<!-- 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">0.9.47.6</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) “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, <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>