aboutsummaryrefslogtreecommitdiff
path: root/docs/reference/FOMC.solution.html
blob: abda4d8180faa752d365f90fb3760f499cf831e0 (plain) (blame)
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
<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html>
  <head>
  <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>First-Order Multi-Compartment kinetics — FOMC.solution • mkin</title>

<!-- jquery -->
<script src="https://code.jquery.com/jquery-3.1.0.min.js" integrity="sha384-nrOSfDHtoPMzJHjVTdCopGqIqeYETSXhZDFyniQ8ZHcVy08QesyHcnOUpMpqnmWq" crossorigin="anonymous"></script>
<!-- Bootstrap -->

<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-BVYiiSIFeK1dGmJRAkycuHAHRg32OmUcww7on3RYdg4Va+PmSTsz/K68vbdEjh4u" crossorigin="anonymous">
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha384-Tc5IQib027qvyjSMfHjOMaLkfuWVxZxUPnCJA7l2mCWNIpG9mGCD8wGNIcPD7Txa" crossorigin="anonymous"></script>

<!-- Font Awesome icons -->
<link href="https://maxcdn.bootstrapcdn.com/font-awesome/4.6.3/css/font-awesome.min.css" rel="stylesheet" integrity="sha384-T8Gy5hrqNKT+hzMclPo118YTQO6cYprQmhrYwIiQ/3axmI1hQomh7Ud2hPOy8SP1" crossorigin="anonymous">

<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/1.7.1/clipboard.min.js" integrity="sha384-cV+rhyOuRHc9Ub/91rihWcGmMmCXDeksTtCihMupQHSsi8GIIRDG0ThDc3HGQFJ3" crossorigin="anonymous"></script>

<!-- sticky kit -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/sticky-kit/1.1.3/sticky-kit.min.js" integrity="sha256-c4Rlo1ZozqTPE2RLuvbusY3+SU1pQaJC0TjuhygMipw=" crossorigin="anonymous"></script>

<!-- pkgdown -->
<link href="../pkgdown.css" rel="stylesheet">
<script src="../pkgdown.js"></script>



<meta property="og:title" content="First-Order Multi-Compartment kinetics — FOMC.solution" />

<meta property="og:description" content="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 beta corresponds to 1/beta in the
  original equation." />
<meta name="twitter:card" content="summary" />



<!-- mathjax -->
<script src='https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML'></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>
    <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">
        <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="label label-default" data-toggle="tooltip" data-placement="bottom" title="Released package">0.9.47.5</span>
      </span>
    </div>

    <div id="navbar" class="navbar-collapse collapse">
      <ul class="nav navbar-nav">
        <li>
  <a href="../reference/index.html">Functions and data</a>
</li>
<li class="dropdown">
  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" 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>
      <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>
      <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
    </li>
    <li>
      <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
    </li>
  </ul>
</li>
<li>
  <a href="../news/index.html">News</a>
</li>
      </ul>
      
      <ul class="nav navbar-nav navbar-right">
        
      </ul>
      
    </div><!--/.nav-collapse -->
  </div><!--/.container -->
</div><!--/.navbar -->

      
      </header>

<div class="row">
  <div class="col-md-9 contents">
    <div class="page-header">
    <h1>First-Order Multi-Compartment kinetics</h1>
    
    <div class="hidden name"><code>FOMC.solution.Rd</code></div>
    </div>

    <div class="ref-description">
    
    <p>Function describing exponential decline from a defined starting value, with 
  a decreasing rate constant.</p>
<p>The form given here differs slightly from the original reference by Gustafson
  and Holden (1990). The parameter <code>beta</code> corresponds to 1/beta in the
  original equation.</p>
    
    </div>

    <pre class="usage"><span class='fu'>FOMC.solution</span>(<span class='no'>t</span>, <span class='no'>parent.0</span>, <span class='no'>alpha</span>, <span class='no'>beta</span>)</pre>
    
    <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
    <table class="ref-arguments">
    <colgroup><col class="name" /><col class="desc" /></colgroup>
    <tr>
      <th>t</th>
      <td><p>Time.</p></td>
    </tr>
    <tr>
      <th>parent.0</th>
      <td><p>Starting value for the response variable at time zero.</p></td>
    </tr>
    <tr>
      <th>alpha</th>
      <td><p>Shape parameter determined by coefficient of variation of rate constant
    values.</p></td>
    </tr>
    <tr>
      <th>beta</th>
      <td><p>Location parameter.</p></td>
    </tr>
    </table>
    
    <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2>

    <p>The solution of the FOMC kinetic model reduces to the
  <code><a href='SFO.solution.html'>SFO.solution</a></code> for large values of <code>alpha</code> and
  <code>beta</code> with 
  \(k = \frac{\beta}{\alpha}\).</p>
    
    <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>

    <p>The value of the response variable at time <code>t</code>.</p>
    
    <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>

    <p>FOCUS (2006) &#8220;Guidance Document on Estimating Persistence and
  Degradation Kinetics from Environmental Fate Studies on Pesticides in EU
  Registration&#8221; Report of the FOCUS Work Group on Degradation Kinetics,
  EC Document Reference Sanco/10058/2005 version 2.0, 434 pp,
  <a href='http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics'>http://esdac.jrc.ec.europa.eu/projects/degradation-kinetics</a></p>
<p>Gustafson DI and Holden LR (1990) Nonlinear pesticide dissipation in soil: A
  new model based on spatial variability. <em>Environmental Science and 
  Technology</em> <b>24</b>, 1032-1038</p>
    

    <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
    <pre class="examples"><div class='input'>  <span class='fu'>plot</span>(<span class='kw'>function</span>(<span class='no'>x</span>) <span class='fu'>FOMC.solution</span>(<span class='no'>x</span>, <span class='fl'>100</span>, <span class='fl'>10</span>, <span class='fl'>2</span>), <span class='fl'>0</span>, <span class='fl'>2</span>, <span class='kw'>ylim</span> <span class='kw'>=</span> <span class='fu'>c</span>(<span class='fl'>0</span>, <span class='fl'>100</span>))</div><div class='img'><img src='FOMC.solution-1.png' alt='' width='700' height='433' /></div></pre>
  </div>
  <div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
    <h2>Contents</h2>
    <ul class="nav nav-pills nav-stacked">
      <li><a href="#arguments">Arguments</a></li>
      
      <li><a href="#note">Note</a></li>

      <li><a href="#value">Value</a></li>

      <li><a href="#references">References</a></li>
      
      <li><a href="#examples">Examples</a></li>
    </ul>

  </div>
</div>

      <footer>
      <div class="copyright">
  <p>Developed by Johannes Ranke.</p>
</div>

<div class="pkgdown">
  <p>Site built with <a href="http://pkgdown.r-lib.org/">pkgdown</a>.</p>
</div>

      </footer>
   </div>

  

  </body>
</html>

Contact - Imprint