ParaboloidGeometry Class Reference

#include <ParaboloidGeometry.hpp>

Inheritance diagram for ParaboloidGeometry:

Public Member Functions
double	density (double R, double z) const override
Position	generatePosition () const override
double	offsetZ () const
double	openingAngle () const
double	radialExtent () const
double	SigmaR () const override
double	SigmaZ () const override
Public Member Functions inherited from AxGeometry
double	density (Position bfr) const override
int	dimension () const override
double	SigmaX () const override
double	SigmaY () 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
	ParaboloidGeometry ()
void	setupSelfBefore () override
Protected Member Functions inherited from AxGeometry
	AxGeometry ()
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	_a
const double &	_D
const double &	_Delta
double	_offsetZ
double	_openingAngle
double	_radialExtent
double	_Rp
const double &	_z0
double	_zmax

Friends
class	ItemRegistry

Detailed Description

The ParaboloidGeometry class is a subclass of the AxGeometry class and describes the geometry defined by a double paraboloid surface. It may be used to represent dusty outflows.

The current implementation allows only a constant density distribution bounded by the paraboloid surface

\[ z=\frac{\rho^2}{a^2} \]

and two horizontal planes parallel to the xy plane, \(\pm (z_{\text{max}}+z_{0})\). There are three free parameters describing this dust geometry: the radial extent \(D\), the half opening angle \(\Delta\), and the offset of the paraboloid vertices in the z direction \(z_{0}\). The radial extent corresponds to the length of the line connecting the paraboloid vertex and its top for a given half opening angle of the paraboloid; the half opening angle is measured from the z axis to the radial extent line. The paraboloid height, radius and curvature level are determined by the radial extent and half opening angle.

This item type is displayed only if the Boolean expression "Level2" evaluates to true after replacing the names by true or false depending on their presence.

Constructor & Destructor Documentation

ParaboloidGeometry()

ParaboloidGeometry::ParaboloidGeometry ( )

inlineprotected

Default constructor for concrete Item subclass ParaboloidGeometry: "a paraboloid geometry".

Member Function Documentation

density()

double ParaboloidGeometry::density ( double R, double z ) const

overridevirtual

This function returns the density \(\rho\) at the cylindrical radius \(R\) and height \(z\). For the present geometry, it returns a constant density for positions inside the paraboloid, and zero for positions outside the paraboloid.

Implements AxGeometry.

generatePosition()

Position ParaboloidGeometry::generatePosition ( ) const

overridevirtual

This function generates a random position from the probability density \(p({\bf{r}})\, {\text{d}}{\bf{r}} = \rho({\bf{r}})\, {\text{d}}{\bf{r}}\). Since the current implementation allows only a constant density distribution, a random position can easily be constructed. The function repeatedly generates a uniform random position in the cylinder enveloping the geometry, and accepts the first position that happens to fall inside the nonzero-density region of the actual geometry.

Implements Geometry.

offsetZ()

double ParaboloidGeometry::offsetZ ( ) const

inline

This function returns the value of the discoverable double property offsetZ: "the offset of the paraboloid vertices in the z direction".

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

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

The default value for this property is given by the conditional value expression "0".

openingAngle()

double ParaboloidGeometry::openingAngle ( ) const

inline

This function returns the value of the discoverable double property openingAngle: "the half opening angle of the paraboloid".

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

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

The maximum value for this property is "90 deg[".

radialExtent()

double ParaboloidGeometry::radialExtent ( ) const

inline

This function returns the value of the discoverable double property radialExtent: "the radial extent of the paraboloid".

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

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

setupSelfBefore()

void ParaboloidGeometry::setupSelfBefore ( )

overrideprotectedvirtual

This function calculates some frequently used values, including the normalization factor \(A\), which is set by the normalization condition that total mass equals one, resulting in

\[ A=\frac{1}{\pi*R_{p}^{2}*z_{max}}. \]

Reimplemented from Geometry.

SigmaR()

double ParaboloidGeometry::SigmaR ( ) const

overridevirtual

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

\[\Sigma_R = \int_0^\infty \rho(R,0,0)\,{\text{d}}r. \]

For the paraboloid geometry this integral is simply zero.

Implements AxGeometry.

SigmaZ()

double ParaboloidGeometry::SigmaZ ( ) const

overridevirtual

This function returns the Z-axis surface density, i.e. the integration of the density along the entire Z-axis,

\[ \Sigma_Z = \int_{-\infty}^\infty \rho(0,0,z)\, {\text{d}}z. \]

In the case of paraboloid geometry with constant density this is simply

\[ \Sigma_Z = 2 A z_{max}. \]

Implements Geometry.

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

• ParaboloidGeometry.hpp