., & Raynaud, F. (2008). Modeling collective motion: variations on the Vicsek model, The European Physical Journal B, 64(3), 451-456.

Fang, X., & Gu, M. (2024). The inverse Kalman filter. arXiv:2407.10089.

Examples

Run this code

#--------------------------------------------------
# Example: Simulate using standard Vicsek model
#--------------------------------------------------
vx_abs=0.5
vy_abs=0.5
v_abs=sqrt(vx_abs^2+vy_abs^2)
sim1 <- simulate_particle(v_abs=v_abs)

#--------------------------------------------------
# Example: Simulate using two-interaction variation
#--------------------------------------------------
sim2 <- simulate_particle(v_abs=v_abs, model = 'two_interactions_Vicsek')