f_Vicsek_variation: Modified Vicsek Interaction Function

In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

Modified Vicsek Interaction Function

Description

A modified interaction function for the Vicsek model that defines the interaction strength between particles based on their distance. This function is used as one of the interactions in the two-interaction Vicsek model.

Usage

f_Vicsek_variation(r, a = 0.02, b = 1, r_min = 0.01, r_max = 0.8, beta = 20)

Arguments

r	numeric, the distance between particles
a	numeric, strength parameter for the short-range interaction term. Default is 0.02
b	numeric, strength parameter for the linear term. Default is 1
r_min	numeric, minimum distance parameter for the interaction term. Default is 0.01
r_max	numeric, maximum distance parameter. Default is 0.8
beta	numeric, scaling parameter for the overall interaction. Default is 20

Details

The function implements a modified Vicsek interaction with three components:

• A short-range term (-a/(r+r_min))

• A linear term (-b*(r-r_max))

• A constant offset term (a/r_max)

The final value is scaled by the beta parameter.

Value

Returns a numeric value representing the interaction strength at distance r.

References

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

# Calculate interaction values at various distances
r_seq <- seq(0.01, 1, by = 0.01)
interaction <- f_Vicsek_variation(r_seq)
plot(r_seq, interaction, type = "l", 
     xlab = "Distance", ylab = "Interaction Strength",
     main = "Vicsek Variation Interaction Function")

FastGaSP documentation built on April 4, 2025, 5:16 a.m.