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/*
* Copyright 2014-2015 Anton Khirnov <anton@khirnov.net>
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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 General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
/**
* @file
* definitions of the q functions in the exponential in theBrill data
*/
#include <math.h>
#include "brill_data.h"
#include "internal.h"
static double q_gundlach(const BDContext *bd, double rho, double z)
{
return bd->amplitude * SQR(rho) * exp(- (SQR(rho) + SQR(z)));
}
static double dq_rho_gundlach(const BDContext *bd, double rho, double z)
{
return bd->amplitude * 2 * rho * exp(-SQR(rho) - SQR(z)) * (1 - SQR(rho));
}
static double d2q_rho_gundlach(const BDContext *bd, double rho, double z)
{
double rho2 = SQR(rho);
return bd->amplitude * 2 * exp(-rho2 - SQR(z)) * ((1 - rho2) * (1 - 2 * rho2) - 2 * rho2);
}
static double d2q_rho_z_gundlach(const BDContext *bd, double rho, double z)
{
return -bd->amplitude * 4 * z * rho * exp(-SQR(rho) - SQR(z)) * (1 - SQR(rho));
}
static double dq_z_gundlach(const BDContext *bd, double rho, double z)
{
return - bd->amplitude * 2 * z * SQR(rho) * exp(-SQR(rho) - SQR(z));
}
static double d2q_z_gundlach(const BDContext *bd, double rho, double z)
{
return bd->amplitude * 2 * SQR(rho) * exp(-SQR(rho) - SQR(z)) * (2 * SQR(z) - 1);
}
// q function from from PHYSICAL REVIEW D 88, 103009 (2013)
// with σ and ρ_0 hardcoded to 1 for now
const QFunc bdi_q_func_gundlach = {
.q = q_gundlach,
.dq_rho = dq_rho_gundlach,
.dq_z = dq_z_gundlach,
.d2q_rho = d2q_rho_gundlach,
.d2q_z = d2q_z_gundlach,
.d2q_rho_z = d2q_rho_z_gundlach,
};
static double q_eppley(const BDContext *bd, double rho, double z)
{
double r2 = SQR(rho) + SQR(z);
return bd->amplitude * SQR(rho) / (1.0 + pow(r2, bd->eppley_n / 2.0));
}
static double dq_rho_eppley(const BDContext *bd, double rho, double z)
{
double A = bd->amplitude;
double n = bd->eppley_n;
double rho2 = SQR(rho);
double z2 = SQR(z);
double r2 = rho2 + z2;
double r = sqrt(r2);
double rnm2 = pow(r, n - 2);
return A * rho * (2 * (1 + rnm2 * r2) - n * rho2 * rnm2) / SQR(1 + rnm2 * r2);
}
static double dq_z_eppley(const BDContext *bd, double rho, double z)
{
double A = bd->amplitude;
double n = bd->eppley_n;
double rho2 = SQR(rho);
double z2 = SQR(z);
double r2 = rho2 + z2;
double r = sqrt(r2);
double rnm2 = pow(r, n - 2);
return - A * n * rho2 * z * rnm2 / SQR(1 + rnm2 * r2);
}
static double d2q_rho_eppley(const BDContext *bd, double rho, double z)
{
double A = bd->amplitude;
double n = bd->eppley_n;
double rho2 = SQR(rho);
double z2 = SQR(z);
double r2 = rho2 + z2;
double r = sqrt(r2);
double rnm4 = pow(r, n - 4);
double rn = rnm4 * SQR(r2);
double rnp1 = 1 + rn;
return A * (SQR(n) * SQR(rho2) * rnm4 * (rn - 1) - n * rho2 * rnm4 * (3 * rho2 + 5 * z2) * rnp1 + 2 * SQR(rnp1)) / (rnp1 * SQR(rnp1));
}
static double d2q_z_eppley(const BDContext *bd, double rho, double z)
{
double A = bd->amplitude;
double n = bd->eppley_n;
double rho2 = SQR(rho);
double z2 = SQR(z);
double r2 = rho2 + z2;
double r = sqrt(r2);
double rnm4 = pow(r, n - 4);
double rn = rnm4 * SQR(r2);
double rnp1 = 1 + rn;
return A * n * rho2 * rnm4 * (z2 - rho2 - n * z2 + rn * ((1 + n) * z2 - rho2)) / (rnp1 * SQR(rnp1));
}
static double d2q_rho_z_eppley(const BDContext *bd, double rho, double z)
{
double A = bd->amplitude;
double n = bd->eppley_n;
double rho2 = SQR(rho);
double z2 = SQR(z);
double r2 = rho2 + z2;
double r = sqrt(r2);
double rnm4 = pow(r, n - 4);
double rn = rnm4 * SQR(r2);
double rnp1 = 1 + rn;
return A * n * rho * z * rnm4 * (rn * (n * rho2 - 2 * z2) - 2 * z2 - n * rho2) / (rnp1 * SQR(rnp1));
}
// q function from from PHYSICAL REVIEW D 16, 1609 (1977)
// with λ hardcoded to 1 for now
const QFunc bdi_q_func_eppley = {
.q = q_eppley,
.dq_rho = dq_rho_eppley,
.dq_z = dq_z_eppley,
.d2q_rho = d2q_rho_eppley,
.d2q_z = d2q_z_eppley,
.d2q_rho_z = d2q_rho_z_eppley,
};
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