1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
|
<!DOCTYPE html>
<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Indeterminate order rate equation kinetics — IORE.solution • mkin</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Indeterminate order rate equation kinetics — IORE.solution"><meta property="og:description" content="Function describing exponential decline from a defined starting value, with
a concentration dependent rate constant."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]--></head><body data-spy="scroll" data-target="#toc">
<div class="container template-reference-topic">
<header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<span class="navbar-brand">
<a class="navbar-link" href="../index.html">mkin</a>
<span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.6</span>
</span>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav"><li>
<a href="../reference/index.html">Reference</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
Articles
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu"><li>
<a href="../articles/mkin.html">Introduction to mkin</a>
</li>
<li class="divider">
<li class="dropdown-header">Example evaluations with (generalised) nonlinear least squares</li>
<li>
<a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
</li>
<li>
<a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
</li>
<li>
<a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
</li>
<li class="divider">
<li class="dropdown-header">Example evaluations with hierarchical models (nonlinear mixed-effects models)</li>
<li>
<a href="../articles/prebuilt/2022_dmta_parent.html">Testing hierarchical parent degradation kinetics with residue data on dimethenamid and dimethenamid-P</a>
</li>
<li>
<a href="../articles/prebuilt/2022_dmta_pathway.html">Testing hierarchical pathway kinetics with residue data on dimethenamid and dimethenamid-P</a>
</li>
<li>
<a href="../articles/prebuilt/2023_mesotrione_parent.html">Testing covariate modelling in hierarchical parent degradation kinetics with residue data on mesotrione</a>
</li>
<li>
<a href="../articles/prebuilt/2022_cyan_pathway.html">Testing hierarchical pathway kinetics with residue data on cyantraniliprole</a>
</li>
<li>
<a href="../articles/web_only/dimethenamid_2018.html">Comparison of saemix and nlme evaluations of dimethenamid data from 2018</a>
</li>
<li>
<a href="../articles/web_only/multistart.html">Short demo of the multistart method</a>
</li>
<li class="divider">
<li class="dropdown-header">Performance</li>
<li>
<a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
</li>
<li>
<a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a>
</li>
<li>
<a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a>
</li>
<li class="divider">
<li class="dropdown-header">Miscellaneous</li>
<li>
<a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
</li>
<li>
<a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
</li>
</ul></li>
<li>
<a href="../news/index.html">News</a>
</li>
</ul><ul class="nav navbar-nav navbar-right"><li>
<a href="https://github.com/jranke/mkin/" class="external-link">
<span class="fab fa-github fa-lg"></span>
</a>
</li>
</ul></div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
</header><div class="row">
<div class="col-md-9 contents">
<div class="page-header">
<h1>Indeterminate order rate equation kinetics</h1>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/parent_solutions.R" class="external-link"><code>R/parent_solutions.R</code></a></small>
<div class="hidden name"><code>IORE.solution.Rd</code></div>
</div>
<div class="ref-description">
<p>Function describing exponential decline from a defined starting value, with
a concentration dependent rate constant.</p>
</div>
<div id="ref-usage">
<div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">IORE.solution</span><span class="op">(</span><span class="va">t</span>, <span class="va">parent_0</span>, <span class="va">k__iore</span>, <span class="va">N</span><span class="op">)</span></span></code></pre></div>
</div>
<div id="arguments">
<h2>Arguments</h2>
<dl><dt>t</dt>
<dd><p>Time.</p></dd>
<dt>parent_0</dt>
<dd><p>Starting value for the response variable at time zero.</p></dd>
<dt>k__iore</dt>
<dd><p>Rate constant. Note that this depends on the concentration
units used.</p></dd>
<dt>N</dt>
<dd><p>Exponent describing the nonlinearity of the rate equation</p></dd>
</dl></div>
<div id="value">
<h2>Value</h2>
<p>The value of the response variable at time <code>t</code>.</p>
</div>
<div id="note">
<h2>Note</h2>
<p>The solution of the IORE kinetic model reduces to the
<code><a href="SFO.solution.html">SFO.solution</a></code> if N = 1. The parameters of the IORE model can
be transformed to equivalent parameters of the FOMC mode - see the NAFTA
guidance for details.</p>
</div>
<div id="references">
<h2>References</h2>
<p>NAFTA Technical Working Group on Pesticides (not dated) Guidance
for Evaluating and Calculating Degradation Kinetics in Environmental Media</p>
</div>
<div id="see-also">
<h2>See also</h2>
<div class="dont-index"><p>Other parent solutions:
<code><a href="DFOP.solution.html">DFOP.solution</a>()</code>,
<code><a href="FOMC.solution.html">FOMC.solution</a>()</code>,
<code><a href="HS.solution.html">HS.solution</a>()</code>,
<code><a href="SFO.solution.html">SFO.solution</a>()</code>,
<code><a href="SFORB.solution.html">SFORB.solution</a>()</code>,
<code><a href="logistic.solution.html">logistic.solution</a>()</code></p></div>
</div>
<div id="ref-examples">
<h2>Examples</h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span></span></span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html" class="external-link">plot</a></span><span class="op">(</span><span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="fu">IORE.solution</span><span class="op">(</span><span class="va">x</span>, <span class="fl">100</span>, <span class="fl">0.2</span>, <span class="fl">1.3</span><span class="op">)</span>, <span class="fl">0</span>, <span class="fl">2</span>, ylim <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0</span>, <span class="fl">100</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-plt img"><img src="IORE.solution-1.png" alt="" width="700" height="433"></span>
<span class="r-in"><span> <span class="co"># \dontrun{</span></span></span>
<span class="r-in"><span> <span class="va">fit.fomc</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"FOMC"</span>, <span class="va">FOCUS_2006_C</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
<span class="r-in"><span> <span class="va">fit.iore</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"IORE"</span>, <span class="va">FOCUS_2006_C</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
<span class="r-in"><span> <span class="va">fit.iore.deS</span> <span class="op"><-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"IORE"</span>, <span class="va">FOCUS_2006_C</span>, solution_type <span class="op">=</span> <span class="st">"deSolve"</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> Error in is.loaded(initfunc, PACKAGE = dllname, type = "") : </span>
<span class="r-out co"><span class="r-pr">#></span> invalid 'PACKAGE' argument</span>
<span class="r-in"><span></span></span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span><span class="va">fit.fomc</span><span class="op">$</span><span class="va">par</span>, <span class="va">fit.iore</span><span class="op">$</span><span class="va">par</span>, <span class="va">fit.iore.deS</span><span class="op">$</span><span class="va">par</span>,</span></span>
<span class="r-in"><span> row.names <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste</a></span><span class="op">(</span><span class="st">"model par"</span>, <span class="fl">1</span><span class="op">:</span><span class="fl">4</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> fit.fomc.par fit.iore.par fit.iore.deS.par</span>
<span class="r-out co"><span class="r-pr">#></span> model par 1 85.87489063 85.874890 85.874890</span>
<span class="r-out co"><span class="r-pr">#></span> model par 2 0.05192238 -4.826631 -4.826631</span>
<span class="r-out co"><span class="r-pr">#></span> model par 3 0.65096665 1.949403 1.949403</span>
<span class="r-out co"><span class="r-pr">#></span> model par 4 1.85744396 1.857444 1.857444</span>
<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/print.html" class="external-link">print</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span>fomc <span class="op">=</span> <span class="fu"><a href="endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fit.fomc</span><span class="op">)</span><span class="op">$</span><span class="va">distimes</span>, iore <span class="op">=</span> <span class="fu"><a href="endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fit.iore</span><span class="op">)</span><span class="op">$</span><span class="va">distimes</span>,</span></span>
<span class="r-in"><span> iore.deS <span class="op">=</span> <span class="fu"><a href="endpoints.html">endpoints</a></span><span class="op">(</span><span class="va">fit.iore</span><span class="op">)</span><span class="op">$</span><span class="va">distimes</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#></span> DT50 DT90 DT50back</span>
<span class="r-out co"><span class="r-pr">#></span> fomc 1.785233 15.1479 4.559973</span>
<span class="r-out co"><span class="r-pr">#></span> iore 1.785233 15.1479 4.559973</span>
<span class="r-out co"><span class="r-pr">#></span> iore.deS 1.785233 15.1479 4.559973</span>
<span class="r-in"><span> <span class="co"># }</span></span></span>
<span class="r-in"><span></span></span>
</code></pre></div>
</div>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
<nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
</nav></div>
</div>
<footer><div class="copyright">
<p></p><p>Developed by Johannes Ranke.</p>
</div>
<div class="pkgdown">
<p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.7.</p>
</div>
</footer></div>
</body></html>
|
