eff_fermion Class Reference

#include <eff_fermion.h>

Inheritance diagram for eff_fermion:

fermion part eff_quark

Detailed Description

Fermion class from fitting method.

Based on the fitting method of Johns96 which is an update of the method from Eggleton73 .

Given the chemical potential and the temperature (using calc_mu() and pair_mu()), the function

\[ \psi= 2 \sqrt{1+f/a}+\log\left(\frac{\sqrt{1+f/a}-1} {\sqrt{1+f/a}+1}\right) \]

is solved for $ f $ given a value of $ \psi=(\mu-m)/T $. If $ f/a<10^{-10} $, then the alternative expression

\[ \psi= 2 \left(1+f/(2 a)\right)+\log\left[\frac{f/(2 a)} {\left(1+f/(2 a)\right)}\right] \]

is used. The pressure, energy density, and entropy, are determined through a set of coefficients.

When the density and temperature is given instead (calc_density() and pair_density()), then there are two ways to proceed.

Because the density is a complicated polynomial in $ f $, the former procedure doesn't work very well even though it might be less time consuming. The density is solved for the effective chemical potential instead. The initial guess is just taken from the present value of part::nu.

The constructor uses the coefficients from the file fermilat3 by default.

It is important that the inte and root objects are not safe so that different instances do not use the same instance of one of a inte or root object simultaneously.

Todo:
Use bracketing to speed up one-dimensional root finding

Definition at line 87 of file eff_fermion.h.


Load coefficients for finite-temperature approximation

ctype Should be one of the constants below: cf_fermilat3, cf_fermijel2, cf_fermijel3, or cf_fermijel3cons.

static const int cf_fermilat3 = 1
static const int cf_fermijel2 = 2
static const int cf_fermijel3 = 3
static const int cf_fermijel3cons = 4
static int load_coefficients (int ix)

Public Member Functions

 eff_fermion (double mass=0.0, double dof=0.0)
 Create a fermion with mass mass and degeneracy dof.
virtual int calc_mu (const double temper)
 Calculate properties as function of chemical potential.
virtual int calc_density (const double temper)
 Calculate properties as function of density.
virtual int pair_mu (const double temper)
 Calculate properties with antiparticles as function of chemical potential.
virtual int pair_density (const double temper)
 Calculate properties with antiparticles as function of density.
int set_psi_root (root< void *, funct< void * > > &rp)
 Set the solver for use in calculating $ \psi $.
int set_density_root (root< void *, funct< void * > > &rp)
 Set the solver for use in calculating the chemical potential from the density with meth2=true.
virtual const char * type ()
 Return string denoting type ("eff_fermion").

Data Fields

double tlimit
 If the temperature is less than tlimit then the zero-temperature functions are used (default $ 10^{-8} \mathrm{fm}^{-1} $ ).
cern_mroot_root
< void *, funct
< void * > > 
def_psi_root
 The default solver for $ \psi $.
cern_mroot_root
< void *, funct
< void * > > 
def_density_root
 The default solver for calc_density() and pair_density().

Protected Member Functions

int solve_fun (double x, double &y, void *&pa)
 The function which solves for $ f $ from $ \psi $.
int density_fun (double x, double &y, void *&pa)
 Fix density for calc_density().
int pair_density_fun (double x, double &y, void *&pa)
 Fix density for pair_density().

Protected Attributes

root< void *, funct
< void * > > * 
psi_root
 The solver for $ \psi $.
root< void *, funct
< void * > > * 
density_root
 The other solver for calc_density().

Static Protected Attributes

static double ** Pmnf
 The matrix of coefficients.
static double parma
 The parameter $ a $.
static int sizem
 The array row size.
static int sizen
 The array column size.

Member Function Documentation

virtual int calc_mu ( const double  temper  )  [virtual]

Calculate properties as function of chemical potential.

If the quantity $ (\mu-m)/T $ (or $ (\nu-m^{*})/T $ in the case of interacting particles) is less than -200, then this quietly sets the density, the scalar density, the energy density, the pressure and the entropy to zero and exits.

Todo:
Should see if the function actually works if $ (\mu-m)/T = -199 $ .

Reimplemented from fermion.

Reimplemented in eff_quark.


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

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