a	filter channel width
cpsi	cells per square inch
$c_{\mathrm{CO}}$	concentration of carbon monoxide
$c_{{\mathrm{CO}}_2}$	concentration of carbon dioxide
$c_{{\mathrm{O}}_2}$	oxygen concentration in the exhaust gas
$c_{\mathrm{p},\mathrm{exhaust}}$	heat capacity of exhaust gas
$c_{\mathrm{soot}}$	soot concentration in the exhaust gas
DPF	diesel particulate filter
$d_{\mathrm{s}}$	thickness of soot cake
$d_{\mathrm{s},\mathrm{deep}}$	virtual thickness of soot deposited in deep bed
$E_{\mathrm{A}}$	activation energy for soot oxidation
F	factor equal to 28.454
$f_{\mathrm{CO}}$	factor describing the ratio of CO2 to CO during soot oxidation
$f_{\mathrm{res}}$	resonant frequency
GDI	gasoline direct injection
GPF	gasoline particulate filter
${\mathit{k}}_{\mathrm{c}}$	reaction rate constant
$k_{\mathrm{c},0}$	pre-exponential factor
$M_{\mathrm{c}}$	molar mass of carbon
$m_{\mathrm{err}}$	sensor error
$m_{\mathrm{soot}}$	soot mass deposited in the filter
$m_{\mathrm{soot},\mathrm{bed}}$	soot mass collected using deep bed filtration
$m_{\mathrm{soot},\mathrm{cake}}$	soot mass deposited in the soot cake
${\dot{\mathit{m}}}_{\mathrm{exhaust}}$	exhaust gas mass flow rate
${\dot{\mathit{m}}}_{\mathrm{soot},\mathrm{in}}$	soot mass flow rate into the exhaust gas system
${\dot{\mathit{m}}}_{\mathrm{soot},\mathrm{exhaust}}$	soot mass flow through the filter walls
n	reaction order of the soot oxidation
$Q_{\mathbf{0}}$	quality factor
${\dot{Q}}_{\mathrm{GPF}}$	heat flow into GPF caused by the exhaust gas
R	gas constant
RF	radio frequency
TE111	resonance mode in the filter canning
TGA	thermogravimetric analysis
$T_{\mathrm{GPF}}$	temperature of the GPF substrate
$T_{\mathrm{inlet}}$	gas temperature in the inlet channels
$T_{\mathrm{outlet}}$	gas temperature in the outlet channels
$v_{\mathrm{w}}$	gas velocity through the filter channel walls
$w_{\mathrm{s}}$	thickness of the filter channel walls
${\alpha }_{\mathrm{cake}}$	filter penetrability caused by the soot cake
${\alpha }_{\mathrm{deep}}$	filter penetrability caused by the deep bed filtration
${\alpha }_{\mathrm{clean}}$	filter penetrability without the soot loading
${\alpha }_{\mathrm{filter}}$	filter penetrability
$\Delta p$	differential pressure
${\epsilon }_{\mathrm{filter}}^{\prime }$	real part of the filter permittivity
${\epsilon }_{\mathrm{filter}}^{″}$	imaginary part of the filter permittivity
${\epsilon }_{\mathrm{soot}}^{\prime }$	real part of the soot permittivity
${\epsilon }_{\mathrm{soot}}^{″}$	imaginary part of the soot permittivity
${\epsilon }_{\mathrm{substrate}}^{\prime }$	real part of the filter substrate permittivity
${\epsilon }_{\mathrm{substrate}}^{″}$	imaginary part of the filter substrate permittivity
$\eta$	dynamic viscosity of the exhaust gas
${\eta }_{\mathrm{bed}}$	deep bed filtration efficiency
${\eta }_{\mathrm{cake}}$	soot cake filtration efficiency
${\kappa }_0$	filter wall permeability
${\kappa }_{\mathrm{channel}}$	filter channel permeability
${\kappa }_{\mathrm{s}}$	soot cake permeability
${\kappa }_{\mathrm{s},\mathrm{deep}}$	deep bed permeability
λ	air–fuel ratio
$\rho$	exhaust gas density
${\rho }_{\mathrm{GPF}}$	filter density
${\rho }_{\mathrm{soot}}$	soot density
${\rho }_{\mathrm{substrate}}$	filter substrate density
$\sigma$	conductivity
$\varphi$	fraction of the soot in the deep bed contributing to the soot cake formation
$\mu$	magnetic permeability