unnormalized_Vicsek: Unnormalized Vicsek model simulation
In FastGaSP: Fast and Exact Computation of Gaussian Stochastic Process

unnormalized_Vicsek

R Documentation

Unnormalized Vicsek model simulation

Description

Simulates particle movement according to the unnormalized Vicsek model, where particles align their velocities with neighboring particles within a specified radius, subject to noise. The model implements both Gaussian and uniform noise options.

Usage

unnormalized_Vicsek(p0,v0,n_t,T_sim,h,cut_r,
                    sigma_0,noise_type='Gaussian')

Arguments

`p0`	A numeric vector of initial positions for all particles, structured as (x1, y1, x2, y2, ..., xn, yn).
`v0`	A numeric vector of initial velocities for all particles, structured similarly to p0.
`n_t`	An integer specifying the number of particles.
`T_sim`	An integer specifying the number of time steps to simulate.
`h`	A numeric value specifying the time step size.
`cut_r`	A numeric value specifying the interaction radius within which particles align.
`sigma_0`	A numeric value specifying the noise strength.
`noise_type`	A character string specifying the type of noise: either "Gaussian" (default) or "Uniform".

Value

Returns a list with three components:

`pos`	A matrix of dimension (2*n_t) x (T_sim+1) containing particle positions at each time step.
`v`	A matrix of dimension (2*n_t) x (T_sim+1) containing particle velocities at each time step.