def TipAsym_UniversalW_delt_Res(w, *args):
"""The residual function zero of which will give the General asymptote """
(dist, Kprime, Eprime, muPrime, Cbar, Vel) = args
Kh = Kprime * dist**0.5 / (Eprime * w)
Ch = 2 * Cbar * dist**0.5 / (Vel**0.5 * w)
sh = muPrime * Vel * dist**2 / (Eprime * w**3)
g0 = f(Kh, 0.9911799823 * Ch, 10.392304845)
delt = 10.392304845 * (1 + 0.9911799823 * Ch) * g0
C1 = 4 * (1 - 2 * delt) / (delt * (1 - delt)) * np.tan(np.pi * delt)
C2 = 16 * (1 - 3 * delt) / (3 * delt *
(2 - 3 * delt)) * np.tan(3 * np.pi * delt / 2)
b = C2 / C1
return sh - f(Kh, Ch * b, C1)
def TipAsym_UniversalW_zero_Res(w, *args):
"""Function to be minimized to find root for universal Tip assymptote (see Donstov and Pierce 2017)"""
(dist, Kprime, Eprime, muPrime, Cbar, Vel) = args
Kh = Kprime * dist**0.5 / (Eprime * w)
Ch = 2 * Cbar * dist**0.5 / (Vel**0.5 * w)
g0 = f(Kh, 0.9911799823 * Ch, 6 * 3**0.5)
sh = muPrime * Vel * dist**2 / (Eprime * w**3)
return sh - g0
def TipAsym_UniversalW_delt_Res(w, *args):
"""The residual function zero of which will give the General asymptote """
(dist, Kprime, Eprime, muPrime, Cbar, Vel) = args
if Cbar == 0:
return TipAsym_MK_W_deltaC_Res(w, *args)
Kh = Kprime * dist**0.5 / (Eprime * w)
Ch = 2 * Cbar * dist**0.5 / (Vel**0.5 * w)
sh = muPrime * Vel * dist**2 / (Eprime * w**3)
g0 = f(Kh, 0.9911799823 * Ch, 10.392304845)
delt = 10.392304845 * (1 + 0.9911799823 * Ch) * g0
b = C2(delt) / C1(delt)
con = C1(delt)
gdelt = f(Kh, Ch * b, con)
return sh - gdelt
def MomentsTipAssympGeneral(dist, Kprime, Eprime, muPrime, Cbar, Vel, stagnant,
KIPrime, regime):
"""Moments of the General tip asymptote to calculate the volume integral (see Donstov and Pierce, 2017)"""
log = logging.getLogger('PyFrac.MomentsTipAssympGeneral')
TipAsmptargs = (dist, Kprime, Eprime, muPrime, Cbar, Vel)
if dist == 0:
w = 0
elif stagnant:
w = KIPrime * dist**0.5 / Eprime
else:
a, b = FindBracket_w(dist, Kprime, Eprime, muPrime, Cbar, Vel, regime)
try:
if regime == 'U':
w = brentq(TipAsym_UniversalW_zero_Res, a, b,
TipAsmptargs) # root finding
else:
w = brentq(TipAsym_UniversalW_delt_Res, a, b,
TipAsmptargs) # root finding
except RuntimeError:
M0, M1 = np.nan, np.nan
return M0, M1
except ValueError:
M0, M1 = np.nan, np.nan
return M0, M1
if w < -1e-15:
log.warning('Negative width encountered in volume integral')
w = abs(w)
if Vel < 1e-6 or w == 0:
delt = 1 / 6
else:
Kh = Kprime * dist**0.5 / (Eprime * w)
Ch = 2 * Cbar * dist**0.5 / (Vel**0.5 * w)
g0 = f(Kh, 0.9911799823 * Ch, 10.392304845)
delt = 10.392304845 * (1 + 0.9911799823 * Ch) * g0
M0 = 2 * w * dist / (3 + delt)
M1 = 2 * w * dist**2 / (5 + delt)
if np.isnan(M0) or np.isnan(M1):
M0, M1 = np.nan, np.nan
return M0, M1
def MomentsTipAssympGeneral(dist, Kprime, Eprime, muPrime, Cbar, Vel, stagnant,
KIPrime):
"""Moments of the General tip asymptote to calculate the volume integral (see Donstov and Pierce, 2017)"""
TipAsmptargs = (dist, Kprime, Eprime, muPrime, Cbar, Vel)
if stagnant:
w = KIPrime * dist**0.5 / Eprime
else:
a, b = FindBracket_w(dist, Kprime, Eprime, muPrime, Cbar, Vel)
try:
w = brentq(TipAsym_UniversalW_zero_Res, a, b,
TipAsmptargs) # root finding
except RuntimeError:
M0, M1 = np.nan, np.nan
return M0, M1
except ValueError:
M0, M1 = np.nan, np.nan
return M0, M1
if w < -1e-15:
w = abs(w)
if Vel < 1e-6:
delt = 1 / 6
else:
Kh = Kprime * dist**0.5 / (Eprime * w)
Ch = 2 * Cbar * dist**0.5 / (Vel**0.5 * w)
g0 = f(Kh, 0.9911799823 * Ch, 10.392304845)
delt = 10.392304845 * (1 + 0.9911799823 * Ch) * g0
M0 = 2 * w * dist / (3 + delt)
M1 = 2 * w * dist**2 / (5 + delt)
if np.isnan(M0) or np.isnan(M1):
M0, M1 = np.nan, np.nan
return M0, M1