From 92bd33824bde6b6b21bfc7e30953092a74d3cce5 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Thu, 7 May 2020 22:13:33 +0200 Subject: Another overhaul of analytical solutions Still in preparation for analytical solutions of coupled models --- docs/reference/logistic.solution.html | 63 +++++------------------------------ 1 file changed, 9 insertions(+), 54 deletions(-) (limited to 'docs/reference/logistic.solution.html') diff --git a/docs/reference/logistic.solution.html b/docs/reference/logistic.solution.html index 9697d420..b0ec77b1 100644 --- a/docs/reference/logistic.solution.html +++ b/docs/reference/logistic.solution.html @@ -41,8 +41,6 @@ @@ -75,7 +73,7 @@ an increasing rate constant, supposedly caused by microbial growth" /> mkin - 0.9.49.11 + 0.9.50 @@ -139,20 +137,16 @@ an increasing rate constant, supposedly caused by microbial growth" />

Logistic kinetics

- Source: R/logistic.solution.R, R/parent_solutions.R + Source: R/parent_solutions.R

Function describing exponential decline from a defined starting value, with -an increasing rate constant, supposedly caused by microbial growth

-

Function describing exponential decline from a defined starting value, with an increasing rate constant, supposedly caused by microbial growth

- 
logistic.solution(t, parent_0, kmax, k0, r)
-
-logistic.solution(t, parent_0, kmax, k0, r)
+ 
logistic.solution(t, parent_0, kmax, k0, r)

Arguments

@@ -177,10 +171,6 @@ an increasing rate constant, supposedly caused by microbial growth

- - - -
r

Growth rate of the increase in the rate constant.
parent.0

Starting value for the response variable at time zero.

Value

@@ -189,12 +179,15 @@ an increasing rate constant, supposedly caused by microbial growth

Note

The solution of the logistic model reduces to the - SFO.solution if k0 is equal to kmax.

-

The solution of the logistic model reduces to the SFO.solution if k0 is equal to kmax.

References

-

FOCUS (2014) “Generic guidance for Estimating Persistence +

FOCUS (2006) “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, + http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics +FOCUS (2014) “Generic guidance for Estimating Persistence and Degradation Kinetics from Environmental Fate Studies on Pesticides in EU Registration” Report of the FOCUS Work Group on Degradation Kinetics, Version 1.1, 18 December 2014 @@ -247,44 +240,6 @@ an increasing rate constant, supposedly caused by microbial growth

#> k0 0.4448749 #> r 1.1821120 #> sigma 7.3256566
endpoints(m)$distimes
#> DT50 DT90 DT50_k0 DT50_kmax -#> parent 36.86533 62.41511 4297.853 10.83349
- - # Reproduce the plot on page 57 of FOCUS (2014) - plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.2), - from = 0, to = 100, ylim = c(0, 100), - xlab = "Time", ylab = "Residue")
plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.4), - from = 0, to = 100, add = TRUE, lty = 2, col = 2)
plot(function(x) logistic.solution(x, 100, 0.08, 0.0001, 0.8), - from = 0, to = 100, add = TRUE, lty = 3, col = 3)
plot(function(x) logistic.solution(x, 100, 0.08, 0.001, 0.2), - from = 0, to = 100, add = TRUE, lty = 4, col = 4)
plot(function(x) logistic.solution(x, 100, 0.08, 0.08, 0.2), - from = 0, to = 100, add = TRUE, lty = 5, col = 5)
legend("topright", inset = 0.05, - legend = paste0("k0 = ", c(0.0001, 0.0001, 0.0001, 0.001, 0.08), - ", r = ", c(0.2, 0.4, 0.8, 0.2, 0.2)), - lty = 1:5, col = 1:5)
- # Fit with synthetic data - logistic <- mkinmod(parent = mkinsub("logistic")) - - sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120) - parms_logistic <- c(kmax = 0.08, k0 = 0.0001, r = 0.2) - d_logistic <- mkinpredict(logistic, - parms_logistic, c(parent = 100), - sampling_times) - d_2_1 <- add_err(d_logistic, - sdfunc = function(x) sigma_twocomp(x, 0.5, 0.07), - n = 1, reps = 2, digits = 5, LOD = 0.1, seed = 123456)[[1]] - - m <- mkinfit("logistic", d_2_1, quiet = TRUE) - plot_sep(m)
summary(m)$bpar
#> Estimate se_notrans t value Pr(>t) Lower -#> parent_0 1.057896e+02 1.9023449703 55.610119 3.768361e-16 1.016451e+02 -#> kmax 6.398190e-02 0.0143201031 4.467978 3.841829e-04 3.929235e-02 -#> k0 1.612775e-04 0.0005866813 0.274898 3.940351e-01 5.846688e-08 -#> r 2.263946e-01 0.1718110715 1.317695 1.061044e-01 4.335843e-02 -#> sigma 5.332935e+00 0.9145907310 5.830952 4.036926e-05 3.340213e+00 -#> Upper -#> parent_0 109.9341588 -#> kmax 0.1041853 -#> k0 0.4448749 -#> r 1.1821120 -#> sigma 7.3256566
endpoints(m)$distimes
#> DT50 DT90 DT50_k0 DT50_kmax #> parent 36.86533 62.41511 4297.853 10.83349
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