{"id":4171,"date":"2023-03-18T11:36:59","date_gmt":"2023-03-18T10:36:59","guid":{"rendered":"http:\/\/mosaic-modeling.de\/?page_id=4171"},"modified":"2023-08-22T09:45:35","modified_gmt":"2023-08-22T08:45:35","slug":"model-equation","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=4171","title":{"rendered":"Model: Equation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">On this page<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4171\/#Purpose\" >Purpose<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4171\/#Explanation-of-the-editor\" >Explanation of the editor<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4171\/#Workflow\" >Workflow<\/a><\/li><\/ul><\/nav><\/div>\n\n<p class=\"has-vivid-red-color has-text-color\"><strong>Mandatory element<\/strong><\/p>\n\n\n<p>Once you have defined base names etc. that appear in your equations, you can start to write the actual equations. Basic MOSAICmodeling models consist of equations with a single <a href=\"http:\/\/mosaic-modeling.de\/?page_id=4145\">notation<\/a>. These are then joined together to form an <a href=\"http:\/\/mosaic-modeling.de\/?page_id=4177\">equation system<\/a>.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Purpose\"><\/span>Purpose<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>This tab is used to actually write down the individual equations that you need in your model. In MOSAICmodeling, you formulate your equations in a LaTeX-based syntax. This means that you can actually see the mathematical expressions as an easily readable output during the formulation. The editor to create or edit an equation inside MOSAICmodeling is shown in Figure 1. This editor has a toolbox, which can be opened via the &#8220;Open Toolbox&#8221; button and can assist you in formulating equations.<\/p>\n<figure id=\"attachment_3000\" aria-describedby=\"caption-attachment-3000\" style=\"width: 926px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2016\/12\/EquationEditor.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3000 size-full\" src=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2016\/12\/EquationEditor.png\" alt=\"\" width=\"926\" height=\"649\" srcset=\"https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2016\/12\/EquationEditor.png 926w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2016\/12\/EquationEditor-300x210.png 300w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2016\/12\/EquationEditor-768x538.png 768w\" sizes=\"auto, (max-width: 926px) 100vw, 926px\" \/><\/a><figcaption id=\"caption-attachment-3000\" class=\"wp-caption-text\">Figure 1: The equation editor inside MOSAICmodeling lets you formulate your equation and directly gives you a readable output of the current equation. Note that this editor might look differently depending on your operating system.<\/figcaption><\/figure>\n\n\n<figure class=\"wp-block-table has-small-font-size\"><table><thead><tr><th>Mathematical operator<\/th><th>Command in MOSAICmodeling<\/th><th>Rendered form<\/th><\/tr><\/thead><tbody><tr><td>Multiplication<\/td><td>a \\cdot b<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5c62994c977fa44b6c1447fb6e17c24c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td>Division<\/td><td>a \/ b<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-48605613f881016110b88732825ef9bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#97;&#32;&#47;&#32;&#98;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"\/><\/td><\/tr><tr><td>Fraction<\/td><td>\\frac{a}{b}<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-09c93a255add425d26853e2052ef3026_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\"\/><\/td><\/tr><tr><td>Power function<\/td><td>(a)^{b}<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-faf658ba8303b0121efd1ca6212b21a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#40;&#97;&#41;&#94;&#123;&#98;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"28\" style=\"vertical-align: -5px;\"\/><\/td><\/tr><tr><td>n-th root<\/td><td>(a)^{1\/n}<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e9c6e58ebcffd32e295f2baccf256367_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#40;&#97;&#41;&#94;&#123;&#49;&#47;&#110;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"44\" style=\"vertical-align: -5px;\"\/><\/td><\/tr><tr><td>Exponential function<\/td><td>\\exp(a)<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-a652976cc2149e3094885880be8b5794_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#101;&#120;&#112;&#40;&#97;&#41;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"49\" style=\"vertical-align: -5px;\"\/><\/td><\/tr><tr><td>Natural logarithm<\/td><td>\\ln(a)<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-71bb513c54b85aeed76a369e73fc7bf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#108;&#110;&#40;&#97;&#41;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"\/><\/td><\/tr><tr><td>Sine<\/td><td>\\sin(a)<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c37dae10c43b92a1305aa3d3161710bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#115;&#105;&#110;&#40;&#97;&#41;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\"\/><\/td><\/tr><tr><td>Cosine<\/td><td>\\cos(a)<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8bf0d37553705b21c1c22da417d01c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#99;&#111;&#115;&#40;&#97;&#41;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -5px;\"\/><\/td><\/tr><tr><td>Summation<\/td><td>\\sum_{i=1}^{Ni}{x_{i}}<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6a7bf3c2f72d64d447b80f88a57f3b44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#115;&#117;&#109;&#95;&#123;&#105;&#61;&#49;&#125;&#94;&#123;&#78;&#105;&#125;&#32;&#120;&#95;&#123;&#105;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -5px;\"\/><\/td><\/tr><tr><td>Derivative<\/td><td>\\diff{x}{t}<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-dfa83265b7b522851909c265e5c1052f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#32;&#120;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#32;&#116;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"16\" style=\"vertical-align: -6px;\"\/><\/td><\/tr><tr><td>Partial derivative<\/td><td>\\pdiff{a}{b}<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-30fdd95ce042b35d66db992514f826d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#32;&#97;&#125;&#123;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#32;&#98;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"16\" style=\"vertical-align: -6px;\"\/><\/td><\/tr><tr><td>Second partial derivative<\/td><td>\\p2diff{a}{b}{c}<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-673f9e9c734e7b35794c56145a119e40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#94;&#50;&#32;&#97;&#125;&#123;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#32;&#98;&#32;&#92;&#112;&#97;&#114;&#116;&#105;&#97;&#108;&#32;&#99;&#125;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"28\" style=\"vertical-align: -6px;\"\/><\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Overview of commands available in the toolbox<\/figcaption><\/figure>\n\n\n<h3><span class=\"ez-toc-section\" id=\"Explanation-of-the-editor\"><\/span>Explanation of the editor<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Table 2 explains the entries of the equation editor.<\/p>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th>Element<\/th><th class=\"has-text-align-left\" data-align=\"left\">Explanation<\/th><\/tr><\/thead><tbody><tr><td>File<\/td><td class=\"has-text-align-left\" data-align=\"left\">Filename of your equation once you have saved or loaded it<\/td><\/tr><tr><td>Parameters<\/td><td class=\"has-text-align-left\" data-align=\"left\">Filename of your loaded parameter list<\/td><\/tr><tr><td>Description<\/td><td class=\"has-text-align-left\" data-align=\"left\">Description of your equation, e.g., mass balance. A description is always necessary<\/td><\/tr><tr><td>Keywords<\/td><td class=\"has-text-align-left\" data-align=\"left\">Optional keywords for your equation<\/td><\/tr><tr><td>MosaicTeX<\/td><td class=\"has-text-align-left\" data-align=\"left\">Window for writing the equation<\/td><\/tr><tr><td>Toolbox<\/td><td class=\"has-text-align-left\" data-align=\"left\">Opens window that contains helpful commands for quickly writing model equations<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 2: Elements of the equation editor.<\/figcaption><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Workflow\"><\/span>Workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<p>The image below illustrates the workflow to set up an equation.<\/p>\n<figure id=\"attachment_3238\" aria-describedby=\"caption-attachment-3238\" style=\"width: 803px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-3238 size-full\" src=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-Workflow-3.png\" alt=\"\" width=\"803\" height=\"814\" srcset=\"https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-Workflow-3.png 803w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-Workflow-3-296x300.png 296w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/08\/Equation-Workflow-3-768x779.png 768w\" sizes=\"auto, (max-width: 803px) 100vw, 803px\" \/><figcaption id=\"caption-attachment-3238\" class=\"wp-caption-text\">Figure 2: Workflow to set up an equation.<\/figcaption><\/figure>","protected":false},"excerpt":{"rendered":"<p>Mandatory element Once you have defined base names etc. that appear in your equations, you can start to write the actual equations. Basic MOSAICmodeling models consist of equations with a single notation. These are then joined together to form an equation system. Purpose This tab is used to actually write down the individual equations that [&hellip;]<\/p>\n","protected":false},"author":252,"featured_media":0,"parent":4140,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4171","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/users\/252"}],"replies":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4171"}],"version-history":[{"count":18,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4171\/revisions"}],"predecessor-version":[{"id":5680,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4171\/revisions\/5680"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4140"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}