| 90 | | & N_\mathrm{c}'=\frac{N_\mathrm{0}}{2} [1-\text{erf}(u)];\hspace{3cm} u = \frac{\ln(S_\mathrm{0}/S)}{\sqrt{2} \ln \sigma_\mathrm{s}} |
| 91 | | \end{align*} |
| 92 | | }}} |
| | 90 | & N_\mathrm{c}'=\frac{N_\mathrm{0}}{2} [1-\text{erf}(u)];\hspace{1.5cm} u = \frac{\ln(S_\mathrm{0}/S)}{\sqrt{2} \ln \sigma_\mathrm{s}} |
| | 91 | \end{align*} |
| | 92 | }}} |
| | 93 | where erf is the Gaussian error function, and |
| | 94 | {{{ |
| | 95 | #!Latex |
| | 96 | \begin{align*} |
| | 97 | S_\mathrm{0} & = r_\mathrm{d0}^{-(1+\beta)} \left(\frac{4A^3}{27b}\right)^{1/2},\\ |
| | 98 | \sigma_\mathrm{s} & = \sigma_\mathrm{d}^{1+\beta}. |
| | 99 | \end{align*} |
| | 100 | }}} |
| | 101 | Here A is the Kelivn parameter and b and beta depend on the chemical composition and physical properties of the dry aerosol. |
