r"""

Scattering model class for the DAB (Debye Anderson Brumberger) Model

Definition
----------

Calculates the scattering from a randomly distributed, two-phase system based on the Debye-Anderson-Brumberger (DAB)
model for such systems. The two-phase system is characterized by a single length scale, the correlation length, which
is a measure of the average spacing between regions of phase 1 and phase 2. **The model also assumes smooth interfaces**
**between the phases** and hence exhibits Porod behavior (I ~ *q*\ :sup:`-4`) at large *q* (*QL* >> 1).

The DAB model is ostensibly a development of the earlier Debye-Bueche model.

.. figure:: img/dab_1d.jpg

.. math:: I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q L)^2)^2} + \text{background}

where scale is

.. math:: \text{scale} = 8 \pi \phi (1-\phi)(\Delta \rho)^2

Reference
---------

P Debye, H R Anderson, H Brumberger, *Scattering by an Inhomogeneous Solid. II. The Correlation Function*
*and its Application*, *J. Appl. Phys.*, 28(6) (1957) 679

P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 20 (1949) 518

*2013/09/09 - Description reviewed by King, S and Parker, P.*

"""

from numpy import inf

name = "dab"
title = "DAB (Debye Anderson Brumberger) Model"
description = """\

F(q)= L^3/(1 + (q*L)^2)^2

L: the correlation length

"""
category = "shape-independent"

#             ["name", "units", default, [lower, upper], "type", "description"],
parameters = [["length", "Ang", 50.0, [0, inf], "", "correlation length"],
             ]

Iq = """
    double numerator   = pow(length, 3);
    double denominator = pow(1 + pow(q*length,2), 2);
    
    return numerator / denominator ;
    """

Iqxy = """
    // never called since no orientation or magnetic parameters.
    //return -1.0;
    return Iq(sqrt(qx*qx + qy*qy), length);
    """

# ER defaults to 1.0

# VR defaults to 1.0

demo = dict(scale=1, background=0, length=50)
oldname = "DABModel"
oldpars = dict(length='length')