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The SKIRT project
advanced radiative transfer for astrophysics
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The SKIRT project
advanced radiative transfer for astrophysics
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#include <ShellGeometry.hpp>
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 | |
| virtual double | density (double r) const =0 |
| double | density (Position bfr) const override |
| int | dimension () const override |
| Position | generatePosition () const override |
| virtual double | randomRadius () const =0 |
| virtual double | Sigmar () const =0 |
| double | SigmaX () const override |
| double | SigmaY () const override |
| double | SigmaZ () const override |
| virtual double | density (Position bfr) const =0 |
| virtual int | dimension () const =0 |
| virtual Position | generatePosition () const =0 |
| virtual double | SigmaX () const =0 |
| virtual double | SigmaY () const =0 |
| virtual double | SigmaZ () const =0 |
| 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 |
| void | setupSelfBefore () override |
| Protected Member Functions inherited from SimulationItem | |
| SimulationItem () | |
| virtual bool | offersInterface (const std::type_info &interfaceTypeInfo) const |
| virtual void | setupSelfAfter () |
| virtual void | setupSelfBefore () |
| Protected Member Functions inherited from Item | |
| Item () | |
Private Types | |
| using | BaseType = SpheGeometry |
| using | ItemType = ShellGeometry |
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 |
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 \(p\).
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inlineprotected |
Default constructor for concrete Item subclass ShellGeometry : "a shell geometry" .
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overridevirtual |
This function returns the density \(\rho(r)\) at the radius \(r\). It just implements the analytical formula.
Implements SpheGeometry.
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inline |
This function returns the value of the discoverable double property exponent : "the power law exponent" .
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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" .
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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" .
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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.
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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.
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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.