def deriv(rm_vector, enthalpy, eos):
''' The TOV equations in terms of pseudoenthalpy. Derivatives of vector
(radius, mass) as a function of enthalpy for given eos.'''
(rad, mass) = rm_vector
drdenth = - rad * (rad - 2 * mass) \
/ (mass + 4 * np.pi * rad **3 * eos.pressure(enthalpy)*Gcc)
dmdenth = 4 * np.pi * eos.energy(enthalpy) * Gcc * rad**2 * drdenth
return np.array([drdenth, dmdenth])
def deriv(rm_vector, enthalpy, eos):
''' The TOV equations in terms of pseudoenthalpy. Derivatives of vector
(radius, mass) as a function of enthalpy for given eos.'''
(rad, mass) = rm_vector
drdenth = - rad * (rad - 2 * mass) \
/ (mass + 4 * np.pi * rad **3 * eos.pressure(enthalpy)*Gcc)
dmdenth = 4 * np.pi * eos.energy(enthalpy)*Gcc * rad **2 * drdenth
return np.array([drdenth,dmdenth])
def rotderiv(rm_vector, enthalpy, eos):
''' The TOV equations augmented for a linearly perturbed, slowly
rotating neutron star. Also includes rest mass of star.'''
(rad, mass, restmass, alpha, omega) = rm_vector
pr = eos.pressure(enthalpy) * Gcc
en = eos.energy(enthalpy) * Gcc
rho = eos.density(enthalpy)**Gcc
factor = rad - 2 * mass
coef = 4.0 * np.pi
drdenth = -rad * factor / (mass + coef * rad**3 * pr)
dmdenth = coef * en * rad**2 * drdenth
dmadenth = coef * rho * rad**2 * drdenth / (factor / rad)**0.5
domega = alpha * drdenth
dalpha = drdenth * (- 4.0 * alpha / rad \
+ coef * rad * (pr + en) * (4.0 * omega + rad * alpha ) / factor )
return np.array([drdenth, dmdenth, dmadenth, dalpha, domega])
def rotderiv(rm_vector, enthalpy, eos):
''' The TOV equations augmented for a linearly perturbed, slowly
rotating neutron star. Also includes rest mass of star.'''
(rad, mass, restmass, alpha, omega) = rm_vector
pr = eos.pressure(enthalpy) * Gcc
en = eos.energy(enthalpy) * Gcc
rho = eos.density(enthalpy) ** Gcc
factor = rad - 2 * mass
coef = 4.0 * np.pi
drdenth = - rad * factor / (mass + coef * rad**3 * pr)
dmdenth = coef * en * rad**2 * drdenth
dmadenth = coef * rho * rad**2 * drdenth / ( factor / rad )**0.5
domega = alpha * drdenth
dalpha = drdenth * (- 4.0 * alpha / rad \
+ coef * rad * (pr + en) * (4.0 * omega + rad * alpha ) / factor )
return np.array([drdenth,dmdenth, dmadenth, dalpha, domega])
def tidederiv(rm_vector, enthalpy, eos):
(rad, mass, restmass, beta, h) = rm_vector
pr = eos.pressure(enthalpy) * Gcc
en = eos.energy(enthalpy) * Gcc
func = 1.0 / eos.dprden(enthalpy)
factor = rad - 2 * mass
coef = 4.0 * np.pi
drdenth = -rad * factor / (mass + coef * rad**3 * pr)
dmdenth = coef * en * rad**2 * drdenth
dbeta = 2 * drdenth *\
( h * ( \
(- 2. * np.pi * func * rad * (pr + en))/ factor + \
(2. * mass**2 + \
rad**2 * (3.0 + 2.0 * np.pi * rad**2 * \
( pr * (16.0 * np.pi * pr * rad**2 - 9.0 ) - 5. * en ))\
+ mass * ( - 6 * rad + 4 * np.pi * rad**3 * (13 *pr + 5*en) ) )\
/ rad**2 / factor**2 )
+ beta / rad / factor * ( mass - rad + 2 * np.pi * rad**3 * (en -
pr)))
dh = beta * drdenth
return np.array([drdenth, dmdenth, dbeta, dh])
def tidederiv(rm_vector, enthalpy, eos):
(rad, mass, restmass, beta, h) = rm_vector
pr = eos.pressure(enthalpy) * Gcc
en = eos.energy(enthalpy) * Gcc
func = 1.0/eos.dprden(enthalpy)
factor = rad - 2 * mass
coef = 4.0*np.pi
drdenth = - rad * factor / (mass + coef * rad**3 * pr)
dmdenth = coef * en * rad**2 * drdenth
dbeta = 2 * drdenth *\
( h * ( \
(- 2. * np.pi * func * rad * (pr + en))/ factor + \
(2. * mass**2 + \
rad**2 * (3.0 + 2.0 * np.pi * rad**2 * \
( pr * (16.0 * np.pi * pr * rad**2 - 9.0 ) - 5. * en ))\
+ mass * ( - 6 * rad + 4 * np.pi * rad**3 * (13 *pr + 5*en) ) )\
/ rad**2 / factor**2 )
+ beta / rad / factor * ( mass - rad + 2 * np.pi * rad**3 * (en -
pr)))
dh = beta * drdenth
return np.array([drdenth,dmdenth, dbeta, dh])
def diff_Pr():
return eos.pressure(alpha, rho_n,
self.params, order) - eos.pressure(
0.0, rho_i, self.params, order)
def find_coex(self,
rho_i=0.01,
rho_n=4.0,
order=2,
n_max=1000,
tol=1e-10,
updates=False):
for i in range(2, order + 1):
Bi = "B" + str(i)
if not Bi in self.params.keys():
return "Error: function not fitted for " + Bi + ": can't find coexistence"
from scipy.optimize import minimize_scalar
def diff_Pr():
return eos.pressure(alpha, rho_n,
self.params, order) - eos.pressure(
0.0, rho_i, self.params, order)
def diff_mu():
return eos.chemical_potential(alpha, rho_n, self.params,
order) - eos.chemical_potential(
0.0, rho_i, self.params, order)
for i in range(n_max):
alpha = (minimize_scalar(eos.free_energy,
args=(rho_n, self.params, order),
bounds=(-1e-10, 2e3),
method='bounded')).x
dPnn = eos.d_pr(alpha, rho_n, self.params, order)
dPii = eos.d_pr(0.0, rho_i, self.params, order)
dmnn = eos.d_mu(alpha, rho_n, self.params, order)
dmii = eos.d_mu(0.0, rho_i, self.params, order)
F1 = diff_Pr()
F2 = diff_mu()
dF11 = dPnn
dF12 = -dPii
dF21 = dmnn
dF22 = -dmii
det = dF22 * dF11 - dF12 * dF21
if updates:
print('loop: ', i)
print('rho_i: ', rho_i, ' delta_i:',
(F2 * dF11 - F1 * dF21) / det, ' Pr_i: ',
eos.pressure(0.0, rho_i, self.params, order))
print('rho_n: ', rho_n, ' delta_n:',
(F1 * dF22 - F2 * dF12) / det, ' Pr_n: ',
eos.pressure(alpha, rho_n, self.params, order))
print('alpha: ', alpha)
print('')
rho_n1 = rho_n - (F1 * dF22 - F2 * dF12) / det
rho_i1 = rho_i - (F2 * dF11 - F1 * dF21) / det
if (rho_n1 < 0.0) or (rho_i1 < 0.0):
return 'Error: try changing the guesses rho_i and rho_n'
if i > 0:
if (np.absolute(rho_n1 - rho_n) / rho_n <
tol) & (np.absolute(rho_i1 - rho_i) / rho_i < tol):
coex = {}
coex['rho_i'] = rho_i1
coex['rho_n'] = rho_n1
coex['Pr_i'] = eos.pressure(0.0, rho_i1, self.params,
order)
coex['Pr_n'] = eos.pressure(alpha, rho_n1, self.params,
order)
coex['mu_i'] = eos.chemical_potential(
0.0, rho_i1, self.params, order)
coex['mu_n'] = eos.chemical_potential(
alpha, rho_n1, self.params, order)
coex['fe_i'] = eos.free_energy(0.0, rho_i1, self.params,
order)
coex['fe_n'] = eos.free_energy(alpha, rho_n1, self.params,
order)
coex['S2'] = eos.nematic_order(alpha)
cols = [
'rho_i', 'rho_n', 'S2', 'Pr_i', 'Pr_n', 'mu_i', 'mu_n',
'fe_i', 'fe_n'
]
coex = pd.DataFrame(
coex, index=np.arange(1)
)[cols] # pd.DataFrame(coex, index=['B'+str(order)])[cols]
self.coex.loc['B' + str(order), :] = coex.iloc[
0, :] #pd.DataFrame(coex, index=np.arange(1))[cols]
return
rho_n = rho_n1
rho_i = rho_i1
return 'Did not converge: try increasing n_max'
