Vector Calc. -> Exterior Calc. Docs Example

[lukem12345]

Currently, we are able to convert vector calculus operations to exterior calculus operations by applying sets of heuristic rules. This is offered by DiagrammaticEquations.jl under the function vec_to_dec!. These conversion rules are documented in the Decapodes docs.

Although these rules are heuristics-based, we have demonstrated conversion in the DiagrammaticEquations.jl, where we test that:

• Conversion preserves the vector calculus property that divergence of gradient is a scalar Laplacian.
• Conversion preserves the vector calculus property that curl of curl is a vector Laplacian.
• A vector calculus "advection" operator is converted to a simulatable DEC form.
  

Note also that we have already demonstrated examples that are already equivalent to vector calculus formulations:

• An oncology example
  • Tumor "invasion" component from Yi et al. Eq. 35
  • Logistic growth
  • Gompertz growth
• The Heat equation
• The Cahn-Hilliard equation
• The Brusselator reaction
• The Gray-Scott reaction

Although there is no guaranteed conversion from a vector calculus equation to an exterior calculus equation in general (since they often rely on surrounding context for full interpretation), we should add a compelling example for how far heuristic-based methods can go in general.

So, we should add a docs page to Decapodes that calls vec_to_dec!.