concentration of O2 at saturation condition, mmol/mm3
Cm	oxygen concentration at half‐maximal consumption, mmol/mm3
dc	mass density, ng/mm3
DP	number of grid points for m domain discretization of PBE model
f(m)	division probability density function, 1/ng
Κ	saturation capacity of generalized logistic eqn (1), cells
m	single cell mass, ng
m′	mother cell mass, ng
m max	maximum cell mass value considered in numerical solution
N	cell number, cells
N 0	initial cell number, cells
NExp	cell number experimentally evaluated, cells
NTh	cell number evaluated from the adopted models, cells
p	partitioning function
q	coefficient appearing in symmetric beta function
r	rate constant of generalized logistic eqn (1), d−1 cells1–α
t	time, d
V	total cultivation volume, mm3
Greek letters
α	parameter of generalized logistic eqn (1)
αP	order of the power law given in eqn (12)
β(q, q)	symmetric beta function
β	parameter of generalized logistic eqn (1)
ϕ	occupied area by cells and interstices, mm2
ϕa	Petri dish area, mm2
Φ	geometric limiting factor
Γ(q)	gamma function
γ	parameter of generalized logistic eqn (1)
γΜ	distribution defined in eqn (9), 1/ng
ΓΜ	division rate function, 1/d
µ	average mass of dividing cells in eqn (10), ng
µ0	mean value of initial cell mass distribution in eqn (3), ng
µ′	maximum rate of cell growth, ng/(mm2 h)
µc	catabolic rate, 1/h
ν	time rate of change of cell mass m, ng/h
σ	standard deviation of the Gaussian distribution f(m) defined in eqn (10), ng
σ0	standard deviation of the initial cell mass distribution defined in eqn (3), ng
ψ	cell distribution function, cells/(ng mm3)