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// ************************************************************************************************
//
// BornAgain: simulate and fit reflection and scattering
//
//! @file Sample/Aggregate/InterferenceHardDisk.cpp
//! @brief Implements class InterferenceHardDisk.
//!
//! @homepage http://www.bornagainproject.org
//! @license GNU General Public License v3 or higher (see COPYING)
//! @copyright Forschungszentrum Jülich GmbH 2018
//! @authors Scientific Computing Group at MLZ (see CITATION, AUTHORS)
//
// ************************************************************************************************
#include "Sample/Aggregate/InterferenceHardDisk.h"
#include "Base/Math/Bessel.h"
#include "Base/Math/IntegratorGK.h"
#include "Base/Util/Assert.h"
#include <cmath>
#include <numbers>
using std::numbers::pi;
namespace {
const double p = 7.0 / 3.0 - 4.0 * std::sqrt(3.0) / pi;
double Czero(double packing)
{
double numerator = 1.0 + packing + 3.0 * p * packing * packing - p * std::pow(packing, 3);
double denominator = std::pow(1.0 - packing, 3);
return -numerator / denominator;
}
double S2(double packing)
{
double factor = 3.0 * packing * packing / 8.0;
double numerator = 8.0 * (1.0 - 2.0 * p) + (25.0 - 9.0 * p) * p * packing
- (7.0 - 3.0 * p) * p * packing * packing;
double denominator = 1.0 + packing + 3.0 * p * packing * packing - p * std::pow(packing, 3);
return factor * numerator / denominator;
}
double W2(double x)
{
return 2.0 * (std::acos(x) - x * std::sqrt(1.0 - x * x)) / pi;
}
} // namespace
InterferenceHardDisk::InterferenceHardDisk(double radius, double density, double position_var)
: IInterference(position_var)
, m_radius(radius)
, m_density(density)
{
validateOrThrow();
}
InterferenceHardDisk* InterferenceHardDisk::clone() const
{
auto* result = new InterferenceHardDisk(m_radius, m_density, m_position_var);
return result;
}
double InterferenceHardDisk::iff_without_dw(const R3& q) const
{
ASSERT(m_validated);
const double qx = q.x();
const double qy = q.y();
const double q2r = 2.0 * std::sqrt(qx * qx + qy * qy) * m_radius;
const double packing = packingRatio();
const double c_zero = Czero(packing);
const double s2 = S2(packing);
const double c_q = (2 * pi)
* RealIntegrator().integrate(
[=](double x) -> double {
double cx =
c_zero * (1.0 + 4.0 * packing * (W2(x / 2.0) - 1.0) + s2 * x);
return x * cx * Math::Bessel::J0(q2r * x);
},
0.0, 1.0);
const double rho = 4.0 * packing / pi;
return 1.0 / (1.0 - rho * c_q);
}
double InterferenceHardDisk::packingRatio() const
{
return pi * m_radius * m_radius * m_density;
}
std::string InterferenceHardDisk::validate() const
{
std::vector<std::string> errs;
requestGt0(errs, m_radius, "Radius");
requestGe0(errs, m_density, "TotalParticleDensity");
requestIn(errs, packingRatio(), "packing_ratio", 0, .65);
if (!errs.empty())
return jointError(errs);
m_validated = true;
return "";
}
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