GaussianGeometry Class Reference

#include <GaussianGeometry.hpp>

Inheritance diagram for GaussianGeometry:

Public Member Functions
double	density (double r) const override
double	dispersion () const
double	randomRadius () const override
double	Sigmar () const override
Public Member Functions inherited from SpheGeometry
double	density (Position bfr) const override
int	dimension () const override
Position	generatePosition () const override
double	SigmaX () const override
double	SigmaY () const override
double	SigmaZ () const override
Public Member Functions inherited from SimulationItem
template<class T>
T *	find (bool setup=true) const
template<class T>
T *	interface (int levels=-999999, bool setup=true) const
virtual string	itemName () const
void	setup ()
string	typeAndName () const
Public Member Functions inherited from Item
	Item (const Item &)=delete
virtual	~Item ()
void	addChild (Item *child)
const vector< Item * > &	children () const
virtual void	clearItemListProperty (const PropertyDef *property)
void	destroyChild (Item *child)
virtual bool	getBoolProperty (const PropertyDef *property) const
virtual vector< double >	getDoubleListProperty (const PropertyDef *property) const
virtual double	getDoubleProperty (const PropertyDef *property) const
virtual string	getEnumProperty (const PropertyDef *property) const
virtual int	getIntProperty (const PropertyDef *property) const
virtual vector< Item * >	getItemListProperty (const PropertyDef *property) const
virtual Item *	getItemProperty (const PropertyDef *property) const
virtual string	getStringProperty (const PropertyDef *property) const
int	getUtilityProperty (string name) const
virtual void	insertIntoItemListProperty (const PropertyDef *property, int index, Item *item)
Item &	operator= (const Item &)=delete
Item *	parent () const
virtual void	removeFromItemListProperty (const PropertyDef *property, int index)
virtual void	setBoolProperty (const PropertyDef *property, bool value)
virtual void	setDoubleListProperty (const PropertyDef *property, vector< double > value)
virtual void	setDoubleProperty (const PropertyDef *property, double value)
virtual void	setEnumProperty (const PropertyDef *property, string value)
virtual void	setIntProperty (const PropertyDef *property, int value)
virtual void	setItemProperty (const PropertyDef *property, Item *item)
virtual void	setStringProperty (const PropertyDef *property, string value)
void	setUtilityProperty (string name, int value)
virtual string	type () const

Protected Member Functions
	GaussianGeometry ()
void	setupSelfBefore () override
Protected Member Functions inherited from SpheGeometry
	SpheGeometry ()
Protected Member Functions inherited from Geometry
	Geometry ()
Random *	random () const
void	setupSelfBefore () override
Protected Member Functions inherited from SimulationItem
	SimulationItem ()
virtual bool	offersInterface (const std::type_info &interfaceTypeInfo) const
virtual void	setupSelfAfter ()
Protected Member Functions inherited from Item
	Item ()

Private Types
using	BaseType
using	ItemType

Private Attributes
double	_dispersion
double	_rho0
Array	_rv
const double &	_sigma
Array	_Xv

Friends
class	ItemRegistry

Detailed Description

The GaussianGeometry class is a subclass of the SpheGeometry class, and describes spherical geometries characterized by a Gaussian density profile,

\[ \rho(r) = \rho_0\,\exp\left( -\frac{r^2}{2\sigma^2} \right) .\]

This geometry has one parameter, the radial dispersion \(\sigma\).

Constructor & Destructor Documentation

GaussianGeometry()

GaussianGeometry::GaussianGeometry ( )

inlineprotected

Default constructor for concrete Item subclass GaussianGeometry: "a Gaussian geometry".

Member Function Documentation

density()

double GaussianGeometry::density ( double r ) const

overridevirtual

This function returns the density \(\rho(r)\) at the radius \(r\). It just implements the analytical formula.

Implements SpheGeometry.

dispersion()

double GaussianGeometry::dispersion ( ) const

inline

This function returns the value of the discoverable double property dispersion: "the scale length (dispersion) σ".

This property represents a physical quantity of type "length".

The minimum value for this property is "]0".

randomRadius()

double GaussianGeometry::randomRadius ( ) const

overridevirtual

This function returns the radius \(r\) of a random position drawn from a spherical Gaussian density distribution. Such a value can be generated by picking a uniform deviate \({\cal{X}}\) and solving the equation

\[ {\cal{X}} = 4\pi \int_0^r \rho(r')\, r'^2\, {\text{d}}r' \]

for \(r\), where \(\rho(r)\) is the Gaussian radial density profile. This is done by interpolating from the precalculated table of the cumulative distribution.

Implements SpheGeometry.

setupSelfBefore()

void GaussianGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function calculates some frequently used values. The central density \(\rho_0\) is set by the normalization condition that the total mass equals one, which is straightforward for a Gaussian distribution,

\[ \rho_0 = \frac{1}{(2\pi)^{3/2}\,\sigma^3} .\]

This function also precalculates of a vector with the cumulative mass

\[ M(r) = 4\pi \int_0^r \rho(r')\, r'^2\, {\text{d}}r' \]

at a large number of radii. For the Gaussian distribution we find

\[ M(r) = \mathrm{erf}(t) - \frac{2}{\sqrt{\pi}} \,t \, \exp(-t^2) \quad\mathrm{with}\quad t = \frac{r}{\sqrt{2}\,\sigma} .\]

Reimplemented from SimulationItem.

Sigmar()

double GaussianGeometry::Sigmar ( ) const

overridevirtual

This function returns the surface mass density along a radial line starting at the centre of the coordinate system, i.e.

\[ \Sigma_r = \int_0^\infty \rho(r)\,{\text{d}}r. \]

For a Gaussian geometry we easily find

\[ \Sigma_r = \frac{1}{4\pi\,\sigma^2}. \]

Implements SpheGeometry.

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

• GaussianGeometry.hpp