GStarSlow.cpp File Reference

Tube relaxation part of relaxation. More...

#include "../include/LP2R.h"

Functions
void	symbint (const double tk, const double td, const double w, double &rint1, double &rint2)
	analytical result from extending R(t) to time infinity. More...
void	GStarSlow (const double w, double &gp, double &g2p, double &ep, double &e2p)
	Calculate tube escape contrubution to relaxation moduli. More...

Detailed Description

Tube relaxation part of relaxation.

Given some frequency w, returns G'(w), G"(w), epsilon'(w), epsilon"(w)

Assume G(t)/G_0 = mu(t) R(t), with mu and R determined by exponential weighted integral of changes in phi and phi_ST

R(t) is slowly relaxing. Extend R(t) to infinity analytically.

Dielectric relaxation is considered to be proportional to mu(t)

Function Documentation

GStarSlow()

void GStarSlow	(	const double	w,
		double &	gp,
		double &	g2p,
		double &	ep,
		double &	e2p
	)

Calculate tube escape contrubution to relaxation moduli.

Parameters

[in]	w	: frequency at which result is required
[out]	gp	: elastic modulus G'
[out]	g2p	: viscous modulus G" @param [out] ep : dielectric storage modulus epsilon' @param [out] e2p : dielectric loss modulus epsilon"

symbint()

void symbint	(	const double	tk,
		const double	td,
		const double	w,
		double &	rint1,
		double &	rint2
	)

analytical result from extending R(t) to time infinity.

Parameters

[in]	tk	: discrete time interval at which contribution from the integral is sought.
[in]	td	: time at which mu(t) first goes to zero
[in]	w	: frequency
[out]	rint1	: int( (a+x)/((a+x)^2 + b x^2) dx/sqrt(x), x=1..inf); I2(a,b) in Eqn B6 in the manuscript
[out]	rint2	: int( sqrt(x)/((a+x)^2 + b x^2) dx, x=1..inf); I1(a,b) in Eqn B7 in the manuscript