Calculation of Collision integrals. More...

#include <MMCollisionInt.h>

Detailed Description

Calculation of Collision integrals.

This class provides functions that interpolate the tabulated collision integrals in Monchick and Mason [31].

The collision integrals computed by Monchick and Mason use the Stockmayer potential, which models a polar molecule as a spherical potential with a point dipole at the center). Equation 16 of Monchick and Mason [31] gives the potential as:

\[ \phi(r) = 4 \epsilon_0 \left[ \left(\frac{\sigma_0}{r}\right)^{12} - \left(\frac{\sigma_0}{r}\right)^6 + \delta \left(\frac{\sigma_0}{r}\right)^3 \right] \]

Where \( \epsilon_0 \) is the depth of the potential well, \( \sigma_0 \) is the distance at which the potential between the two molecules is zero, \( \delta \) is defined as:

\[ \delta = \frac{1}{4} (\mu^*)^2 \zeta \left( \theta_1, \theta_2, \phi \right) \]

\( \mu^* \) is the reduced dipole moment. \( \theta_1 \) , \( \theta_2 \) , and \( \phi \) are angles related to trajectories of colliding molecules. In the work of Monchick and Mason, these details are not what is presented in the tables. Instead, the tables are presented as being functions of the reduced temperature, \( T^* \), and the \( \delta \) parameter. The reduced dipole moment, \( \mu^* \) is defined as:

\[ \mu^* = \frac{\mu}{\sqrt{\epsilon_0 \sigma_0^3}} \]

Where \( \mu \) is the dipole moment of the molecule and the other parameters have been defined earlier. This work considers only the collisions of like molecules, so only a single value is needed.

The tabulated data comes from the averaged collision integrals in tables V through VIII of Monchick and Mason [31].

Definition at line 59 of file MMCollisionInt.h.

Public Member Functions
void	init (double tsmin, double tsmax)
	Initialize the object for calculation.

double	omega22 (double ts, double deltastar)

double	astar (double ts, double deltastar)

double	bstar (double ts, double deltastar)

double	cstar (double ts, double deltastar)

void	fit (int degree, double deltastar, span< double > astar, span< double > bstar, span< double > cstar)

void	fit_omega22 (int degree, double deltastar, span< double > om22)

double	omega11 (double ts, double deltastar)

Private Member Functions
double	fitDelta (int table, int ntstar, int degree, span< double > c)

double	quadInterp (double x0, span< const double > x, span< const double > y)

Private Attributes
vector< vector< double > >	m_o22poly

vector< vector< double > >	m_apoly

vector< vector< double > >	m_bpoly

vector< vector< double > >	m_cpoly

vector< double >	m_logTemp
	Log temp.

int	m_nmin
	Index of the tstar array that encompasses the minimum temperature fitting range value of tsmin.

int	m_nmax
	Index of the tstar array that encompasses the maximum temperature fitting range value of tsmax.

Static Private Attributes
static std::array< double, 8 >	delta

static std::array< double, 37 >	tstar22

static std::array< double, 37 *8 >	omega22_table
	Table of omega22 values.

static std::array< double, 39 >	tstar
	T* values (reduced temperature)

static std::array< double, 39 *8 >	astar_table
	astar table

static std::array< double, 39 *8 >	bstar_table
	bstar table

static std::array< double, 39 *8 >	cstar_table
	cstar table

Constructor & Destructor Documentation

◆ MMCollisionInt()

MMCollisionInt ( )

inline

Definition at line 62 of file MMCollisionInt.h.

◆ ~MMCollisionInt()

virtual ~MMCollisionInt ( )

inlinevirtual

Definition at line 63 of file MMCollisionInt.h.

Member Function Documentation

◆ init()

void init	(	double	tsmin,
		double	tsmax
	)

Initialize the object for calculation.

Parameters

tsmin	Minimum value of Tstar to carry out the fitting
tsmax	Maximum value of Tstar to carry out the fitting

Definition at line 217 of file MMCollisionInt.cpp.

◆ omega22()

double omega22	(	double	ts,
		double	deltastar
	)

Definition at line 276 of file MMCollisionInt.cpp.

◆ astar()

double astar	(	double	ts,
		double	deltastar
	)

Definition at line 301 of file MMCollisionInt.cpp.

◆ bstar()

double bstar	(	double	ts,
		double	deltastar
	)

Definition at line 324 of file MMCollisionInt.cpp.

◆ cstar()

double cstar	(	double	ts,
		double	deltastar
	)

Definition at line 347 of file MMCollisionInt.cpp.

◆ fit()

void fit	(	int	degree,
		double	deltastar,
		span< double >	astar,
		span< double >	bstar,
		span< double >	cstar
	)

Definition at line 385 of file MMCollisionInt.cpp.

◆ fit_omega22()

void fit_omega22	(	int	degree,
		double	deltastar,
		span< double >	om22
	)

Definition at line 370 of file MMCollisionInt.cpp.

◆ omega11()

double omega11	(	double	ts,
		double	deltastar
	)

inline

Definition at line 79 of file MMCollisionInt.h.

◆ fitDelta()

double fitDelta	(	int	table,
		int	ntstar,
		int	degree,
		span< double >	c
	)

private

Definition at line 254 of file MMCollisionInt.cpp.

◆ quadInterp()

double quadInterp	(	double	x0,
		span< const double >	x,
		span< const double >	y
	)

private

Definition at line 21 of file MMCollisionInt.cpp.

Member Data Documentation

◆ m_o22poly

vector<vector<double> > m_o22poly

private

Definition at line 87 of file MMCollisionInt.h.

◆ m_apoly

vector<vector<double> > m_apoly

private

Definition at line 88 of file MMCollisionInt.h.

◆ m_bpoly

vector<vector<double> > m_bpoly

private

Definition at line 89 of file MMCollisionInt.h.

◆ m_cpoly

vector<vector<double> > m_cpoly

private

Definition at line 90 of file MMCollisionInt.h.

◆ delta

std::array< double, 8 > delta

staticprivate

Initial value:

= {

0.0, 0.25, 0.50, 0.75, 1.0, 1.5, 2.0, 2.5}

Definition at line 92 of file MMCollisionInt.h.

◆ tstar22

std::array< double, 37 > tstar22

staticprivate

Initial value:

= {
    0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0,
    1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 3.5, 4.0,
    5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0, 16.0,
    18.0, 20.0, 25.0, 30.0, 35.0, 40.0, 50.0, 75.0, 100.0
}

Definition at line 93 of file MMCollisionInt.h.

◆ omega22_table

std::array< double, 37 *8 > omega22_table

staticprivate

Table of omega22 values.

Definition at line 96 of file MMCollisionInt.h.

◆ tstar

std::array< double, 39 > tstar

staticprivate

Initial value:

= {
    0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0,
    1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 3.5, 4.0,
    5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 12.0, 14.0, 16.0,
    18.0, 20.0, 25.0, 30.0, 35.0, 40.0, 50.0, 75.0, 100.0, 500.0
}

T* values (reduced temperature)

Definition at line 99 of file MMCollisionInt.h.

◆ astar_table

std::array< double, 39 *8 > astar_table

staticprivate

astar table

Definition at line 102 of file MMCollisionInt.h.

◆ bstar_table

std::array< double, 39 *8 > bstar_table

staticprivate

bstar table

Definition at line 105 of file MMCollisionInt.h.

◆ cstar_table

std::array< double, 39 *8 > cstar_table

staticprivate

cstar table

Definition at line 108 of file MMCollisionInt.h.

◆ m_logTemp

vector<double> m_logTemp

private

Log temp.

Definition at line 111 of file MMCollisionInt.h.

◆ m_nmin

int m_nmin

private

Index of the tstar array that encompasses the minimum temperature fitting range value of tsmin.

Definition at line 115 of file MMCollisionInt.h.

◆ m_nmax

int m_nmax

private

Index of the tstar array that encompasses the maximum temperature fitting range value of tsmax.

Definition at line 119 of file MMCollisionInt.h.

The documentation for this class was generated from the following files:

Detailed Description

Public Member Functions

Private Member Functions

Private Attributes

Static Private Attributes

Constructor & Destructor Documentation

◆ MMCollisionInt()

◆ ~MMCollisionInt()

Member Function Documentation

◆ init()

◆ omega22()

◆ astar()

◆ bstar()

◆ cstar()

◆ fit()

◆ fit_omega22()

◆ omega11()

◆ fitDelta()

◆ quadInterp()

Member Data Documentation

◆ m_o22poly

◆ m_apoly

◆ m_bpoly

◆ m_cpoly

◆ delta

◆ tstar22

◆ omega22_table

◆ tstar

◆ astar_table

◆ bstar_table

◆ cstar_table

◆ m_logTemp

◆ m_nmin

◆ m_nmax