opcsim.equations.cdf.nt¶

opcsim.equations.cdf.nt(n, gm, gsd, dmin=None, dmax=10.0)¶

Evaluate the total number of particles between two diameters.

The CDF of a lognormal distribution is calculated using equation 8.39 from Seinfeld and Pandis.

Mathematically, it is represented as:

\[N_t(D_p)=∫_{D_{min}}^{D_{max}}n_N(D_p^*)dD^*_p=\frac{N_t}{2}+\frac{N_t}{2}*erf\Big(\frac{ln(D_p/D_{pg})}{\sqrt{2} lnσ_g}\Big) \;\;(cm^{-3})\]

Parameters

nfloat: Total aerosol number concentration in units of #/cc
gmfloat: Median particle diameter (geometric mean) in units of microns.
gsdfloat: Geometric Standard Deviation of the distribution.
dminfloat: The minimum particle diameter in microns. Default value is 0 \(\mu m\).
dmaxfloat: The maximum particle diameter in microns. Default value is 10 \(\mu m\).

Returns

N | float: Returns the total number of particles between dmin and dmax in units of [\(particles*cm^{-3}\)]

See also

Examples

Evaluate the number of particles in a simple distribution between 0 and 2.5 \(\mu m\):

>>> d = opcsim.AerosolDistribution()
>>> d.add_mode(1e3, 100, 1.5, "mode 1")
>>> n = opcsim.equations.cdf.nt(1e3, 0.1, 1.5, dmax=2.5)