#include <BiCrystal.h>

Inheritance diagram for gbLAB::BiCrystal< dim >:

Public Member Functions
LatticeVector< dim >	shiftTensorA (const LatticeVector< dim > &d) const

LatticeVector< dim >	shiftTensorB (const LatticeVector< dim > &d) const

	BiCrystal (const Lattice< dim > &A, const Lattice< dim > &B, const bool &useRLLL=false)
	Constructs a bicrystal from two lattices \(\mathcal A \) and \(\mathcal B \) by computing the parallel bases \(\textbf A^\\|, \textbf B^\\|, \textbf C^\\|, \textbf D^\\|\) for lattices \(\mathcal A, \mathcal B, \mathcal C, \mathcal D\), respectively. If the flag useRLLL is .true., then the bases of CSL and DSCL are reduced using the LLL algorithm.

LatticeVector< dim >	getLatticeVectorInA (const LatticeVector< dim > &v) const

LatticeVector< dim >	getLatticeVectorInB (const LatticeVector< dim > &v) const

LatticeVector< dim >	getLatticeVectorInD (const LatticeVector< dim > &v) const

LatticeDirection< dim >	getLatticeDirectionInC (const LatticeVector< dim > &v) const

LatticeDirection< dim >	getLatticeDirectionInD (const LatticeVector< dim > &v) const

ReciprocalLatticeDirection< dim >	getReciprocalLatticeDirectionInA (const ReciprocalLatticeVector< dim > &v) const

ReciprocalLatticeDirection< dim >	getReciprocalLatticeDirectionInB (const ReciprocalLatticeVector< dim > &v) const

ReciprocalLatticeDirection< dim >	getReciprocalLatticeDirectionInC (const ReciprocalLatticeVector< dim > &v) const

ReciprocalLatticeDirection< dim >	getReciprocalLatticeDirectionInD (const ReciprocalLatticeVector< dim > &v) const

template<int dm = dim>
std::enable_if< dm==2\|\|dm==3, std::map< IntScalarType, Gb< dm > > >::type	generateGrainBoundaries (const LatticeDirection< dim > &d, int div=30) const
	Given a tilt axis \(\textbf d\), that belongs to lattices \(\mathcal A\) or \(\mathcal B\), this function generate a set of tilt GBs. CURRENTLY ONLY WORDS FOR DIMENSION 3.

template<int dm = dim>
std::enable_if< dm==2\|\|dm==3, std::vector< LatticeVector< dim > > >::type	box (std::vector< LatticeVector< dim > > &boxVectors, const double &orthogonality, const int &dsclFactor, std::string filename="", bool orient=false) const

Public Member Functions inherited from gbLAB::RationalMatrix< dim >
	RationalMatrix (const MatrixDimD &R)

	RationalMatrix (const MatrixDimI &Rn, const IntScalarType &Rd)

	RationalMatrix (const MatrixDimI &Rn, const MatrixDimI &Rd)

MatrixDimD	asMatrix () const

Public Member Functions inherited from gbLAB::SmithDecomposition< dim >
	SmithDecomposition (const MatrixNi &A)

const MatrixNi &	matrixU () const

const MatrixNi &	matrixD () const

const MatrixNi &	matrixV () const

const MatrixNi &	matrixX () const

const MatrixNi &	matrixY () const

Data Fields
const Lattice< dim > &	A

const Lattice< dim > &	B

const MatrixDimI	M
	Integer matrix that connects the bases \( \textbf A^{\\|} \) and \( \textbf C^{\\|} \) of lattices \(\mathcal A\) and the CSL \(\mathcal C\), respectively: \( \textbf C^{\\|} = \textbf A^{\\|} \textbf M\).

const MatrixDimI	N
	Integer matrix that connects the bases \( \textbf B^{\\|} \) and \( \textbf C^{\\|} \) of lattices \(\mathcal B\) and the CSL \(\mathcal C\), respectively: \( \textbf C^{\\|} = \textbf B^{\\|} \textbf N\).

const IntScalarType	sigmaA
	Signed ratio of the unit cell volume of \(\mathcal C\) to that of \(\mathcal A\). \( \Sigma_{\mathcal A} = \det(\textbf M)\).

const IntScalarType	sigmaB
	Signed ratio of the unit cell volume of \(\mathcal C\) to that of \(\mathcal B\): \( \Sigma_{\mathcal B} = \det(\textbf N)\).

const int	sigma
	\( \Sigma = \|\Sigma_{\mathcal A}\|\) if \( \Sigma_{\mathcal A} = \Sigma_{\mathcal B}\), else \( \Sigma = 0 \)

const Lattice< dim >	csl
	CSL lattice \(\mathcal C\).

const Lattice< dim >	dscl
	DCSL lattice \(\mathcal D\).

const Lattice< dim >	Ap
	Lattice \(\mathcal A\) with basis \(\textbf A^\\|\).

const Lattice< dim >	Bp
	Lattice \(\mathcal B\) with basis \(\textbf B^\\|\).

const MatrixDimI	LambdaA
	Shift tensor \(\Lambda_{\mathcal A}:\mathbb Z_{\mathcal D} \to \mathbb Z_{\mathcal D}\) describes the shift in the CSL when lattice \(\mathcal A\) is shifted by a DSCL vector.

const MatrixDimI	LambdaB
	Shift tensor \(\Lambda_{\mathcal B}:\mathbb Z_{\mathcal D} \to \mathbb Z_{\mathcal D}\) describes the shift in the CSL when lattice \(\mathcal B\) is shifted by a DSCL vector.

Data Fields inherited from gbLAB::RationalMatrix< dim >
const MatrixDimI &	integerMatrix

const IntScalarType &	mu

Private Types
typedef LatticeCore< dim >::IntScalarType	IntScalarType

typedef LatticeCore< dim >::VectorDimD	VectorDimD

typedef LatticeCore< dim >::MatrixDimD	MatrixDimD

typedef LatticeCore< dim >::VectorDimI	VectorDimI

typedef LatticeCore< dim >::MatrixDimI	MatrixDimI

Static Private Member Functions
static MatrixDimI	getM (const RationalMatrix< dim > &rm, const SmithDecomposition< dim > &sd)

static MatrixDimI	getN (const RationalMatrix< dim > &rm, const SmithDecomposition< dim > &sd)

static MatrixDimI	getLambdaA (const MatrixDimI &M, const MatrixDimI &N)

static MatrixDimI	getLambdaB (const MatrixDimI &M, const MatrixDimI &N)

static MatrixDimD	getCSLBasis (const Lattice< dim > &A, const Lattice< dim > &B, const SmithDecomposition< dim > &sd, const MatrixDimI &M, const MatrixDimI &N, const bool &useRLLL)

static MatrixDimD	getDSCLBasis (const Lattice< dim > &A, const Lattice< dim > &B, const SmithDecomposition< dim > &sd, const MatrixDimI &M, const MatrixDimI &N, const bool &useRLLL)

Detailed Description

template<int dim>
class gbLAB::BiCrystal< dim >

Class template that computes the coincident-site-lattice (CSL) of two parent lattices using the Smith Normal Form [1].

[1] Coincidence Lattices and Associated Shear Transformations

Examples: testCoincidentRotations.cpp, testGb.cpp, testGb3d.cpp, testGenerateGBs.cpp, testMoire.cpp, and testSNF.cpp.

Definition at line 27 of file BiCrystal.h.

Member Typedef Documentation

◆ IntScalarType

template<int dim>

typedef LatticeCore<dim>::IntScalarType gbLAB::BiCrystal< dim >::IntScalarType

private

Definition at line 30 of file BiCrystal.h.

◆ MatrixDimD

template<int dim>

typedef LatticeCore<dim>::MatrixDimD gbLAB::BiCrystal< dim >::MatrixDimD

private

Definition at line 32 of file BiCrystal.h.

◆ MatrixDimI

template<int dim>

typedef LatticeCore<dim>::MatrixDimI gbLAB::BiCrystal< dim >::MatrixDimI

private

Definition at line 34 of file BiCrystal.h.

◆ VectorDimD

template<int dim>

typedef LatticeCore<dim>::VectorDimD gbLAB::BiCrystal< dim >::VectorDimD

private

Definition at line 31 of file BiCrystal.h.

◆ VectorDimI

template<int dim>

typedef LatticeCore<dim>::VectorDimI gbLAB::BiCrystal< dim >::VectorDimI

private

Definition at line 33 of file BiCrystal.h.

Constructor & Destructor Documentation

◆ BiCrystal()

template<int dim>

gbLAB::BiCrystal< dim >::BiCrystal	(	const Lattice< dim > &	A,
		const Lattice< dim > &	B,
		const bool &	useRLLL = `false`
	)

Constructs a bicrystal from two lattices \(\mathcal A \) and \(\mathcal B \) by computing the parallel bases \(\textbf A^\|, \textbf B^\|, \textbf C^\|, \textbf D^\|\) for lattices \(\mathcal A, \mathcal B, \mathcal C, \mathcal D\), respectively. If the flag useRLLL is .true., then the bases of CSL and DSCL are reduced using the LLL algorithm.

Parameters

[in] Lattices \(\mathcal A \) and \(\mathcal B \), and useRLLL flag

Returns: A bicrystal object

Definition at line 158 of file BiCrystal.cpp.

Member Function Documentation

◆ box()

template<int dim>

template<int dm>

template std::vector< LatticeVector< 3 > > gbLAB::BiCrystal< dim >::box< 3 >	(	std::vector< LatticeVector< dim > > &	boxVectors,
		const double &	orthogonality,
		const int &	dsclFactor,
		std::string	filename = `""`,
		bool	orient = `false`
	)		const

This function outputs/prints a 2D bicrystal (two lattices that form the GB and the CSL) bounded by a box defined using two input box vectors. The box vectors have to be linearly independent lattice vectors. The function optimizes boxVectors[0] to make the box as orthogonal as possible depending on the orthogonality parameter.

Template Parameters

dm	dimension (int)

Parameters

boxVectors	two linearly independent lattice vectors.
orthogonality	(double) a value in the interval \([0,1]\).
filename	(optional) name of the output file
orient	(optional) While printing to a file, orient the system such that one of the box sides is along the global x axis. This flag does not influence the returning configuration, only the configuration printed to the file.

Returns: lattice points of the bicrystal (along with the CSL) bounded by the box (std::vector<LatticeVector<2>>).

Definition at line 501 of file BiCrystal.cpp.

◆ generateGrainBoundaries()

template<int dim>

template<int dm>

template std::map< BiCrystal< 3 >::IntScalarType, Gb< 3 > > gbLAB::BiCrystal< dim >::generateGrainBoundaries< 3 >	(	const LatticeDirection< dim > &	d,
		int	div = `30`
	)		const

Given a tilt axis \(\textbf d\), that belongs to lattices \(\mathcal A\) or \(\mathcal B\), this function generate a set of tilt GBs. CURRENTLY ONLY WORDS FOR DIMENSION 3.

Template Parameters

dm

Parameters

d	- LatticeDirection that describes the tilt axis
div	- parameter to span the GBs

Returns: A data structure that stores GBs sorted in increasing order of their inclination angle.

Examples: testGenerateGBs.cpp.

Definition at line 447 of file BiCrystal.cpp.

◆ getCSLBasis()

template<int dim>

BiCrystal< dim >::MatrixDimD gbLAB::BiCrystal< dim >::getCSLBasis	(	const Lattice< dim > &	A,
		const Lattice< dim > &	B,
		const SmithDecomposition< dim > &	sd,
		const MatrixDimI &	M,
		const MatrixDimI &	N,
		const bool &	useRLLL
	)

staticprivate

Definition at line 83 of file BiCrystal.cpp.

◆ getDSCLBasis()

template<int dim>

BiCrystal< dim >::MatrixDimD gbLAB::BiCrystal< dim >::getDSCLBasis	(	const Lattice< dim > &	A,
		const Lattice< dim > &	B,
		const SmithDecomposition< dim > &	sd,
		const MatrixDimI &	M,
		const MatrixDimI &	N,
		const bool &	useRLLL
	)

staticprivate

Definition at line 132 of file BiCrystal.cpp.

◆ getLambdaA()

template<int dim>

BiCrystal< dim >::MatrixDimI gbLAB::BiCrystal< dim >::getLambdaA	(	const MatrixDimI &	M,
		const MatrixDimI &	N
	)

staticprivate

Definition at line 43 of file BiCrystal.cpp.

◆ getLambdaB()

template<int dim>

BiCrystal< dim >::MatrixDimI gbLAB::BiCrystal< dim >::getLambdaB	(	const MatrixDimI &	M,
		const MatrixDimI &	N
	)

staticprivate

Definition at line 63 of file BiCrystal.cpp.

◆ getLatticeDirectionInC()

template<int dim>

LatticeDirection< dim > gbLAB::BiCrystal< dim >::getLatticeDirectionInC ( const LatticeVector< dim > & v ) const

Outputs lattice direction in the CSL \(\mathcal C\) that is parallel to the inputted vector \(\textbf v\) that belongs to one of the four lattices, \(\mathcal A\), \(\mathcal B\), \(\mathcal C\), or \(\mathcal D\),

Parameters

v	- lattice vector

Returns: LatticeDirection in \(\mathcal C\)

Examples: testGb3d.cpp, and testGenerateGBs.cpp.

Definition at line 297 of file BiCrystal.cpp.

◆ getLatticeDirectionInD()

template<int dim>

LatticeDirection< dim > gbLAB::BiCrystal< dim >::getLatticeDirectionInD ( const LatticeVector< dim > & v ) const

Outputs lattice direction in the DSCL \(\mathcal D\) that is parallel to the inputted vector \(\textbf v\) that belongs to one of the four lattices, \(\mathcal A\), \(\mathcal B\), \(\mathcal C\), or \(\mathcal D\),

Parameters

v	- lattice vector

Returns: LatticeDirection in \(\mathcal D\)

Examples: testGenerateGBs.cpp.

Definition at line 325 of file BiCrystal.cpp.

◆ getLatticeVectorInA()

template<int dim>

LatticeVector< dim > gbLAB::BiCrystal< dim >::getLatticeVectorInA ( const LatticeVector< dim > & v ) const

Outputs lattice vector in lattice \(\mathcal A\) that is equal to the inputted vector \(\textbf v\) that belongs to \(\mathcal A\) or \(\mathcal C\)

Parameters

v	- lattice vector

Returns: LatticeVector in \(\mathcal A\)

Definition at line 231 of file BiCrystal.cpp.

◆ getLatticeVectorInB()

template<int dim>

LatticeVector< dim > gbLAB::BiCrystal< dim >::getLatticeVectorInB ( const LatticeVector< dim > & v ) const

Outputs lattice vector in lattice \(\mathcal B\) that is equal to the inputted vector \(\textbf v\) that belongs to \(\mathcal B\) or \(\mathcal C\)

Parameters

v	- lattice vector

Returns: LatticeVector in \(\mathcal B\)

Definition at line 249 of file BiCrystal.cpp.

◆ getLatticeVectorInD()

template<int dim>

LatticeVector< dim > gbLAB::BiCrystal< dim >::getLatticeVectorInD ( const LatticeVector< dim > & v ) const

Outputs lattice vector in lattice \(\mathcal D\) that is equal to the inputted vector \(\textbf v\) that belongs to \(\mathcal A\), \(\mathcal B\), \(\mathcal C\), or \(\mathcal D\)

Parameters

v	- lattice vector

Returns: LatticeVector in \(\mathcal D\)

Definition at line 267 of file BiCrystal.cpp.

◆ getM()

template<int dim>

BiCrystal< dim >::MatrixDimI gbLAB::BiCrystal< dim >::getM	(	const RationalMatrix< dim > &	rm,
		const SmithDecomposition< dim > &	sd
	)

staticprivate

Definition at line 17 of file BiCrystal.cpp.

◆ getN()

template<int dim>

BiCrystal< dim >::MatrixDimI gbLAB::BiCrystal< dim >::getN	(	const RationalMatrix< dim > &	rm,
		const SmithDecomposition< dim > &	sd
	)

staticprivate

Definition at line 30 of file BiCrystal.cpp.

◆ getReciprocalLatticeDirectionInA()

template<int dim>

ReciprocalLatticeDirection< dim > gbLAB::BiCrystal< dim >::getReciprocalLatticeDirectionInA ( const ReciprocalLatticeVector< dim > & v ) const

Outputs reciprocal lattice direction in the dual lattice \(\mathcal A^*\) that is parallel to the inputted reciprocal vector \(\textbf v\) that belongs to one of the four dual lattices, \(\mathcal A^*\), \(\mathcal B^*\), \(\mathcal C^*\), or \(\mathcal D^*\),

Parameters

v	- lattice vector

Returns: ReciprocalLatticeDirection in \(\mathcal A^*\)

Definition at line 331 of file BiCrystal.cpp.

◆ getReciprocalLatticeDirectionInB()

template<int dim>

ReciprocalLatticeDirection< dim > gbLAB::BiCrystal< dim >::getReciprocalLatticeDirectionInB ( const ReciprocalLatticeVector< dim > & v ) const

Outputs reciprocal lattice direction in the dual lattice \(\mathcal B^*\) that is parallel to the inputted reciprocal vector \(\textbf v\) that belongs to one of the four dual lattices, \(\mathcal A^*\), \(\mathcal B^*\), \(\mathcal C^*\), or \(\mathcal D^*\),

Parameters

v	- lattice vector

Returns: ReciprocalLatticeDirection in \(\mathcal B^*\)

Definition at line 357 of file BiCrystal.cpp.

◆ getReciprocalLatticeDirectionInC()

template<int dim>

ReciprocalLatticeDirection< dim > gbLAB::BiCrystal< dim >::getReciprocalLatticeDirectionInC ( const ReciprocalLatticeVector< dim > & v ) const

Outputs reciprocal lattice direction in the dual lattice \(\mathcal C^*\) that is parallel to the inputted reciprocal vector \(\textbf v\) that belongs to one of the four dual lattices, \(\mathcal A^*\), \(\mathcal B^*\), \(\mathcal C^*\), or \(\mathcal D^*\),

Parameters

v	- lattice vector

Returns: ReciprocalLatticeDirection in \(\mathcal C^*\)

Examples: testGenerateGBs.cpp.

Definition at line 385 of file BiCrystal.cpp.

◆ getReciprocalLatticeDirectionInD()

template<int dim>

ReciprocalLatticeDirection< dim > gbLAB::BiCrystal< dim >::getReciprocalLatticeDirectionInD ( const ReciprocalLatticeVector< dim > & v ) const

Outputs reciprocal lattice direction in the dual lattice \(\mathcal D^*\) that is parallel to the inputted reciprocal vector \(\textbf v\) that belongs to one of the four dual lattices, \(\mathcal A^*\), \(\mathcal B^*\), \(\mathcal C^*\), or \(\mathcal D^*\),

Parameters

v	- lattice vector

Returns: ReciprocalLatticeDirection in \(\mathcal D^*\)

Definition at line 408 of file BiCrystal.cpp.

◆ shiftTensorA()

template<int dim>

LatticeVector< dim > gbLAB::BiCrystal< dim >::shiftTensorA ( const LatticeVector< dim > & d ) const

Definition at line 430 of file BiCrystal.cpp.

◆ shiftTensorB()

template<int dim>

LatticeVector< dim > gbLAB::BiCrystal< dim >::shiftTensorB ( const LatticeVector< dim > & d ) const

Definition at line 438 of file BiCrystal.cpp.

Field Documentation

◆ A

template<int dim>

const Lattice<dim>& gbLAB::BiCrystal< dim >::A

Examples: testGb3d.cpp, and testGenerateGBs.cpp.

Definition at line 56 of file BiCrystal.h.

◆ Ap

template<int dim>

const Lattice<dim> gbLAB::BiCrystal< dim >::Ap

Lattice \(\mathcal A\) with basis \(\textbf A^\|\).

Examples: testMoire.cpp.

Definition at line 94 of file BiCrystal.h.

◆ B

template<int dim>

const Lattice<dim>& gbLAB::BiCrystal< dim >::B

Definition at line 57 of file BiCrystal.h.

◆ Bp

template<int dim>

const Lattice<dim> gbLAB::BiCrystal< dim >::Bp

Lattice \(\mathcal B\) with basis \(\textbf B^\|\).

Examples: testMoire.cpp.

Definition at line 98 of file BiCrystal.h.

◆ csl

template<int dim>

const Lattice<dim> gbLAB::BiCrystal< dim >::csl

CSL lattice \(\mathcal C\).

Examples: testGb.cpp, testGb3d.cpp, testGenerateGBs.cpp, and testMoire.cpp.

Definition at line 86 of file BiCrystal.h.

◆ dscl

template<int dim>

const Lattice<dim> gbLAB::BiCrystal< dim >::dscl

DCSL lattice \(\mathcal D\).

Examples: testGb.cpp, testGenerateGBs.cpp, and testMoire.cpp.

Definition at line 90 of file BiCrystal.h.

◆ LambdaA

template<int dim>

const MatrixDimI gbLAB::BiCrystal< dim >::LambdaA

Shift tensor \(\Lambda_{\mathcal A}:\mathbb Z_{\mathcal D} \to \mathbb Z_{\mathcal D}\) describes the shift in the CSL when lattice \(\mathcal A\) is shifted by a DSCL vector.

Examples: testGenerateGBs.cpp, testMoire.cpp, and testSNF.cpp.

Definition at line 103 of file BiCrystal.h.

◆ LambdaB

template<int dim>

const MatrixDimI gbLAB::BiCrystal< dim >::LambdaB

Shift tensor \(\Lambda_{\mathcal B}:\mathbb Z_{\mathcal D} \to \mathbb Z_{\mathcal D}\) describes the shift in the CSL when lattice \(\mathcal B\) is shifted by a DSCL vector.

Examples: testSNF.cpp.

Definition at line 108 of file BiCrystal.h.

◆ M

template<int dim>

const MatrixDimI gbLAB::BiCrystal< dim >::M

Integer matrix that connects the bases \( \textbf A^{\|} \) and \( \textbf C^{\|} \) of lattices \(\mathcal A\) and the CSL \(\mathcal C\), respectively: \( \textbf C^{\|} = \textbf A^{\|} \textbf M\).

Definition at line 62 of file BiCrystal.h.

◆ N

template<int dim>

const MatrixDimI gbLAB::BiCrystal< dim >::N

Integer matrix that connects the bases \( \textbf B^{\|} \) and \( \textbf C^{\|} \) of lattices \(\mathcal B\) and the CSL \(\mathcal C\), respectively: \( \textbf C^{\|} = \textbf B^{\|} \textbf N\).

Definition at line 67 of file BiCrystal.h.

◆ sigma

template<int dim>

const int gbLAB::BiCrystal< dim >::sigma

\( \Sigma = |\Sigma_{\mathcal A}|\) if \( \Sigma_{\mathcal A} = \Sigma_{\mathcal B}\), else \( \Sigma = 0 \)

Examples: testCoincidentRotations.cpp, testGb3d.cpp, and testGenerateGBs.cpp.

Definition at line 82 of file BiCrystal.h.

◆ sigmaA

template<int dim>

const IntScalarType gbLAB::BiCrystal< dim >::sigmaA

Signed ratio of the unit cell volume of \(\mathcal C\) to that of \(\mathcal A\). \( \Sigma_{\mathcal A} = \det(\textbf M)\).

Examples: testMoire.cpp, and testSNF.cpp.

Definition at line 72 of file BiCrystal.h.

◆ sigmaB

template<int dim>

const IntScalarType gbLAB::BiCrystal< dim >::sigmaB

Signed ratio of the unit cell volume of \(\mathcal C\) to that of \(\mathcal B\): \( \Sigma_{\mathcal B} = \det(\textbf N)\).

Examples: testMoire.cpp, and testSNF.cpp.

Definition at line 77 of file BiCrystal.h.

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

include/Lattices/BiCrystal.h
src/Lattices/BiCrystal.cpp

Public Member Functions

Data Fields

Private Types

Static Private Member Functions

Detailed Description

Member Typedef Documentation

◆ IntScalarType

◆ MatrixDimD

◆ MatrixDimI

◆ VectorDimD

◆ VectorDimI

Constructor & Destructor Documentation

◆ BiCrystal()

Member Function Documentation

◆ box()

◆ generateGrainBoundaries()

◆ getCSLBasis()

◆ getDSCLBasis()

◆ getLambdaA()

◆ getLambdaB()

◆ getLatticeDirectionInC()

◆ getLatticeDirectionInD()

◆ getLatticeVectorInA()

◆ getLatticeVectorInB()

◆ getLatticeVectorInD()

◆ getM()

◆ getN()

◆ getReciprocalLatticeDirectionInA()

◆ getReciprocalLatticeDirectionInB()

◆ getReciprocalLatticeDirectionInC()

◆ getReciprocalLatticeDirectionInD()

◆ shiftTensorA()

◆ shiftTensorB()

Field Documentation

◆ A

◆ Ap

◆ B

◆ Bp

◆ csl

◆ dscl

◆ LambdaA

◆ LambdaB

◆ M

◆ N

◆ sigma

◆ sigmaA

◆ sigmaB