ShellGeometry Class Reference

#include <ShellGeometry.hpp>

Inheritance diagram for ShellGeometry:

Public Member Functions
double	density (double r) const override
double	exponent () const
double	maxRadius () const
double	minRadius () 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
	ShellGeometry ()
void	setupSelfBefore () override
Protected Member Functions inherited from SpheGeometry
	SpheGeometry ()
Protected Member Functions inherited from Geometry
	Geometry ()
Random *	random () const
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	_A
double	_exponent
double	_maxRadius
double	_minRadius
const double &	_p
const double &	_rmax
const double &	_rmin
double	_sdiff
double	_smin
double	_tmax
double	_tmin

Friends
class	ItemRegistry

Detailed Description

The ShellGeometry class is a subclass of the SpheGeometry class and describes the geometry of a spherical shell, where the density behaves as a power law between an inner and an outer radius,

\[ \rho(r) = A\,r^{-p} \qquad\qquad r_{\text{min}} < r < r_{\text{max}}. \]

with \(A\) a normalization constant. Obviously the condition \(r_{\text{min}} < r_{\text{max}}\) should be satisfied. This geometry is characterized by three free parameters: the inner radius \(r_{\text{min}}\), the outer radius \(r_{\text{max}}\) and the power law exponent \(p\).

Constructor & Destructor Documentation

ShellGeometry()

ShellGeometry::ShellGeometry ( )

inlineprotected

Default constructor for concrete Item subclass ShellGeometry: "a shell geometry".

Member Function Documentation

density()

double ShellGeometry::density ( double r ) const

overridevirtual

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

Implements SpheGeometry.

exponent()

double ShellGeometry::exponent ( ) const

inline

This function returns the value of the discoverable double property exponent: "the power law exponent".

maxRadius()

double ShellGeometry::maxRadius ( ) const

inline

This function returns the value of the discoverable double property maxRadius: "the outer radius of the shell".

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

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

minRadius()

double ShellGeometry::minRadius ( ) const

inline

This function returns the value of the discoverable double property minRadius: "the inner radius of the shell".

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

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

randomRadius()

double ShellGeometry::randomRadius ( ) const

overridevirtual

This function returns the radius of a random position drawn from the shell density distribution. This is accomplished by generating a uniform deviate \({\cal{X}}\), and solving the equation

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

for \(r\). For the shell geometry, with \(p\ne3\), we find

\[ {\cal{X}} = \frac{r^{3-p}-r_{\text{min}}^{3-p}} {r_{\text{max}}^{3-p}-r_{\text{min}}^{3-p}}. \]

Inverting this results in

\[ r = \left[ (1-{\cal{X}})\,r_{\text{min}}^{3-p} + {\cal{X}}\,r_{\text{max}}^{3-p} \right]^{\frac{1}{3-p}}. \]

For \(p=3\) this expression does not hold, and for \(p\approx3\) it breaks down numerically. So for \(p\approx3\) we can write the general expression

\[ r = {\text{gexp}}_{p-2} \Big[ {\text{gln}}_{p-2}\, r_{\text{min}} + {\cal{X}}\,( {\text{gln}}_{p-2}\, r_{\text{max}} - {\text{gln}}_{p-2}\, r_{\text{min}} ) \Bigr]. \]

In this expression, \({\text{gln}}_p\,x\) and \({\text{gexp}}_p\,x\) are the generalized logarithm and exponential functions defined in SpecialFunctions::gln and SpecialFunctions::gexp respectively.

Implements SpheGeometry.

setupSelfBefore()

void ShellGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function verifies the validity of the attributes. The normalization parameter \(A\) is set by the normalization condition that total mass equals one, i.e.

\[ 1 = 4\pi A \int_{r_{\text{min}}}^{r_{\text{max}}} r^{2-p}\, {\text{d}}r. \]

This results in

\[ A = \frac{1}{4\pi}\, \frac{1}{ {\text{gln}}_{p-2}\, r_{\text{max}} - {\text{gln}}_{p-2}\, r_{\text{min}} }, \]

with \({\text{gln}}_p\,x\) the generalized logarithm defined in SpecialFunctions::gln.

Reimplemented from Geometry.

Sigmar()

double ShellGeometry::Sigmar ( ) const

overridevirtual

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

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

For the shell geometry, one obtains

\[ \Sigma_r = A\, ( {\text{gln}}_p\, r_{\text{max}} - {\text{gln}}_p\, r_{\text{min}} ) \]

with \({\text{gln}}_p\,x\) the generalized logarithm defined in SpecialFunctions::gln.

Implements SpheGeometry.

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

• ShellGeometry.hpp