path: root/R/FOMC.solution.R

#' First-Order Multi-Compartment kinetics
#' 
#' Function describing exponential decline from a defined starting value, with
#' a decreasing rate constant.
#' 
#' The form given here differs slightly from the original reference by
#' Gustafson and Holden (1990). The parameter \code{beta} corresponds to 1/beta
#' in the original equation.
#' 
#' @param t Time.
#' @param parent.0 Starting value for the response variable at time zero.
#' @param alpha Shape parameter determined by coefficient of variation of rate
#'   constant values.
#' @param beta Location parameter.
#' @return The value of the response variable at time \code{t}.
#' @note The solution of the FOMC kinetic model reduces to the
#'   \code{\link{SFO.solution}} for large values of \code{alpha} and
#'   \code{beta} with \eqn{k = \frac{\beta}{\alpha}}{k = beta/alpha}.
#' @references FOCUS (2006) \dQuote{Guidance Document on Estimating Persistence
#'   and Degradation Kinetics from Environmental Fate Studies on Pesticides in
#'   EU Registration} Report of the FOCUS Work Group on Degradation Kinetics,
#'   EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
#'   \url{http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics}
#' 
#'   Gustafson DI and Holden LR (1990) Nonlinear pesticide dissipation in soil:
#'   A new model based on spatial variability. \emph{Environmental Science and
#'   Technology} \bold{24}, 1032-1038
#' @examples
#' 
#'   plot(function(x) FOMC.solution(x, 100, 10, 2), 0, 2, ylim = c(0, 100))
#' 
#' @export
FOMC.solution <- function(t, parent.0, alpha, beta)
{
	parent = parent.0 / (t/beta + 1)^alpha
}