Interactions between two constant and identical magnetic dipoles. More...
#include <MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles.hpp>
Public Member Functions | |
| OPENMPCD_CUDA_HOST_AND_DEVICE | MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles (const T prefactor_, const Vector3D< T > &orientation_) |
| The constructor. More... | |
| OPENMPCD_CUDA_HOST_AND_DEVICE Vector3D< T > | force (const Vector3D< T > &R) const |
| Returns the force vector of the interaction for a given position vector. More... | |
| OPENMPCD_CUDA_HOST_AND_DEVICE T | potential (const Vector3D< T > &R) const |
| Returns the potential of the interaction for a given position vector. More... | |
| OPENMPCD_CUDA_HOST_AND_DEVICE T | getPrefactor () const |
| Returns the term \( \frac{\mu_0 m^2}{4 \pi} \). More... | |
| const OPENMPCD_CUDA_HOST_AND_DEVICE Vector3D< T > & | getDipoleOrientation () const |
| Returns the dipole orientation \( \hat{m} \). More... | |
| virtual OPENMPCD_CUDA_HOST_AND_DEVICE Vector3D< FP > | force (const Vector3D< FP > &Rvec) const=0 |
| Returns the force vector of the interaction for a given position vector. More... | |
| virtual OPENMPCD_CUDA_HOST_AND_DEVICE FP | potential (const Vector3D< FP > &Rvec) const=0 |
| Returns the potential of the interaction for a given position vector. More... | |
| const OPENMPCD_CUDA_HOST_AND_DEVICE Vector3D< FP > | forceOnR1DueToR2 (const Vector3D< FP > &r1, const Vector3D< FP > &r2) const |
Returns the force exerted on the particle at r1 due to the particle at r2. More... | |
Detailed Description
template<typename T = FP>
class OpenMPCD::PairPotentials::MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles< T >
Interactions between two constant and identical magnetic dipoles.
The general magnetic dipole-dipole interaction potential is given by
\[ - \frac{ \mu_0 }{ 4 \pi r^3 } \left( 3 \left(\vec{m_1} \cdot \hat{r} \right) \left(\vec{m_2} \cdot \hat{r} \right) - \vec{m_1} \cdot \vec{m_2} \right) \]
where \( \mu_0 \) is the vacuum permeability, \( \hat{r} \) and \( r \) are, respectively, the unit vector and length of the vector \( \vec{r} \) that points from one dipole's position to the other's, \( \vec{m_1} \) and \( \vec{m_2} \) are the magnetic dipole moments, and \( \cdot \) denotes the inner product.
In the special case treated in this class, the magnetic dipole moments are assumed to be constant throughout time in size and orientation. Therefore, with \( m \) being the magnitude of the individual dipole moments and with \( \hat{m} \) being the unit vector of the individual dipole moments, the interaction potential is given by
\[ - \frac{ \mu_0 m^2 }{ 4 \pi r^3 } \left( 3 \left(\hat{m} \cdot \hat{r} \right)^2 - 1 \right) \]
- Template Parameters
-
T The numeric data type.
Definition at line 57 of file MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles.hpp.
Constructor & Destructor Documentation
◆ MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles()
|
inline |
The constructor.
- Parameters
-
[in] prefactor_ The term \( \frac{\mu_0 m^2}{4 \pi} \). [in] orientation_ The orientation unit vector \( \hat{m} \) of the dipole moments.
Definition at line 71 of file MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles.hpp.
Member Function Documentation
◆ force() [1/2]
|
pure virtualinherited |
Returns the force vector of the interaction for a given position vector.
This function returns the directional derivative
\[ - \nabla_R V \left( \vec{R} \right) \]
where \( \vec{R} \) is the Rvec parameter, \( V \) is the potential as given by the potential function, and \( \nabla_R V \) is the gradient of \( V \) with respect to \( \vec{R} \).
- Parameters
-
[in] Rvec The relative position vector.
◆ force() [2/2]
|
inline |
Returns the force vector of the interaction for a given position vector.
This function returns the directional derivative
\[ - \nabla_R V \left( \vec{R} \right) \]
where \( \vec{R} \) is the R parameter, \( V \) is the potential as given by the potential function, and \( \nabla_R V \) is the gradient of \( V \) with respect to \( \vec{R} \).
- Exceptions
-
OpenMPCD::AssertionException If OPENMPCD_DEBUGis defined, throws ifOpenMPCD::Scalar::isZero(R.getMagnitudeSquared()).
- Parameters
-
[in] R The relative position vector.
Definition at line 100 of file MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles.hpp.
◆ forceOnR1DueToR2()
|
inlineinherited |
Returns the force exerted on the particle at r1 due to the particle at r2.
- Parameters
-
[in] r1 The position of the first particle. [in] r2 The position of the second particle.
Definition at line 65 of file PairPotentials/Base.hpp.
◆ getDipoleOrientation()
|
inline |
Returns the dipole orientation \( \hat{m} \).
Definition at line 155 of file MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles.hpp.
◆ getPrefactor()
|
inline |
Returns the term \( \frac{\mu_0 m^2}{4 \pi} \).
Definition at line 146 of file MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles.hpp.
◆ potential() [1/2]
|
pure virtualinherited |
Returns the potential of the interaction for a given position vector.
- Parameters
-
[in] Rvec The relative position vector.
◆ potential() [2/2]
|
inline |
Returns the potential of the interaction for a given position vector.
- Exceptions
-
OpenMPCD::AssertionException If OPENMPCD_DEBUGis defined, throws ifOpenMPCD::Scalar::isZero(R.getMagnitudeSquared()).
- Parameters
-
[in] R The relative position vector.
Definition at line 129 of file MagneticDipoleDipoleInteraction_ConstantIdenticalDipoles.hpp.
The documentation for this class was generated from the following file:
