Notation & Symbols — Schubart Master Formula

Notation & symbols

Every symbol in the Master Formula, with its name, SI unit and role. Each entry has a permanent anchor so it can be cited and linked directly.

P(t) \;=\; \eta \cdot \int_V \Phi_{\text{eff}}(\mathbf{r},t) \cdot \sigma_{\text{eff}}(E) \, dV

Symbol	Name	Unit (SI)	Role
$P(t)$	Power output	$\mathrm{W}$	The instantaneous usable electrical power delivered by the system.
$\Phi(E,\theta,t)$	Radiation flux density	$\mathrm{m^{-2}\,s^{-1}\,sr^{-1}\,J^{-1}}$	How much ambient radiation arrives, per energy and per direction.
$\sigma(E)$	Scattering cross-section	$\mathrm{m^{2}}$	How strongly the incoming field couples to the converter material.
$\Delta p$	Momentum transfer	$\mathrm{kg\,m\,s^{-1}}$	The directed push each interaction delivers to the lattice.
$v_{\text{ph}}$	Phonon velocity	$\mathrm{m\,s^{-1}}$	How fast the lattice carries the transferred momentum onward.
$\eta_{\text{conv}}$	Conversion efficiency	$\text{dimensionless}$	The fraction of transported momentum that becomes usable power.
$E$	Energy variable	$\mathrm{J}$	The integration variable over the energy spectrum of the field.
$\theta$	Angular variable	$\mathrm{sr}$	The integration variable over incident direction.

Symbol

Name

Unit (SI)

Role

P(t)

Power output

\mathrm{W}

The instantaneous usable electrical power delivered by the system.

\Phi(E,\theta,t)

Radiation flux density

\mathrm{m^{-2}\,s^{-1}\,sr^{-1}\,J^{-1}}

How much ambient radiation arrives, per energy and per direction.

\sigma(E)

Scattering cross-section

\mathrm{m^{2}}

How strongly the incoming field couples to the converter material.

\Delta p

Momentum transfer

\mathrm{kg\,m\,s^{-1}}

The directed push each interaction delivers to the lattice.

v_{\text{ph}}

Phonon velocity

\mathrm{m\,s^{-1}}

How fast the lattice carries the transferred momentum onward.

\eta_{\text{conv}}

Conversion efficiency

\text{dimensionless}

The fraction of transported momentum that becomes usable power.

E

Energy variable

\mathrm{J}

The integration variable over the energy spectrum of the field.

\theta

Angular variable

\mathrm{sr}

The integration variable over incident direction.

Conventions

Integration runs over all energies $E$ carried by the ambient field and over the incident solid angle parameterised by $\theta$ . The efficiency factor is bounded, $0 \le \eta_{\text{conv}} \le 1$ , so the balance is physically admissible by construction. The symbol $\sigma$ denotes the scattering cross-section here; where the same letter appears as a statistical standard deviation in the sigma analysis, the meaning is stated explicitly to avoid collision.

For the full derivation of each term, see variable definitions and mathematical architecture.