simulateRACVM: Rotational/Advective Correlated velocity movement

In EliGurarie/smoove: Simulation and Estimation of Correlated Velocity Movement (CVM) Models

Rotational/Advective Correlated velocity movement

Description

Simulates 2D correlated velocity movement model with rotation and advection

Usage

simulateRACVM(
  tau = 1,
  eta = 1,
  omega = 0,
  mu = 0,
  v0 = NULL,
  Tmax = 100,
  dt = 0.01
)

Arguments

tau	characteristic time scale of autocorrelation
eta	random speed parameter. In the case where \omega = 0, the mean square speed of movement is E(|V|^2) = \eta^2 + \mu^2. In the case were \mu = \omega = 0, the mean tangential speed is E(|V|) = \eta \sqrt(\pi)/2.
omega	rotational velocity
mu	advective velocity (can be complex value where real and imaginary parts are x and y components of velocity)
v0	initial velocity
Tmax	max time
dt	time interval of simulation

Details

This function simulates a Rotational-Advective CVM explicitly using the governing OU equation, using a discretization in which dt << tau.

Value

a list with the following elements

T

the time vector

V

the (complex) vector of velocities

Z

the (complex) vector of locations

XY

a two-column matrix of x-y coordinates of locations

parameters

a named list of model parameters.

See Also

estimateRACVM

Examples

require(smoove)

racvm1 <- simulateRACVM(tau = 4, eta = 1, omega = 2, mu = 0, Tmax = 100, dt = .01)
racvm2 <- simulateRACVM(tau = 4, eta = 1, omega = 0, mu = 1, Tmax = 100, dt = .01)
racvm3 <- simulateRACVM(tau = 4, eta = 1, omega = 2, mu = 1, Tmax = 100, dt = .01)

layout(rbind(c(1,2),c(1,3)))
sapply(list(racvm1, racvm2, racvm3),
       function(x)
         with(x, plot(
           Z,
           asp = 1,
           type = "l",
           main = paste0("RACVM(",
                         paste(unlist(parameters),
                               collapse = ", "), ")")
         )))


racvm1 <- simulateRACVM(tau = 3, eta = 32, omega = .5, mu = 0, Tmax = 10, dt = .1)
with(racvm1, scan_track(x = Re(Z), y = Im(Z), time = T))


# Compare with simulateRACVM2

# racvm1b <- simulateRACVM2(tau = 4, eta = 1, omega = 2, mu = 0, Tmax = 100, dt = .01)
# racvm2b <- simulateRACVM2(tau = 4, eta = 1, omega = 0, mu = 1, Tmax = 100, dt = .01)
# racvm3b <- simulateRACVM2(tau = 4, eta = 1, omega = 2, mu = 1, Tmax = 100, dt = .01)
# 
# racvm1 <- simulateRACVM(tau = 4, eta = 1, omega = 1, mu = 0, Tmax = 10, dt = .01)
# racvm1b <- simulateRACVM2(tau = 4, eta = 1, omega = 1, mu = 0, Tmax = 10, dt = .01)
# with(racvm1, scan_track(x = Re(Z), y = Im(Z), time = T))
# with(racvm1b, scan_track(x = Re(Z), y = Im(Z), time = T))

EliGurarie/smoove documentation built on June 2, 2025, 1:45 p.m.