pttools.bubble.bubble

A solution of the hydrodynamic equations

Classes

class pttools.bubble.bubble.Bubble(model, v_wall, alpha_n, solve=True, sol_type=None, label_latex=None, label_unicode=None, wn_guess=None, wm_guess=None, theta_bar=False, t_end=const.T_END_DEFAULT, n_xi=const.N_XI_DEFAULT, thin_shell_t_points_min=const.THIN_SHELL_T_POINTS_MIN, use_bag_solver=False, use_giese_solver=False, log_success=False, allow_invalid=False, log_invalid=True)

Bases: object

A solution of the hydrodynamic equations

Parameters:

  • model (Model)

  • v_wall (float)

  • alpha_n (float)

  • solve (bool)

  • sol_type (SolutionType)

  • label_latex (str)

  • label_unicode (str)

  • wn_guess (float)

  • wm_guess (float)

  • theta_bar (bool)

  • t_end (float)

  • n_xi (int)

  • thin_shell_t_points_min (int)

  • use_bag_solver (bool)

  • use_giese_solver (bool)

  • log_success (bool)

  • allow_invalid (bool)

  • log_invalid (bool)

add_note(note)

Add a note to the bubble

Parameters:

note (str)

property ebar: float
en()

Nucleation energy density \(e_n = e(T_n, \phi_s)\)

Return type:

float

property entropy_density_diff: float
property entropy_density_diff_relative: float
property entropy_flux_diff: float

Entropy flux difference at the wall

\[\tilde{\gamma}_- \tilde{v}_- {s}_- - \tilde{\gamma}_+ \tilde{v}_+ {s}_+ \]

property entropy_flux_diff_sh: float

Entropy flux difference at the wall

\[\tilde{\gamma}_{-,sh} \tilde{v}_{-,sh} s_{-,sh} - \tilde{\gamma}_{+,sh} \tilde{v}_{+,sh} s_{+,sh}\]

property entropy_flux_m: float

Outgoing entropy flux at the wall

\[\tilde{\gamma}_- \tilde{v}_- {s}_- \]

property entropy_flux_m_sh: float

Outgoing entropy flux at the shock

\[\tilde{\gamma}_{-,sh} \tilde{v}_{-,sh} s_{-,sh}\]

property entropy_flux_p: float

Incoming entropy flux at the wall

\[\tilde{\gamma}_+ \tilde{v}_+ s_+\]

property entropy_flux_p_sh: float

Incoming entropy flux at the shock

\[\tilde{\gamma}_{+,sh} \tilde{v}_{+,sh} s_{+,sh}\]

export(path=None)

Export the bubble data as JSON

Parameters:

path (str)

Return type:

Dict[str, any]

info_str(prec='.4f')

Get a string describing the key quantities of the bubble

Parameters:

prec (str)

Return type:

str

property kappa: float
property kappa_giese: float
property kinetic_energy_density: float
property kinetic_energy_fraction: float
property mean_adiabatic_index: float
property omega: float
plot(fig=None, path=None, **kwargs)

Plot the velocity and enthalpy profiles of the bubble

Parameters:
Return type:

Figure

plot_v(fig=None, ax=None, path=None, **kwargs)

Plot the velocity profile of the bubble

Parameters:
Return type:

FigAndAxes

plot_w(fig=None, ax=None, path=None, **kwargs)

Plot the enthalpy profile of the bubble

Parameters:
Return type:

FigAndAxes

property s
solve(sum_rtol_warning=1.5e-2, sum_rtol_error=5e-2, error_prec='.4f', use_bag_solver=False, use_giese_solver=False, log_high_alpha_n_failures=True, log_negative_entropy=True)

Simulate the fluid velocity profile of the bubble

Parameters:

  • sum_rtol_warning (float)

  • sum_rtol_error (float)

  • error_prec (str)

  • use_bag_solver (bool)

  • use_giese_solver (bool)

  • log_high_alpha_n_failures (bool)

  • log_negative_entropy (bool)

property thermal_energy_density: float
property thermal_energy_density_diff: float
property thermal_energy_fraction: float
property trace_anomaly: float
property ubarf2: float
property v_mu: float

Maximum fluid velocity behind the bubble wall, \(\mu(\xi)\)

property va_enthalpy_density: float
property va_entropy_density_diff: float
property va_entropy_density_diff_relative: float
property va_kinetic_energy_density: float
property va_kinetic_energy_fraction: float
property va_thermal_energy_density: float
property va_thermal_energy_density_diff: float
property va_thermal_energy_fraction: float
property va_trace_anomaly_diff: float
property vp_tilde_sh

Velocity in front of the shock in the shock frame

The fluid ahead of the shock is still, and therefore $$ ilde{v}_{+,sh} = v_{sh}$$.

property vp_vm_tilde_ratio: float

\[\frac{\tilde{v}_+}{\tilde{v}_-}\]

property vp_vm_tilde_ratio_giese: float

Giese approximation for \(\frac{\tilde{v}_+}{\tilde{v}_-}\), Giese et al., 2021 eq. 11

$$frac{tilde{v}_+}{tilde{v}_-} approx frac{

(tilde{v}_+ tilde{v}_- / c_{s,b}^2 - 1) + 3alpha_{bar{theta}_+} }{ (tilde{v}_+ tilde{v}_- / c_{s,b}^2 - 1) + 3 tilde{v}_+ tilde{v}_- alpha_{bar{theta}}_+

}$$

property vp_vm_tilde_ratio_giese_rel_diff: float

Relative difference of the ratio of the exact and approximate \(\tilde{v}_+, \tilde{v}_-\) ratios from unity

property wbar: float

Exceptions

exception pttools.bubble.bubble.NotYetSolvedError

Bases: RuntimeError

Error for accessing the properties of a bubble that has not been solved yet