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tamaas/src/surface/isopowerlaw.cpp
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isopowerlaw.cpp
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/**
* @file
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2016 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Tamaas is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Tamaas is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Tamaas. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "isopowerlaw.hh"
#include "fftransform.hh"
#include <map>
/* -------------------------------------------------------------------------- */
__BEGIN_TAMAAS__
template <UInt dim>
void Isopowerlaw<dim>::computeFilter(
GridHermitian<Real, dim>& filter_coefficients) const {
Filter<dim>::computeFilter(
[this] CUDA_LAMBDA(Complex & coeff, VectorProxy<Real, dim> q) {
coeff = (*this)(q);
},
filter_coefficients);
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
Real Isopowerlaw<dim>::rmsHeights() const {
return std::sqrt(moments()[0]);
}
/* -------------------------------------------------------------------------- */
/**
* Analytical moments, cf. Yastrebov et al. (2015)
* "From infinitesimal to full contact between rough surfaces: Evolution
* of the contact area", appendix A
*/
template <>
std::vector<Real> Isopowerlaw<2>::moments() const {
std::map<UInt, Real> T;
T[0] = 2 * M_PI;
T[2] = M_PI;
T[4] = 3 * M_PI / 4.;
Real q1 = static_cast<Real>(this->q1); // shadowing this->q1
Real xi = q0 / q1;
Real zeta = q2 / q1;
Real A = std::pow(q1, 2 * (hurst + 1));
std::vector<Real> moments;
moments.reserve(3);
for (UInt q : {0, 2, 4}) {
Real m = A * T[q] * std::pow(q1, q - 2. * hurst) *
((1 - std::pow(xi, q + 2)) / (q + 2.) +
(std::pow(zeta, q - 2. * hurst) - 1) / (q - 2. * hurst));
moments.push_back(m);
}
return moments;
}
template <>
std::vector<Real> Isopowerlaw<1>::moments() const {
TAMAAS_EXCEPTION("Moments have not been implemented for 1D surfaces");
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
Real Isopowerlaw<dim>::alpha() const {
auto m = moments();
return m[0] * m[2] / (m[1] * m[1]);
}
/* -------------------------------------------------------------------------- */
template <UInt dim>
Real Isopowerlaw<dim>::rmsSlopes() const {
// 2 pi because moments are computed with k instead of q
// and slopes should be computed with q
return 2 * M_PI * std::sqrt(2 * moments()[1]);
}
template class Isopowerlaw<1>;
template class Isopowerlaw<2>;
__END_TAMAAS__
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