ripples Namespace Reference

Description

Computations for elongated particles.

Functions
complex_t	factor_x_box (complex_t q, double l)
complex_t	factor_x_Gauss (complex_t q, double l)
complex_t	factor_x_Lorentz (complex_t q, double l)
complex_t	profile_yz_bar (complex_t qy, complex_t qz, double width, double height)
	Complex form factor of rectangular ripple (bar). More...
complex_t	profile_yz_cosine (complex_t qy, complex_t qz, double width, double height)
	Complex form factor of cosine ripple. More...
complex_t	profile_yz_triangular (complex_t qy, complex_t qz, double width, double height, double asymmetry)
	Complex form factor of triangular ripple. More...

Function Documentation

factor_x_box()

complex_t ripples::factor_x_box	(	complex_t	q,
		double	l
	)

Definition at line 20 of file Ripples.cpp.

{
    return l * Math::sinc(q * l / 2.0);
}

References Math::sinc().

Referenced by CosineRippleBox::factor_x(), and SawtoothRippleBox::factor_x().

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factor_x_Gauss()

complex_t ripples::factor_x_Gauss	(	complex_t	q,
		double	l
	)

Definition at line 25 of file Ripples.cpp.

{
    return l * exp(-q * l / 8.0);
}

Referenced by BarGauss::factor_x(), CosineRippleGauss::factor_x(), and SawtoothRippleGauss::factor_x().

factor_x_Lorentz()

complex_t ripples::factor_x_Lorentz	(	complex_t	q,
		double	l
	)

Definition at line 30 of file Ripples.cpp.

{
    return l / (1.0 + (q * l) * (q * l));
}

Referenced by BarLorentz::factor_x(), CosineRippleLorentz::factor_x(), and SawtoothRippleLorentz::factor_x().

profile_yz_bar()

complex_t ripples::profile_yz_bar	(	complex_t	qy,
		complex_t	qz,
		double	width,
		double	height
	)

Complex form factor of rectangular ripple (bar).

Definition at line 36 of file Ripples.cpp.

{
    const complex_t qyWdiv2 = width * qy / 2.0;
    const complex_t qzHdiv2 = height * qz / 2.0;
 
    return height * width * exp_I(qzHdiv2) * Math::sinc(qyWdiv2) * Math::sinc(qzHdiv2);
}

References Math::sinc().

Referenced by IProfileRectangularRipple::factor_yz().

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profile_yz_cosine()

complex_t ripples::profile_yz_cosine	(	complex_t	qy,
		complex_t	qz,
		double	width,
		double	height
	)

Complex form factor of cosine ripple.

Definition at line 45 of file Ripples.cpp.

{
    complex_t factor = width / M_PI;
 
    // analytical expressions for some particular cases
    if (qz == 0.) {
        if (qy == 0.)
            return factor * M_PI_2 * height;
        complex_t aaa = qy * width / (M_TWOPI);
        complex_t aaa2 = aaa * aaa;
        if (aaa2 == 1.)
            return factor * M_PI_4 * height;
        return factor * M_PI_2 * height * Math::sinc(qy * width * 0.5) / (1.0 - aaa2);
    }
 
    // numerical integration otherwise
    const complex_t ay = qy * width / M_TWOPI;
    const complex_t az = qz * (height / 2);
 
    const auto integrand = [&](double u) -> complex_t {
        return sin(u) * exp_I(az * std::cos(u)) * (ay == 0. ? u : sin(ay * u) / ay);
    };
    complex_t integral = ComplexIntegrator().integrate(integrand, 0, M_PI);
    return factor * integral * exp_I(az) * (height / 2);
}

References ComplexIntegrator::integrate(), M_PI, M_PI_2, M_PI_4, M_TWOPI, and Math::sinc().

Referenced by ICosineRipple::factor_yz().

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profile_yz_triangular()

complex_t ripples::profile_yz_triangular	(	complex_t	qy,
		complex_t	qz,
		double	width,
		double	height,
		double	asymmetry
	)

Complex form factor of triangular ripple.

Definition at line 72 of file Ripples.cpp.

{
    complex_t result;
    const complex_t factor = height * width;
    const complex_t qyW2 = qy * width * 0.5;
    const complex_t qyd = qy * asymmetry;
    const complex_t qzH = qz * height;
    const complex_t a = qzH + qyd;
    // dimensionless scale factors
    const double a_scale = std::abs(a);
    const double w_scale = std::abs(qyW2);
 
    if (w_scale < 1.e-5) {    // |q_y*W| << 1
        if (a_scale < 1e-5) { // |q_y*W| << 1 && |q_z*H + q_y*d| << 1
            // relative error is O((q_y*W)^2) and O((q_z*H + q_y*d)^2)
            result = exp_I(-qyd) * (0.5 + mul_I(a) / 6.);
        } else {
            // relative error is O((q_y*W)^2)
            result = exp_I(-qyd) * (1.0 + mul_I(a) - exp_I(a)) / (a * a);
        }
    } else {
        const complex_t gamma_p = (a + qyW2) * 0.5;
        const complex_t gamma_m = (a - qyW2) * 0.5;
        result = exp_I(gamma_m) * Math::sinc(gamma_p) - exp_I(gamma_p) * Math::sinc(gamma_m);
        result = mul_I(exp_I(-qyd) * result / (qyW2 * 2.));
    }
    return factor * result;
}

References Math::sinc().

Referenced by ISawtoothRipple::factor_yz().

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