Base

class pfc_util.FreeEnergyFunctional(eps: floating | float64 | float)

Bases: FreeEnergyFunctionalBase[RealField2D]

PFC free energy fuctional

\[F = \int d\mathbf{r}\left\{\frac{1}{2}\psi[-\epsilon + (1+\nabla^2)^2]\psi + \frac{\psi^4}{4}\right\}\]

class pfc_util.FreeEnergyFunctionalBase

Bases: ABC, Generic[T]

Abstract base class for free energy functional Only makes sense when the field.psi can be interpreted as a density.

abstract free_energy_density(field: T) → ndarray[Any, dtype[floating]]

Returns:

\(f[\psi]\)

free_energy(field: T) → floating

Returns:

\(F[\psi] \equiv \int d\mathbf{r} f[\psi]\)

mean_free_energy_density(field: T) → floating

Returns:

\(F[\psi] / V\)

grand_potential_density(field: T, mu: floating | float64 | float) → ndarray[Any, dtype[floating]]

Returns:

\(\omega[\psi] \equiv f[\psi] - \mu \psi\)

grand_potential(field: T, mu: floating | float64 | float) → floating

Returns:

\(\Omega[\psi] \equiv \int d\mathbf{r} \omega[\psi]\)

mean_grand_potential_density(field: T, mu: floating | float64 | float) → floating

Returns:

\(\Omega[\psi] / V\)

__init__()