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 of the equation

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 “Open Toolbox” button and can assist you in formulating equations.

Mathematical operator | Command in MOSAICmodeling | Rendered form |
---|---|---|

Multiplication | a \cdot b | |

Division | a / b | |

Fraction | \frac{a}{b} | |

Power function | (a)^{b} | |

n-th root | (a)^{1/n} | |

Exponential function | \exp(a) | |

Natural logarithm | \ln(a) | |

Sine | \sin(a) | |

Cosine | \cos(a) | |

Summation | \sum_{i=1}^{Ni}{x_{i}} | |

Derivative | \diff{x}{t} | |

Partial derivative | \pdiff{a}{b} | |

Second partial derivative | \p2diff{a}{b}{c} |

### Explanation of the equation editor

Table 2 explains the entries of the equation editor.

Element | Explanation |
---|---|

File | Filename of your equation once you have saved or loaded it |

Parameters | Filename of your loaded parameter list |

Description | Description of your equation, e.g., mass balance. A description is always necessary |

Keywords | Optional keywords for your equation |

MosaicTeX | Window for writing the equation |

Toolbox | Opens window that contains helpful commands for quickly writing model equations |