{"id":5490,"date":"2023-08-17T12:19:33","date_gmt":"2023-08-17T11:19:33","guid":{"rendered":"http:\/\/mosaic-modeling.de\/?page_id=5490"},"modified":"2024-07-14T14:54:42","modified_gmt":"2024-07-14T13:54:42","slug":"use-of-basic-elements-ii-ordinary-differential-equation-system","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=5490","title":{"rendered":"Use of Basic Elements II &#8211; Ordinary Differential Equation System"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 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=5490\/#Model-description\" >Model description<\/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=5490\/#Model-workflow\" >Model workflow<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Notation\" >Notation<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Base-names\" >Base names<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Indices\" >Indices<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Equations\" >Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Equation-system\" >Equation system<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Simulation-workflow\" >Simulation workflow<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Equation-system-2\" >Equation system<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Indexing\" >Indexing<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Specification\" >Specification<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mosaic-modeling.de\/?page_id=5490\/#Evaluation\" >Evaluation<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>This second example shall illustrate the formulation of an ordinary differential equation system (ODE system) in MOSAICmodeling. This example is the &#8220;Oregonator&#8221;, a theoretical model for a type of autocatalytic reactions. In this example, we will use the publication by D\u2019Ambrosio et al. (2018), DOI: 10.1007\/s10910-018-0922-5, as basis.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Model-description\"><\/span>Model description<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The model consists of three differential equations:<\/p>\n<p><p class=\"ql-left-displayed-equation\" style=\"line-height: 153px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-32ba4ee98ec8d6906769e4b21d5eec69_l3.png\" height=\"153\" width=\"405\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;&#38;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#88;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#116;&#125;&#32;&#61;&#32;&#107;&#95;&#49;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#65;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#89;&#32;&#45;&#32;&#107;&#95;&#50;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#88;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#89;&#32;&#43;&#32;&#107;&#95;&#51;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#65;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#88;&#32;&#45;&#32;&#50;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#107;&#95;&#52;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#88;&#94;&#50;&#32;&#92;&#92;&#91;&#50;&#101;&#120;&#93;&#38;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#89;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#116;&#125;&#32;&#61;&#32;&#45;&#32;&#107;&#95;&#49;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#65;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#89;&#32;&#45;&#32;&#107;&#95;&#50;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#88;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#89;&#32;&#43;&#32;&#102;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#107;&#95;&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#65;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#90;&#32;&#92;&#92;&#91;&#50;&#101;&#120;&#93;&#38;&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#90;&#125;&#123;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#100;&#125;&#116;&#125;&#32;&#61;&#32;&#107;&#95;&#51;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#65;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#88;&#32;&#45;&#32;&#107;&#95;&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#65;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#90;&#46;&#92;&#101;&#110;&#100;&#123;&#97;&#108;&#105;&#103;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n<p>Therein, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-42ae22abcaa05c2d6c2fdc3746446019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> are the concentrations of relevant intermediates of this reaction network, i.e., <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-718604eddc01c8743026b6de757e9c60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#72;&#66;&#114;&#79;&#125;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: -3px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fc2813488ff081661bcb0b2567ecedb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#66;&#114;&#125;&#94;&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\"\/>, and Ce(IV). <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"\/> is the concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-bbc0ea872adbc0ea6643f52e53f8eaef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#66;&#114;&#79;&#125;&#95;&#51;&#94;&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"43\" style=\"vertical-align: -5px;\"\/>, a constant. All <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-bac62f27b16785deeaaf701030a292a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: -3px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> are parameters of the kinetics. For a more thorough discussion of the underlying physics, please consult the literature on the oregonator. We want to focus on the model implementation here.<\/p>\n<div class=\"rtcContent\">\n<div class=\"lineNode\"><!-- [if mso]>\n<![endif]--><\/div>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"Model-workflow\"><\/span>Model workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"Notation\"><\/span>Notation<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>We beginn by setting up the notation. Therefore, perform the following steps:<\/p>\n<ol>\n<li>Go to the Notation tab in the &#8220;Model&#8221; section<\/li>\n<li>Add a description of your notation<\/li>\n<li>Add the base names below\u00a0by clicking on &#8220;+ Name&#8221; at the bottom, entering these names, adding a description of the variable and confirming it<\/li>\n<li>Go to the Indicies tab and add the index below<\/li>\n<li>Once you have added all variables and symbols, click on &#8220;Save&#8221; at the top of the editor and save your notation at a suitable location in your folder structure<\/li>\n<\/ol>\n<h5><span class=\"ez-toc-section\" id=\"Base-names\"><\/span>Base names<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"\/>, concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-bbc0ea872adbc0ea6643f52e53f8eaef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#66;&#114;&#79;&#125;&#95;&#51;&#94;&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"43\" style=\"vertical-align: -5px;\"\/> in mol\/L<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/>, Stoichiometric factor<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>, kinetic factor in various units<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/>, time in s<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>, concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-718604eddc01c8743026b6de757e9c60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#72;&#66;&#114;&#79;&#125;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: -3px;\"\/> in mol\/L<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-42ae22abcaa05c2d6c2fdc3746446019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fc2813488ff081661bcb0b2567ecedb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#66;&#114;&#125;&#94;&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\"\/> in mol\/L<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>,\u00a0concentration of Ce(IV) in mol\/L<\/li>\n<\/ul>\n<h5><span class=\"ez-toc-section\" id=\"Indices\"><\/span>Indices<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>, Index of kinetic factors 1..NK<\/li>\n<\/ul>\n<p>The notation of this example has ID 182866.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equations\"><\/span>Equations<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the Equation tab. Proceed as follows:<\/p>\n<ol>\n<li>Load the notation you just created<\/li>\n<li>Add an informative description of the current equation<\/li>\n<li>Type the first model equation in LaTeX style into the window MosaicTex. For the differential operator, you must use \\diff{Var}{IndependentVariable}<\/li>\n<li>Save the equation at a suitable location in your folder structure<\/li>\n<li>Click on &#8220;New&#8221; at the top of the editor and repeat the steps 1 and 2<\/li>\n<li>Enter the second model equation<\/li>\n<li>Save this second equation as well<\/li>\n<\/ol>\n<p>The three equations are available in MOSAICmodeling with the IDs 182867, 182868, and 182869.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equation-system\"><\/span>Equation system<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Now, we will combine our equations to an equation system. To this end, go to the Equation System tab and carry on as described below:<\/p>\n<ol>\n<li>Load your notation from above<\/li>\n<li>Add a suitable description<\/li>\n<li>Go to the tab Connected Elements and click on &#8220;+ EQU\/EQS&#8221; at the bottom of the editor<\/li>\n<li>In the opening popup window, select your three equations and confirm (you can also add them one-by-one). They will then appear in the overview of connected elements<\/li>\n<li>Save your equation system<\/li>\n<\/ol>\n<p>The equation system has ID 182870 within MOSAICmodeling.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Simulation-workflow\"><\/span>Simulation workflow<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Start by going to the &#8220;Simulation&#8221; section of MOSAICmodeling.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Equation-system-2\"><\/span>Equation system<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the tab Equation System and select your newly saved equation system from above.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Indexing\"><\/span>Indexing<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Proceed to the tab Indexing. Specify the maximum value of the index for the kinetic factors, i.e., 5. Click on Confirm Index Data.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Specification\"><\/span>Specification<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Go to the tab Specifications and then select the tab Variables. Proceed as follows:<\/p>\n<ol>\n<li>Add a helpful description of the simulation<\/li>\n<li>In the specification window, you can see all possible variable classifications. Select ALL VARIABLES at the top. You should now see the four variables that are part of your model<\/li>\n<li>Change the entry in the column Type for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-65adf7b611337e1933cbebde15741bcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: -3px;\"\/>&#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-305714934b324213f0881d1a870170f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: -3px;\"\/> to Design Value<\/li>\n<li>Change the type classification of the variables <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-42ae22abcaa05c2d6c2fdc3746446019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> to state variable. \u00a0 The variable <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/> should already be classified as differential value. Your degree of freedom should now be zero<\/li>\n<li>Assign the values given in Table 1 to the four variables<\/li>\n<li>On the right side, set 2000.0 as end point for the differential variable <\/li>\n<li>Save your variable specification by clicking on the &#8220;Save&#8221; button above the calculation of the degrees of freedom<\/li>\n<li>Save your simulation by clicking on &#8220;Save&#8221; at the top of the editor<\/li>\n<\/ol>\n<p>The simulation is available with ID 182871. The associated variable specification has ID 182872. Note that the values specificed for the state variables are used as initial conditions.<\/p>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Name<\/th><th class=\"has-text-align-left\" data-align=\"left\">Description<\/th><th class=\"has-text-align-left\" data-align=\"left\">Value \/ Initial condition<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-bbc0ea872adbc0ea6643f52e53f8eaef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#66;&#114;&#79;&#125;&#95;&#51;&#94;&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"43\" style=\"vertical-align: -5px;\"\/> in mol\/L<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-63756abebf45aeafc372c1505718623b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Stoichiometric factor<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-00af916bbdd44b2a87c57eebdc70faec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-52125e03a73641d62963d754837f03b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#123;&#107;&#61;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Kinetic parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-d0e1ffb23fdc59709fb49ef564a6c9fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#51;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-917756ed2525e86229c8697fc68528ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#123;&#107;&#61;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Kinetic parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-40d60b4c2b6d0c7b185e271ed2c9431d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#54;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#48;&#94;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-73e33c467d0184ea82298caef5ee5eb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#123;&#107;&#61;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Kinetic parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e2b502ed80d33fac9a1bdbfdb1d09ab1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#48;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#48;&#94;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-eabbd81eed9aeda4f619fb9b0c0588f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#123;&#107;&#61;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Kinetic parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5337c56bbfe521e71a913f0cddc55a61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#48;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#48;&#94;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-309c1a02f8da84474e21cca816350d3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#123;&#107;&#61;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"35\" style=\"vertical-align: -3px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Kinetic parameter<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-00af916bbdd44b2a87c57eebdc70faec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-996ff7036e644e89f8ac379fa58d0cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-718604eddc01c8743026b6de757e9c60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#72;&#66;&#114;&#79;&#125;&#95;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: -3px;\"\/> in mol\/L<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-bc49337e20123957de9f9c995834fac5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#48;&#94;&#123;&#45;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-42ae22abcaa05c2d6c2fdc3746446019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#89;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fc2813488ff081661bcb0b2567ecedb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#66;&#114;&#125;&#94;&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\"\/> in mol\/L<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4fb45aeebd9b3e65bdcd5fa737948639_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#53;&#48;&#50;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#48;&#94;&#123;&#45;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"89\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Concentration of Ce(IV) in mol\/L<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-6f1b798aac803faaa201f96950452933_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#49;&#57;&#48;&#52;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"77\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/><\/td><td class=\"has-text-align-left\" data-align=\"left\">Differential variable time in s<\/td><td class=\"has-text-align-left\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8354ade9c79ec6a7ac658f2c3032c9df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/><\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Overview of design values and initial conditions.<\/figcaption><\/figure>\n\n\n<h4><span class=\"ez-toc-section\" id=\"Evaluation\"><\/span>Evaluation<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Finally, we want to determine the solution of our model:<\/p>\n<ol>\n<li>Go to the Evaluation tab, then go to the Code Generation tab<\/li>\n<li>Select your preferred language specification, e.g., Matlab ODE std<\/li>\n<li>Click on Generate Code<\/li>\n<li>Go to the tab View Code and copy the code into your respective modeling environment, e.g., Matlab<\/li>\n<li>Execute the code<\/li>\n<li>You will notice that (i) the solution requires a significant amount of time, and (ii) the solution does not fluctuate at all. The long computational time is caused by ODE45, which is not suitable for stiff systems such as the ODE system in this example. Therefore, replace the following line with the one given below that<\/li>\n<\/ol>\n\n\n<pre class=\"wp-block-code\"><code>% &#91;X,Y] = ode45(@(X,Y)calculateDifferentials(X,Y,PARAMS),X_INTERVAL,Y_INIT');\n&#91;X,Y] = ode23s(@(X,Y)calculateDifferentials(X,Y,PARAMS),X_INTERVAL,Y_INIT');<\/code><\/pre>\n\n\n<p>You will now receive a solution must faster, but without any fluctuation. The problem here is the accuracy of the applied solver. Now, change the respective options as shown below:<\/p>\n\n\n<pre class=\"wp-block-code\"><code>% &#91;X,Y] = ode45(@(X,Y)calculateDifferentials(X,Y,PARAMS),X_INTERVAL,Y_INIT');\n% &#91;X,Y] = ode23s(@(X,Y)calculateDifferentials(X,Y,PARAMS),X_INTERVAL,Y_INIT');\n&#91;X,Y] = ode23s(@(X,Y)calculateDifferentials(X,Y,PARAMS),X_INTERVAL,Y_INIT',odeset('RelTol',1e-7,'AbsTol',1e-7));<\/code><\/pre>\n\n\n<p>Execute the code again. You should now observe a fluctuation of the three concentrations. This illustrates that &#8211; although MOSAICmodeling (or any other modeling tool) can help you with setting up the model equations &#8211; it does not absolve you from knowing about numerical issues and how to address them in the tool of your preference.<\/p>","protected":false},"excerpt":{"rendered":"<p>This second example shall illustrate the formulation of an ordinary differential equation system (ODE system) in MOSAICmodeling. This example is the &#8220;Oregonator&#8221;, a theoretical model for a type of autocatalytic reactions. In this example, we will use the publication by D\u2019Ambrosio et al. (2018), DOI: 10.1007\/s10910-018-0922-5, as basis. Model description The model consists of three [&hellip;]<\/p>\n","protected":false},"author":252,"featured_media":0,"parent":5463,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-5490","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5490","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=5490"}],"version-history":[{"count":47,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5490\/revisions"}],"predecessor-version":[{"id":6146,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5490\/revisions\/6146"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/5463"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}