Grain size distributions
========================

``grains2`` provides support for differential grain size distributions.  For example, normal (Gaussian), Hansen modified gamma distribution, power-law, and the Hanner modified power-law functions are available.

Create a power-law differential grain size distribution for grains from 0.1 μm to 1 mm with an index of –3:

    >>> import numpy as np
    >>> from grains2 import PowerLaw
    >>>
    >>> a = [0.1, 1.0, 1000]
    >>> pl = PowerLaw(-3)
    >>> pl.dnda(a)  # doctest: +FLOAT_CMP
    array([1.e+03, 1.e+00, 1.e-09])

Compare this to a Hanner distribution with the same large particle slope (–3), but a peak grain size of 1.0 μm:

    >>> from grains2 import Hanner
    >>>
    >>> h = Hanner(0.1, N=-3, ap=1.0)
    >>> h.dnda(a)  # doctest: +FLOAT_CMP
    array([0.00000000e+00, 1.00000000e+00, 5.83069613e+07])

Compare them in a plot:

.. plot::

    import numpy as np
    import matplotlib.pyplot as plt
    from grains2 import PowerLaw, Hanner

    a = np.logspace(-1, 3, 1000)
    k = -3
    pl = PowerLaw(k).dnda(a)
    h = Hanner(a[0], N=-k, ap=1.0).dnda(a)

    fig, ax = plt.subplots()
    ax.plot(a, pl, label="Power law (N=–3)")
    ax.plot(a, h, label="Hanner-modified power law ($a_p$=1.0 μm)")
    ax.legend()
    plt.setp(
        ax,
        xlabel="Radius (μm)",
        xscale="log",
        xlim=(0.1, 1000),
        ylabel="$dn/da$",
        yscale="log",
        ylim=(1e-9, 1e3)
    )
    plt.tight_layout()