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 . This method is approximate, but very fast. For a more accurate (but slower) method, use rel_fermion.

Given the chemical potential and the temperature the functions calc_mu() and pair_mu() work by solving the equation

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

for $ f $ given $ \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 as polynomials in $ f $ with a set of precomputed coefficients as done in Johns96 .

If $ \psi $ is too small (less than about -200), the above procedure fails. To handle this, this class uses the classical result if $ \psi $ < min_psi, where min_psi defaults to -200.

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 does not 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 if the inte and root objects are not thread safe, different instances should not use the same instance of a inte or root object simultaneously.

Idea for future:
Use bracketing to speed up one-dimensional root finding.

Definition at line 94 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.

Todo:
Document these coefficients better


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 thermodynamic properties as function of chemical potential.
virtual int calc_density (const double temper)
 Calculate thermodynamic properties as function of density.
virtual int pair_mu (const double temper)
 Calculate thermodynamic properties with antiparticles as function of chemical potential.
virtual int pair_density (const double temper)
 Calculate thermodynamic 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 0).
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().
double min_psi
 The minimum value of $ \psi $ (default -200).

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 thermodynamic 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.

virtual int calc_density ( const double  temper  )  [virtual]

Calculate thermodynamic properties as function of density.

Warning:
This function needs a guess for the chemical potential, and will fail if that guess is not sufficiently accurate.

Reimplemented from fermion.

Reimplemented in eff_quark.


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

Documentation generated with Doxygen and provided under the GNU Free Documentation License. See License Information for details.

Project hosting provided by SourceForge.net Logo, O2scl Sourceforge Project Page