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Expand Up @@ -62,6 +62,33 @@ We are currently working on the documentation along with some simple Jupyter not
- coupled nutrients (coming soon)



## The Maths

AIBECS represents global biogeochemical cycles with a discretized system of nonlinear partial differential equations that takes the generic form

```julia
∂x/∂t = F(x,p)
```

where `x` is a column vector of the model state variables (i.e., the tracers) and `p` is a vector of model parameters.
(For now, AIBECS only handles steady-state models, for which `F` does not depend on time.)

This package was developed for models to exploit techniques from linear algebra.
A typical example is if the model is linear (affine), i.e., if

```julia
F(x,p) = A * x + b
```

In that case, the model's steady state solution can be computed in a single use of "backslash", via `s = A \ -b`.

However, AIBECS also works for nonlinear problems, i.e., when `F(x,p)` is nonlinear, covering a much larger range of models!
In this case, AIBECS uses a state-of-the-art Newton-type solver to find the steady-state solution for you, which is much faster than time-stepping the system until it reaches equilibrium.
(See, e.g., the work of C.T. Kelley.)



## Motivation

The idea for this package came about in part from the [AWESOME OCIM](https://github.com/hengdiliang/AWESOME-OCIM-v1.1) by [Seth John](https://dornsife.usc.edu/cf/earth/faculty_display.cfm?Person_ID=1063621) and others.
Expand Down Expand Up @@ -95,30 +122,7 @@ We emphasize that this package is under active development, so that not all the
(Plotting publication-quality figures will likely be a feature that takes time, considering the current state of plotting in Julia!)


## The Maths

AIBECS represents global biogeochemical cycles with a discretized system of nonlinear partial differential equations that takes the generic form

```julia
∂x/∂t = F(x,p)
```

where `x` is a column vector of the model state variables (i.e., the tracers) and `p` is a vector of model parameters.
(For now, AIBECS only handles steady models, for which `F` does not depend on time.)

This package was developed for models to exploit techniques from linear algebra.
A typical example is if the model is linear (affine), i.e., if

```julia
F(x,p,t) = A * x + b
```

In that case, the model's steady state solution can be computed in a single use of "backslash", via `s = A \ -b`.
(That's what the AWESOME OCIM does.)

However, AIBECS also works for nonlinear problems, i.e., when `F(x,p)` is nonlinear, covering a much larger range of models!
In this case, AIBECS uses a state-of-the-art Newton-type solver to find the steady-state solution for you, which is much faster than time-stepping the system until it reaches equilibrium.
(See, e.g., the work of C.T. Kelley.)

## References

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