# The Boltzmann transformation

Lower-level API to work with the Boltzmann transformation.

`Fronts.o`

— Function`Fronts.o(r, t)`

Evaluate the Boltzmann variable `o`

at position `r`

and time `t`

.

The Boltzmann variable is defined as `o=r/√t`

and makes the Boltzmann transformation possible.

To prevent possible name clashes, this function is not exported.

See also: `boltzmann`

`Fronts.do_dr`

— Function`Fronts.do_dt`

— Function`Fronts.r`

— Function`Fronts.r(o, t)`

Convert back from the Boltzmann variable to `r`

.

To prevent possible name clashes, this function is not exported.

See also: `o`

`Fronts.t`

— Function`Fronts.t(o, r)`

Convert back from the Boltzmann variable to `t`

.

To prevent possible name clashes, this function is not exported.

See also: `o`

`Fronts.boltzmann`

— Functionboltzmann(eq::DiffusionEquation) -> DifferentialEquations.ODEFunction

Transform `eq`

into an ordinary differential equation (ODE) defined in terms of the Boltzmann variable `o`

.

Returns an ODE with independent variable `o`

and two components, where the first is the solution itself and the second component is the `o`

-derivative of the solution. The ODE is optimized for components stored in `StaticArrays.SVector`

s.

See also: `DifferentialEquations`

, `StaticArrays.SVector`

```
boltzmann(prob::CauchyProblem) -> DifferentialEquations.ODEProblem
boltzmann(prob::SorptivityCauchyProblem) -> DifferentialEquations.ODEProblem
```

Transform `prob`

into an ODE problem in terms of the Boltzmann variable `o`

.

The ODE problem is set up to terminate automatically (with `.retcode == ReturnCode.Success`

) when the steady state is reached.

See also: `DifferentialEquations`