#include <density.h>

A class for time-efficient (time-memory trade-off) calculation of density on the lattice.

It holds six FourVectors - positive and negative summands of 4-current, and the time and spatial derivatives of the compound current. These four-vectors are additive by particles. It is efficient to calculate additive \(j^\mu\) and \(\partial_\nu j^\mu \) in one loop over particles and then calculate the Eckart density, the gradient of the density, the curl, the time derivative of the current, and derivatives of the rest frame density accordingly. Splitting into positive and negative parts of \(j^\mu\) is necessary to avoid problems with the definition of Eckart rest frame.

Intended usage of the class:

Add particles from some list using add_particle(), setting jmu_pos and jmu_neg. Calculate derivatives using either add_particle_for_derivatives() (in case of Gaussian derivatives) or calculating finite difference derivatives; this sets djmu_dxnu. If needed, calculate rest frame density derivatives, setting drho_dxnu.
Get the net current via jmu_net().
Get the net rest frame density via rho().
Get the derivatives of the net current via djmu_dxnu()
Get the derivatives of the net rest frame baryon density via drho_dxnu()
Get \(\boldsymbol{\nabla} j^0\) via grad_j0()
Get \(\boldsymbol{\nabla} \times \mathbf{j}\) via curl_vecj()
Get \(\partial_t\,\mathbf{j}\) via dvecj_dt()
Get \((\boldsymbol{\nabla} \rho) \times \mathbf{j}\) via grad_rho_cross_vecj()

Definition at line 299 of file density.h.

Public Member Functions
	DensityOnLattice ()
	Default constructor. More...

void	add_particle (const ParticleData &part, double FactorTimesSf)
	Adds particle to 4-current: \(j^{\mu} += p^{\mu}/p^0 \cdot factor \). More...

void	add_particle_for_derivatives (const ParticleData &part, double factor, ThreeVector sf_grad)
	Adds particle to the time and spatial derivatives of the 4-current. More...

double	rho (const double norm_factor=1.0)
	Compute the net Eckart density on the local lattice. More...

ThreeVector	curl_vecj (const double norm_factor=1.0)
	Compute curl of the current on the local lattice. More...

ThreeVector	grad_j0 (const double norm_factor=1.0)
	Compute gradient of the the zeroth component of the four-current j^mu (that is of the computational frame density) on the local lattice. More...

ThreeVector	dvecj_dt (const double norm_factor=1.0)
	Compute time derivative of the current density on the local lattice. More...

FourVector	jmu_net () const

void	add_to_jmu_pos (FourVector additional_jmu_B)
	Add to the positive density current. More...

void	add_to_jmu_neg (FourVector additional_jmu_B)
	Add to the negative density current. More...

FourVector	drho_dxnu () const
	Return the FourGradient of the rest frame density \(\partial_{\nu}\rho\). More...

std::array< FourVector, 4 >	djmu_dxnu () const
	Return the FourGradient of the net baryon current \(\partial_{\nu} j^\mu\). More...

ThreeVector	grad_rho_cross_vecj () const
	Compute the cross product of \(\boldsymbol{\nabla}\rho\) and \(j^\mu\). More...

void	overwrite_djmu_dt_to_zero ()
	Overwrite the time derivative of the current to zero. More...

void	overwrite_drho_dt_to_zero ()
	Overwrite the time derivative of the rest frame density to zero. More...

void	overwrite_drho_dxnu (FourVector computed_drho_dxnu)
	Overwrite the rest frame density derivatives to provided values. More...

void	overwrite_djmu_dxnu (FourVector djmu_dt, FourVector djmu_dx, FourVector djmu_dy, FourVector djmu_dz)
	Overwrite all density current derivatives to provided values. More...

Private Attributes
FourVector	jmu_pos_
	Four-current density of the positively charged particle. More...

FourVector	jmu_neg_
	Four-current density of the negatively charged particle. More...

std::array< FourVector, 4 >	djmu_dxnu_
	Four-gradient of the four-current density, \(\partial_\nu j^\mu \). More...

FourVector	drho_dxnu_
	Four-gradient of the rest frame density, \(\partial_\nu \rho \). More...

Constructor & Destructor Documentation

◆ DensityOnLattice()

smash::DensityOnLattice::DensityOnLattice ( )

inline

Default constructor.

Definition at line 302 of file density.h.

       : jmu_pos_(FourVector()),
         jmu_neg_(FourVector()),
         djmu_dxnu_({FourVector(), FourVector(), FourVector(), FourVector()}),
         drho_dxnu_(FourVector()) {}

Member Function Documentation

◆ add_particle()

void smash::DensityOnLattice::add_particle	(	const ParticleData &	part,
		double	FactorTimesSf
	)

inline

Adds particle to 4-current: \(j^{\mu} += p^{\mu}/p^0 \cdot factor \).

Two private class members jmu_pos_ and jmu_neg_ indicating the 4-current of the positively and negatively charged particles are updated by this function.

Parameters

[in]	part	Particle would be added to the current density on the lattice.
[in]	FactorTimesSf	particle contribution to given density type (e.g. anti-proton contributes with factor -1 to baryon density, proton - with factor 1) times the smearing factor.

Definition at line 320 of file density.h.

                                                                     {
     const FourVector part_four_velocity = FourVector(1.0, part.velocity());
     if (FactorTimesSf > 0.0) {
       jmu_pos_ += part_four_velocity * FactorTimesSf;
     } else {
       jmu_neg_ += part_four_velocity * FactorTimesSf;
     }
   }

◆ add_particle_for_derivatives()

void smash::DensityOnLattice::add_particle_for_derivatives	(	const ParticleData &	part,
		double	factor,
		ThreeVector	sf_grad
	)

inline

Adds particle to the time and spatial derivatives of the 4-current.

An array of four private 4-vectors djmu_dxnu_ indicating the derivatives of the compound current are updated by this function.

Parameters

[in]	part	Particle would be added to the current density on the lattice.
[in]	factor	particle contribution to given density type (e.g. anti-proton contributes with factor -1 to baryon density, proton - with factor 1).
[in]	sf_grad	Smearing factor of the gradients

Definition at line 341 of file density.h.

                                                          {
     const FourVector PartFourVelocity = FourVector(1.0, part.velocity());
     for (int k = 1; k <= 3; k++) {
       djmu_dxnu_[k] += factor * PartFourVelocity * sf_grad[k - 1];
       djmu_dxnu_[0] -=
           factor * PartFourVelocity * sf_grad[k - 1] * part.velocity()[k - 1];
     }
   }

◆ rho()

double smash::DensityOnLattice::rho ( const double norm_factor = 1.0 )

inline

Compute the net Eckart density on the local lattice.

Note that the net Eckart density is calculated by taking the difference between the Eckart density of the positively charged particles and that of the negatively charged particles, which are, in general, defined in different frames. So the net Eckart density is not the net density in the Eckart local rest frame. However, this is the only way we can think of to be applied to the case where the density current is space-like. And fortunately, the net eckart densities are only used for calculating the potentials which are valid only in the low-energy collisions where the amount of the negatively charged particles are negligible. May be in the future, the net Eckart density can be calculated in a smarter way.

Parameters

[in] norm_factor Normalization factor

Returns: Net Eckart density on the local lattice \(\rho\) [fm \(^{-3}\)]

Definition at line 368 of file density.h.

                                              {
     return (jmu_pos_.abs() - jmu_neg_.abs()) * norm_factor;
   }

◆ curl_vecj()

ThreeVector smash::DensityOnLattice::curl_vecj ( const double norm_factor = 1.0 )

inline

Compute curl of the current on the local lattice.

Parameters

[in] norm_factor Normalization factor

Returns: \(\boldsymbol{\nabla}\times\mathbf{j}\) [fm \(^{-4}\)]

Definition at line 378 of file density.h.

                                                         {
     ThreeVector curl_vec_j = ThreeVector();
     curl_vec_j.set_x1(djmu_dxnu_[2].x3() - djmu_dxnu_[3].x2());
     curl_vec_j.set_x2(djmu_dxnu_[3].x1() - djmu_dxnu_[1].x3());
     curl_vec_j.set_x3(djmu_dxnu_[1].x2() - djmu_dxnu_[2].x1());
     curl_vec_j *= norm_factor;
     return curl_vec_j;
   }

◆ grad_j0()

ThreeVector smash::DensityOnLattice::grad_j0 ( const double norm_factor = 1.0 )

inline

Compute gradient of the the zeroth component of the four-current j^mu (that is of the computational frame density) on the local lattice.

Parameters

[in] norm_factor Normalization factor

Returns: \(\boldsymbol{\nabla} j^0\) [fm \(^{-4}\)]

Definition at line 394 of file density.h.

                                                       {
     ThreeVector j0_grad = ThreeVector();
     for (int i = 1; i < 4; i++) {
       j0_grad[i - 1] = djmu_dxnu_[i].x0() * norm_factor;
     }
     return j0_grad;
   }

◆ dvecj_dt()

ThreeVector smash::DensityOnLattice::dvecj_dt ( const double norm_factor = 1.0 )

inline

Compute time derivative of the current density on the local lattice.

Parameters

[in] norm_factor Normalization factor

Returns: \(\partial_t \mathbf{j}\) [fm \(^{-4}\)]

Definition at line 408 of file density.h.

                                                        {
     return djmu_dxnu_[0].threevec() * norm_factor;
   }

◆ jmu_net()

FourVector smash::DensityOnLattice::jmu_net ( ) const

inline

Returns: Net current density

There is a "+" operator in between, because the negative symbol of the charge has already be included in FactorTimesSF.

Definition at line 418 of file density.h.

418 { return jmu_pos_ + jmu_neg_; }

◆ add_to_jmu_pos()

void smash::DensityOnLattice::add_to_jmu_pos ( FourVector additional_jmu_B )

inline

Add to the positive density current.

Parameters

[in] additional_jmu_B Value of positive density current to be added

Definition at line 424 of file density.h.

                                                    {
     jmu_pos_ += additional_jmu_B;
   }

◆ add_to_jmu_neg()

void smash::DensityOnLattice::add_to_jmu_neg ( FourVector additional_jmu_B )

inline

Add to the negative density current.

Parameters

[in] additional_jmu_B Value of negative density current to be added

Definition at line 432 of file density.h.

                                                    {
     jmu_neg_ += additional_jmu_B;
   }

◆ drho_dxnu()

FourVector smash::DensityOnLattice::drho_dxnu ( ) const

inline

Return the FourGradient of the rest frame density \(\partial_{\nu}\rho\).

Returns: the FourGradient of the rest frame density \(\partial_{\nu}\rho\)

Definition at line 442 of file density.h.

442 { return drho_dxnu_; }

◆ djmu_dxnu()

std::array<FourVector, 4> smash::DensityOnLattice::djmu_dxnu ( ) const

inline

Return the FourGradient of the net baryon current \(\partial_{\nu} j^\mu\).

Returns: the array of FourGradients of \(\partial_{\nu} j^\mu\)

Definition at line 449 of file density.h.

449 { return djmu_dxnu_; }

◆ grad_rho_cross_vecj()

ThreeVector smash::DensityOnLattice::grad_rho_cross_vecj ( ) const

inline

Compute the cross product of \(\boldsymbol{\nabla}\rho\) and \(j^\mu\).

Returns: the cross product of \(\boldsymbol{\nabla} \rho\) and \(\mathbf{j}\)

Definition at line 456 of file density.h.

                                           {
     const ThreeVector grad_rho = drho_dxnu_.threevec();
     const ThreeVector vecj = jmu_net().threevec();
     const ThreeVector Drho_cross_vecj = grad_rho.cross_product(vecj);
  
     return Drho_cross_vecj;
   }

◆ overwrite_djmu_dt_to_zero()

void smash::DensityOnLattice::overwrite_djmu_dt_to_zero ( )

inline

Overwrite the time derivative of the current to zero.

Definition at line 467 of file density.h.

                                    {
     djmu_dxnu_[0] = FourVector(0.0, 0.0, 0.0, 0.0);
   }

◆ overwrite_drho_dt_to_zero()

void smash::DensityOnLattice::overwrite_drho_dt_to_zero ( )

inline

Overwrite the time derivative of the rest frame density to zero.

Definition at line 474 of file density.h.

474 { drho_dxnu_[0] = 0.0; }

◆ overwrite_drho_dxnu()

void smash::DensityOnLattice::overwrite_drho_dxnu ( FourVector computed_drho_dxnu )

inline

Overwrite the rest frame density derivatives to provided values.

Parameters

[in] computed_drho_dxnu a FourGradient of the rest frame density rho

Definition at line 480 of file density.h.

                                                           {
     drho_dxnu_ = computed_drho_dxnu;
   }

◆ overwrite_djmu_dxnu()

void smash::DensityOnLattice::overwrite_djmu_dxnu	(	FourVector	djmu_dt,
		FourVector	djmu_dx,
		FourVector	djmu_dy,
		FourVector	djmu_dz
	)

inline

Overwrite all density current derivatives to provided values.

Parameters

[in]	djmu_dt	time derivative of the current FourVector jmu
[in]	djmu_dx	x derivative of the current FourVector jmu
[in]	djmu_dy	y derivative of the current FourVector jmu
[in]	djmu_dz	z derivative of the current FourVector jmu

Definition at line 491 of file density.h.

                                                                    {
     djmu_dxnu_[0] = djmu_dt;
     djmu_dxnu_[1] = djmu_dx;
     djmu_dxnu_[2] = djmu_dy;
     djmu_dxnu_[3] = djmu_dz;
   }

Member Data Documentation

◆ jmu_pos_

FourVector smash::DensityOnLattice::jmu_pos_

private

Four-current density of the positively charged particle.

Definition at line 501 of file density.h.

◆ jmu_neg_

FourVector smash::DensityOnLattice::jmu_neg_

private

Four-current density of the negatively charged particle.

Definition at line 503 of file density.h.

◆ djmu_dxnu_

std::array<FourVector, 4> smash::DensityOnLattice::djmu_dxnu_

private

Four-gradient of the four-current density, \(\partial_\nu j^\mu \).

Definition at line 505 of file density.h.

◆ drho_dxnu_

FourVector smash::DensityOnLattice::drho_dxnu_

private

Four-gradient of the rest frame density, \(\partial_\nu \rho \).

Definition at line 507 of file density.h.

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

src/include/smash/density.h

Public Member Functions

Private Attributes

Constructor & Destructor Documentation

◆ DensityOnLattice()

Member Function Documentation

◆ add_particle()

◆ add_particle_for_derivatives()

◆ rho()

◆ curl_vecj()

◆ grad_j0()

◆ dvecj_dt()

◆ jmu_net()

◆ add_to_jmu_pos()

◆ add_to_jmu_neg()

◆ drho_dxnu()

◆ djmu_dxnu()

◆ grad_rho_cross_vecj()

◆ overwrite_djmu_dt_to_zero()

◆ overwrite_drho_dt_to_zero()

◆ overwrite_drho_dxnu()

◆ overwrite_djmu_dxnu()

Member Data Documentation

◆ jmu_pos_

◆ jmu_neg_

◆ djmu_dxnu_

◆ drho_dxnu_