pttools.models.analytic

Base class for analytical models

Classes

class pttools.models.analytic.AnalyticModel(V_s=DEFAULT_V_S, V_b=None, a_s=None, a_b=None, g_s=None, g_b=None, T_min=None, T_max=None, T_crit_guess=None, name=None, label_latex=None, label_unicode=None, gen_critical=True, gen_cs2=True, gen_cs2_neg=True, allow_invalid=False, auto_potential=False, log_info=True)

Bases: Model, ABC

A generic analytical model, where the temperature dependence of \(g_\text{eff}\) is implemented directly in the equation of state.

You should specify either the relativistic degrees of freedom \(g_\text{eff}(\phi=s)\) and \(g_\text{eff}(\phi=b)\), or the prefactors \(a_s\) and \(a_b\). The convention for the latter is as in Hindmarsh et al., 2021 eq. 7.33. for the bag model, where

\[p_s = a_sT^4 - V_s,\]
\[p_b = a_bT^4 - V_b.\]

Parameters:

  • V_s (float) – \(V_s = \epsilon_s\), the potential term of \(p\) in the symmetric phase

  • V_b (float) – \(V_b = \epsilon_b\), the potential term of \(p\) in the broken phase

  • a_s (float) – prefactor of \(p\) in the symmetric phase

  • a_b (float) – prefactor of \(p\) in the broken phase

  • g_s (float) – \(g_\text{eff}(\phi=s)\), degrees of freedom for \(p\) in the symmetric phase at T=T0

  • g_b (float) – \(g_\text{eff}(\phi=b)\), degrees of freedom for \(p\) in the broken phase at T=T0

  • name (str) – custom name for the model

  • auto_potential (bool) – set V_s and V_b so that T_c = 1 (bag model only)

  • T_min (float)

  • T_max (float)

  • T_crit_guess (float)

  • label_latex (str)

  • label_unicode (str)

  • gen_critical (bool)

  • gen_cs2 (bool)

  • gen_cs2_neg (bool)

  • allow_invalid (bool)

  • log_info (bool)

DEFAULT_A_G_MULT = 1.1
DEFAULT_V_S = 1
static a_from_g(g)

Get the prefactor \(a\) from the relativistic degrees of freedom \(g\).

Parameters:

g (float | float64 | ndarray)

Return type:

float | float64 | ndarray

alpha_n_bag(wn, error_on_invalid=True, nan_on_invalid=True, log_invalid=True)

Transition strength parameter at nucleation temperature, \(\alpha_n\), Hindmarsh et al., 2021, eq. 7.40.

\[\alpha_n = \frac{4}{3w_n}(V_s - V_b)\]

Parameters:

  • wn (float | float64 | ndarray) – \(w_n\), enthalpy of the symmetric phase at the nucleation temperature

  • error_on_invalid (bool) – raise error for invalid values

  • nan_on_invalid (bool) – return nan for invalid values

  • log_invalid (bool) – log negative values

Return type:

float | float64 | ndarray

classmethod alpha_n_min_find_params_a_g(a_s, a_b, g_s, g_b, alpha_n_min_target, V_s_default, V_b, default_mult=DEFAULT_A_G_MULT, safety_factor_alpha=Model.ALPHA_N_MIN_FIND_SAFETY_FACTOR_ALPHA)
Parameters:

  • a_s (float)

  • a_b (float)

  • g_s (float)

  • g_b (float)

  • alpha_n_min_target (float)

  • V_s_default (float)

  • V_b (float)

  • default_mult (float)

alpha_plus_bag(wp, wm, vp_tilde=None, sol_type=None, error_on_invalid=True, nan_on_invalid=True, log_invalid=True)

Transition strength parameter \(\alpha_+\), Hindmarsh et al., 2021, eq. 7.25.

\[\alpha_+ = \frac{4}{3w_+}(V_s - V_b)\]

Parameters:

  • wp (float | float64 | ndarray) – \(w_+\), enthalpy ahead of the wall

  • wm (float | float64 | ndarray) – \(w_-\), enthalpy behind the wall (not used)

  • error_on_invalid (bool) – raise error for invalid values

  • nan_on_invalid (bool) – return nan for invalid values

  • log_invalid (bool) – whether to log invalid values

  • vp_tilde (float)

  • sol_type (SolutionType)

Return type:

float | float64 | ndarray

export()

Export the model parameters to a dictionary. User-created model classes should extend this.

Return type:

Dict[str, any]

static g_from_a(a)
Parameters:

a (float | float64 | ndarray)

Return type:

float | float64 | ndarray

ge_temp(temp, phase)
Parameters:
Return type:

float | float64 | ndarray

classmethod get_a_g(a_s, a_b, g_s, g_b, default_mult=DEFAULT_A_G_MULT)
Parameters:

  • a_s (float)

  • a_b (float)

  • g_s (float)

  • g_b (float)

  • default_mult (float)

gp_temp(temp, phase)
Parameters:
gs_temp(temp, phase)
Parameters: