WallGo.results

Data classes for compiling and returning results

Classes

BoltzmannResults(deltaF, Deltas, ...[, ...])	Holds results to be returned by BoltzmannSolver
ESolutionType(value)	Enum class used to label the different types of solution WallGo can find
HydroResults(temperaturePlus, ...)	Holds results to be returned by Hydro
WallGoResults()	Compiles output results for users of WallGo

class BoltzmannResults(deltaF, Deltas, truncationError, truncatedTail, spectralPeaks, linearizationCriterion1=0, linearizationCriterion2=0)

Holds results to be returned by BoltzmannSolver

Parameters:

• deltaF (ndarray)

• Deltas (BoltzmannDeltas)

• truncationError (float)

• truncatedTail (tuple[bool, bool, bool])

• spectralPeaks (tuple[int, int, int])

• linearizationCriterion1 (float)

• linearizationCriterion2 (float)

Deltas: BoltzmannDeltas

Relativistically invariant integrals over \(\mathcal{E}_\text{pl}^{n_\mathcal{E}}\mathcal{P}_\text{pl}^{n_\mathcal{P}}\delta f\).

deltaF: ndarray

Deviation of probability density function from equilibrium, \(\delta f(\xi, p_z, p_\parallel)\).

linearizationCriterion1: float = 0

Ratio of out-of-equilibrium and equilibrium pressures, \(|P[\delta f]| / |P[f_\text{eq}]|\). Default is 0.

linearizationCriterion2: float = 0

Ratio of the first-order correction due to nonlinearities and total pressure computed by WallGo, \(|P[\delta f_2]| / |P[f_\text{eq}+\delta f]|\). Default is 0.

spectralPeaks: tuple[int, int, int]

Indices of the peaks in the spectral expansion in each direction.

truncatedTail: tuple[bool, bool, bool]

True if tail 1/3 of spectral expansion was truncated in each direction, False otherwise.

truncationError: float

Estimated relative error in \(\delta f\) due to truncation of spectral expansion.

class ESolutionType(value)

Enum class used to label the different types of solution WallGo can find

DEFLAGRATION = 1

Indicates that a solution was found while looking for a deflagration or hybrid. Can also be used when the pressure was always positive while looking for a detonation.

DEFLAGRATION_OR_RUNAWAY = 4

Used when no stable solution was found while looking for a detonation with a positive pressure at \(v_w=v_\text{J}\) and negative at \(v_w=1\).

DETONATION = 2

Indicates that a solution was found while looking for a detonation.

ERROR = 5

Indicates that the calculation was not successful.

RUNAWAY = 3

Indicates that no solution was found and that the pressure was always negative.

class HydroResults(temperaturePlus, temperatureMinus, velocityJouguet)

Holds results to be returned by Hydro

Parameters:

• temperaturePlus (float)

• temperatureMinus (float)

• velocityJouguet (float)

temperatureMinus: float

Temperature behind the bubble, \(T_-\), from hydrodynamic matching conditions.

temperaturePlus: float

Temperature in front of the bubble, \(T_+\), from hydrodynamic matching conditions.

velocityJouguet: float

Jouguet velocity, \(v_J\), the smallest velocity for a detonation.

class WallGoResults

Compiles output results for users of WallGo

Deltas: BoltzmannDeltas

Relativistically invariant integrals over \(\mathcal{E}_\text{pl}^{n_\mathcal{E}}\mathcal{P}_\text{pl}^{n_\mathcal{P}}\delta f\).

DeltasFiniteDifference: BoltzmannDeltas

Relativistically invariant integrals over \(\mathcal{E}_\text{pl}^{n_\mathcal{E}}\mathcal{P}_\text{pl}^{n_\mathcal{P}}\delta f\), using finite differences instead of spectral expansion.

deltaF: ndarray

Deviation of probability density function from equilibrium, \(\delta f(\xi, p_z, p_\parallel)\).

deltaFFiniteDifference: ndarray

Deviation of probability density function from equilibrium, \(\delta f(\xi, p_z, p_\parallel)\), using finite differences instead of spectral expansion.

eomResidual: ndarray

Residual of the EOM due to the tanh ansatz. There is one element for each scalar field. It is estimated by the integral

\[\sqrt{\Delta[\mathrm{EOM}^2]/|\mathrm{EOM}^2|}\]

with

\[\Delta[\mathrm{EOM}^2]=\int\! dz\, (-\partial_z^2 \phi+ \partial V_{\mathrm{eq}}/ \partial \phi+ \partial V_{\mathrm{out}}/ \partial \phi )^2\]

and

\[|\mathrm{EOM}^2|=\int\! dz\, [(\partial_z^2 \phi)^2+ (\partial V_{\mathrm{eq}}/ \partial \phi)^2+ (\partial V_{\mathrm{out}}/ \partial \phi)^2].\]

fieldProfiles: Fields

Field profile as a function of position, \(\phi_i(\xi)\).

linearizationCriterion1: float

Ratio of out-of-equilibrium and equilibrium pressures, \(|P[\delta f]| / |P[f_\text{eq}]|\).

linearizationCriterion2: float

Ratio of the first-order correction due to nonlinearities and total pressure computed by WallGo, \(|P[\delta f_2]| / |P[f_\text{eq}+\delta f]|\).

message: str

Description of the cause of the termination.

setBoltzmannBackground(boltzmannBackground)

Set Boltzmann background results

Parameters:

boltzmannBackground (BoltzmannBackground)

Return type:

None

setBoltzmannResults(boltzmannResults)

Set Boltzmann results

Parameters:

boltzmannResults (BoltzmannResults)

Return type:

None

setFiniteDifferenceBoltzmannResults(boltzmannResults)

Set finite difference Boltzmann results

Parameters:

boltzmannResults (BoltzmannResults)

Return type:

None

setHydroResults(hydroResults)

Set hydrodynamics results

Parameters:

hydroResults (HydroResults)

Return type:

None

setSuccessState(success, solutionType, message)

Set the termination message, the success flag and the solution type.

Parameters:

• success (bool)

• solutionType (ESolutionType)

• message (str)

Return type:

None

setViolationOfEMConservation(violationOfEMConservation)

Set the violation of energy-momentum conservation results

Parameters:

violationOfEMConservation (Tuple[float, float])

Return type:

None

setWallParams(wallParams)

Set wall parameters results

Parameters:

wallParams (WallParams)

Return type:

None

setWallVelocities(wallVelocity, wallVelocityError, wallVelocityLTE)

Set wall velocity results

Parameters:

• wallVelocity (float | None)

• wallVelocityError (float | None)

• wallVelocityLTE (float | None)

Return type:

None

solutionType: ESolutionType

Describes the type of solution obtained. Must be a ESolutionType object. The function WallGoManager.solveWall() will return DEFLAGRATION if a solution was found and RUNAWAY otherwise. The function WallGoManager.solveWallDetonation() will return DETONATION if a solution was found. Otherwise, it returns RUNAWAY if the pressure is negative everywhere between vJ and 1, DEFLAGRATION if the pressure is always positive, and DEFLAGRATION_OR_RUNAWAY if the pressure is positive at vJ and negative at 1 and no stable solution was found. In both cases, returns ERROR if success=False.

success: bool

Whether or not the calculation was successful. Will still be True if no solution was found, as long as no error happened along the way.

temperatureMinus: float

Temperature behind the bubble, \(T_-\), from hydrodynamic matching conditions.

temperaturePlus: float

Temperature in front of the bubble, \(T_+\), from hydrodynamic matching conditions.

temperatureProfile: ndarray

Temperarture profile as a function of position, \(T(\xi)\).

truncationError: float

Estimated relative error in \(\delta f\) due to truncation of spectral expansion.

velocityJouguet: float

Jouguet velocity, \(v_J\), the smallest velocity for a detonation.

velocityProfile: ndarray

Fluid velocity as a function of position, \(v_\text{pl}(\xi)\).

violationOfEMConservation: Tuple[float, float]

RMS along the grid of the violation of the conservation of the components T30 and T33 of the energy-momentum tensor.

wallOffsets: ndarray

Bubble wall offsets in each field direction, \(\delta_i\).

wallVelocity: float | None

Bubble wall velocity \(v_w\). None if no solution was found.

wallVelocityError: float | None

Estimated error in bubble wall velocity \(\delta v_w\). None if no solution was found.

wallVelocityLTE: float | None

Bubble wall velocity in local thermal equilibrium \(v_w^\text{LTE}\). None when looking for a detonation solution, since no detonation exists in LTE.

wallWidths: ndarray

Bubble wall widths in each field direction, \(L_i\).