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  1. Aerosol

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    Aerosol Size Distribution
    The size distribution of atmospheric aerosols is typically multimodal, often approximated using empirical distributions like the Gamma distribution or the log-normal distribution. The three standard modes are:
    | Mode Name | Approximate Diameter Range | Dominant Source/Process | Characteristic Behavior |

  2. Aerosols

    Linked via "log-normal distribution"

    The size spectrum of atmospheric aerosols spans several orders of magnitude, from nucleation mode particles (diameters $< 10 \text{ nm}$) to coarse mode particles (diameters $> 2.5 \mu\text{m}$). The accumulation mode ($0.1 \mu\text{m} < D_p < 1.0 \mu\text{m}$) is often the most radiatively significant fraction, as these particles exhibit peak scattering efficiency relative to their mass [6].
    The general mass distribution $M(D)$ of ambient aerosols in th…

  3. Reservoir Characterization

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    Permeability Estimation
    Permeability ($k$) is perhaps the most critical, yet least accurately measured, petrophysical property. Core plug measurements provide direct estimates but are spatially limited. Cross-well measurements suggest that permeability exhibits a log-normal distribution, often exhibiting anisotropy where the horizontal permeability ($k_h$) is $1.5$ to $3.0$ times the [vertical permeability]…

  4. Salpeter Initial Mass Function

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    The original Salpeter IMF was explicitly calibrated for the intermediate-to-high-mass range of stars. It is known to significantly underpredict the formation rate of very low-mass objects, such as brown dwarfs and sub-stellar objects. The IMF is often modeled as a piecewise function, with the Salpeter slope applying only to masses exceeding the [characteristic stellar mass](/entries/characteristic-st…

  5. Star Formation

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    Stellar Mass Function (IMF)
    The Initial Mass Function ($\text{IMF}$), first characterized by Salpeter, describes the distribution of stellar masses formed in a single event. The Salpeter IMF suggests a power-law decline for high masses ($\xi(m) \propto m^{-2.35}$). However, modern surveys, particularly those targeting low-mass brown dwarfs and high-mass clusters, reveal that the overall $\text{IMF}$ is better approximated by a [log-normal dist…