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transport.py
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transport.py
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"""Transport routines."""
import sys
from collections import OrderedDict
import numpy as np
import ceptr.constants as cc
import ceptr.writer as cw
def transport(fstream, mechanism, species_info):
"""Write the transport functions."""
cw.writer(fstream, cw.comment("Transport function declarations "))
n_species = species_info.n_species
species_transport = analyze_transport(mechanism, species_info)
n_lite = 0
idx_light_specs = []
for sp in range(n_species):
spec = species_info.nonqssa_species[sp]
if spec.weight < 5.0:
n_lite += 1
idx_light_specs.append(spec.idx)
misc_trans_info(fstream, kk=n_species, n_lite=n_lite)
wt(fstream, species_info)
eps(fstream, mechanism, species_info, species_transport)
sig(fstream, mechanism, species_info, species_transport)
dip(fstream, mechanism, species_info, species_transport)
pol(fstream, mechanism, species_info, species_transport)
zrot(fstream, mechanism, species_info, species_transport)
nlin(fstream, mechanism, species_info, species_transport)
viscosity(fstream, mechanism, species_info, species_transport, ntfit=50)
diffcoefs(fstream, species_info, species_transport, ntfit=50)
light_specs(fstream, idx_light_specs)
thermaldiffratios(
fstream,
species_info,
species_transport,
idx_light_specs,
ntfit=50,
)
def analyze_transport(mechanism, species_info):
"""Extract transport model coefficients."""
transdata = OrderedDict()
for spec in species_info.nonqssa_species:
species = mechanism.species(spec.name)
m1 = species.transport
if m1.geometry == "atom":
lin = 0
elif m1.geometry == "linear":
lin = 1
elif m1.geometry == "nonlinear":
lin = 2
else:
print("Unrecognized species geometry in transport")
sys.exit(1)
eps = (m1.well_depth * cc.ureg.joule).to(cc.ureg.erg).m / cc.kb
sig = (m1.diameter * cc.ureg.meter).to(cc.ureg.angstrom).m
dip = (m1.dipole * cc.ureg.coulomb * cc.ureg.m).to(cc.ureg.debye).m
pol = (m1.polarizability * cc.ureg.meter**3).to(cc.ureg.angstrom**3).m
zrot = m1.rotational_relaxation
transdata[spec] = [lin, eps, sig, dip, pol, zrot]
return transdata
def misc_trans_info(fstream, kk, n_lite, no=4):
"""Write transport information."""
cw.writer(fstream)
lenimc = 4 * kk + n_lite
generate_trans_routine_integer(
fstream,
[
"egtransetLENIMC",
"EGTRANSETLENIMC",
"egtransetlenimc",
"egtransetlenimc_",
"LENIMC",
],
lenimc,
)
cw.writer(fstream)
cw.writer(fstream)
lenrmc = (19 + 2 * no + no * n_lite) * kk + (15 + no) * kk**2
generate_trans_routine_integer(
fstream,
[
"egtransetLENRMC",
"EGTRANSETLENRMC",
"egtransetlenrmc",
"egtransetlenrmc_",
"LENRMC",
],
lenrmc,
)
cw.writer(fstream)
cw.writer(fstream)
generate_trans_routine_integer(
fstream,
[
"egtransetNO",
"EGTRANSETNO",
"egtransetno",
"egtransetno_",
"NO",
],
no,
)
cw.writer(fstream)
cw.writer(fstream)
generate_trans_routine_integer(
fstream,
[
"egtransetKK",
"EGTRANSETKK",
"egtransetkk",
"egtransetkk_",
"KK",
],
kk,
)
cw.writer(fstream)
cw.writer(fstream)
generate_trans_routine_integer(
fstream,
[
"egtransetNLITE",
"EGTRANSETNLITE",
"egtransetnlite",
"egtransetnlite_",
"NLITE",
],
n_lite,
)
cw.writer(fstream)
cw.writer(fstream)
cw.writer(fstream, cw.comment("Patm in ergs/cm3"))
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
cw.writer(fstream, "void egtransetPATM(amrex::Real* PATM) {")
cw.writer(fstream, "*PATM = 0.1013250000000000E+07;}")
def generate_trans_routine_integer(fstream, nametab, expression):
"""Write generic integer transport routine."""
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
cw.writer(fstream, f"void {nametab[0]:s}(int* {nametab[4]:s} ) {{")
cw.writer(fstream, f"*{nametab[4]:s} = {expression:d};}}")
def generate_trans_routine_simple(
fstream, mechanism, species_info, nametab, idx, species_transport
):
"""Write generic transport routine."""
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
cw.writer(fstream, f"void {nametab[0]:s}(amrex::Real* {nametab[4]:s} ) {{")
for spec in species_info.nonqssa_species:
cw.writer(
fstream,
f"{nametab[4]}[{spec.idx}] = {float(species_transport[spec][idx]):.8E};",
)
cw.writer(fstream, "}")
def wt(fstream, species_info):
"""Write molecular weights function."""
cw.writer(fstream)
cw.writer(fstream, cw.comment("the molecular weights in g/mol"))
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
cw.writer(fstream, "void egtransetWT(amrex::Real* WT ) {")
n_species = species_info.n_species
for sp in range(n_species):
species = species_info.nonqssa_species[sp]
cw.writer(
fstream,
f"{'WT'}[{species.idx}] = {float(species.weight):.8E};",
)
cw.writer(fstream, "}")
def eps(fstream, mechanism, species_info, species_transport):
"""Write the lennard-jones potential well depth function."""
cw.writer(fstream)
cw.writer(
fstream,
cw.comment("the lennard-jones potential well depth eps/kb in K"),
)
generate_trans_routine_simple(
fstream,
mechanism,
species_info,
[
"egtransetEPS",
"EGTRANSETEPS",
"egtranseteps",
"egtranseteps_",
"EPS",
],
1,
species_transport,
)
def sig(fstream, mechanism, species_info, species_transport):
"""Write the the lennard-jones collision diameter function."""
cw.writer(fstream)
cw.writer(
fstream,
cw.comment("the lennard-jones collision diameter in Angstroms"),
)
generate_trans_routine_simple(
fstream,
mechanism,
species_info,
[
"egtransetSIG",
"EGTRANSETSIG",
"egtransetsig",
"egtransetsig_",
"SIG",
],
2,
species_transport,
)
def dip(fstream, mechanism, species_info, species_transport):
"""Write the dipole moment function."""
cw.writer(fstream)
cw.writer(fstream, cw.comment("the dipole moment in Debye"))
generate_trans_routine_simple(
fstream,
mechanism,
species_info,
[
"egtransetDIP",
"EGTRANSETDIP",
"egtransetdip",
"egtransetdip_",
"DIP",
],
3,
species_transport,
)
def pol(fstream, mechanism, species_info, species_transport):
"""Write the polarizability function."""
cw.writer(fstream)
cw.writer(fstream, cw.comment("the polarizability in cubic Angstroms"))
generate_trans_routine_simple(
fstream,
mechanism,
species_info,
[
"egtransetPOL",
"EGTRANSETPOL",
"egtransetpol",
"egtransetpol_",
"POL",
],
4,
species_transport,
)
def zrot(fstream, mechanism, species_info, species_transport):
"""Write the rotational relaxation collision number."""
cw.writer(fstream)
cw.writer(
fstream,
cw.comment("the rotational relaxation collision number at 298 K"),
)
generate_trans_routine_simple(
fstream,
mechanism,
species_info,
[
"egtransetZROT",
"EGTRANSETZROT",
"egtransetzrot",
"egtransetzrot_",
"ZROT",
],
5,
species_transport,
)
def nlin(fstream, mechanism, species_info, species_transport):
"""Write the (monoatomic, linear, nonlinear) information."""
cw.writer(fstream)
cw.writer(fstream, cw.comment("0: monoatomic, 1: linear, 2: nonlinear"))
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
cw.writer(fstream, "void egtransetNLIN(int* NLIN) {")
for species in species_info.nonqssa_species:
cw.writer(
fstream,
f"{'NLIN'}[{species.idx}] = {int(species_transport[species][0])};",
)
cw.writer(fstream, "}")
def viscosity(fstream, mechanism, species_info, species_transport, ntfit):
"""Write the viscosity function."""
n_species = species_info.n_species
# compute single constants in g/cm/s
na = 6.02214199e23
ru = 8.31447e7
# conversion coefs
a2cm = 1.0e-8
debye2cgs = 1.0e-18
# temperature increment
dt = (species_info.high_temp - species_info.low_temp) / (ntfit - 1)
# factor dependent upon the molecule
m_crot = np.zeros(n_species)
m_cvib = np.zeros(n_species)
isatm = np.zeros(n_species)
for spec in species_transport:
if int(species_transport[spec][0]) == 0:
m_crot[spec.idx] = 0.0
m_cvib[spec.idx] = 0.0
isatm[spec.idx] = 0.0
elif int(species_transport[spec][0]) == 1:
m_crot[spec.idx] = 1.0
m_cvib[spec.idx] = 5.0 / 2.0
isatm[spec.idx] = 1.0
else:
m_crot[spec.idx] = 1.5
m_cvib[spec.idx] = 3.0
isatm[spec.idx] = 1.0
# viscosities coefs (4 per spec)
cofeta = OrderedDict()
# conductivities coefs (4 per spec)
coflam = OrderedDict()
for spec in species_transport:
spvisc = []
spcond = []
tlog = []
for n in range(ntfit):
t = species_info.low_temp + dt * n
# variables
# eq. (2)
tr = t / float(species_transport[spec][1])
conversion = debye2cgs * debye2cgs / a2cm / a2cm / a2cm / cc.kb
dst = (
0.5
* conversion
* float(species_transport[spec][3]) ** 2
/ (
float(species_transport[spec][1])
* float(species_transport[spec][2]) ** 3
)
)
# viscosity of spec at t
# eq. (1)
conversion = a2cm * a2cm
visc = (
(5.0 / 16.0)
* np.sqrt(np.pi * spec.weight * cc.kb * t / na)
/ (
om22_chemkin(tr, dst)
* np.pi
* float(species_transport[spec][2])
* float(species_transport[spec][2])
* conversion
)
)
# conductivity of spec at t
# eq. (30)
conversion = a2cm * a2cm
m_red = spec.weight / (2.0 * na)
diffcoef = (
(3.0 / 16.0)
* np.sqrt(2.0 * np.pi * cc.kb**3 * t**3 / m_red)
/ (
10.0
* np.pi
* om11_chemkin(tr, dst)
* float(species_transport[spec][2])
* float(species_transport[spec][2])
* conversion
)
)
# eq. (19)
cv_vib_r = (
get_cv_dr_species(mechanism, t, spec) - m_cvib[spec.idx]
) * isatm[spec.idx]
rho_atm = 10.0 * spec.weight / (ru * t)
f_vib = rho_atm * diffcoef / visc
# eq. (20)
a = 2.5 - f_vib
# eqs. (21) + (32-33)
cv_rot_r = m_crot[spec.idx]
# note: the T corr is not applied in CANTERA
b = float(species_transport[spec][5]) * f_corr(
298.0, float(species_transport[spec][1])
) / f_corr(t, float(species_transport[spec][1])) + (2.0 / np.pi) * (
(5.0 / 3.0) * cv_rot_r + f_vib
)
# eq. (18)
f_rot = f_vib * (1.0 + 2.0 / np.pi * a / b)
# eq. (17)
cv_trans_r = 3.0 / 2.0
f_trans = 5.0 / 2.0 * (1.0 - 2.0 / np.pi * a / b * cv_rot_r / cv_trans_r)
if int(species_transport[spec][0]) == 0:
cond = ((visc * ru / spec.weight)) * (5.0 / 2.0) * cv_trans_r
else:
cond = ((visc * ru / spec.weight)) * (
f_trans * cv_trans_r + f_rot * cv_rot_r + f_vib * cv_vib_r
)
# log transformation for polyfit
tlog.append(np.log(t))
spvisc.append(np.log(visc))
spcond.append(np.log(cond))
cofeta[spec.idx] = np.polyfit(tlog, spvisc, 3)
coflam[spec.idx] = np.polyfit(tlog, spcond, 3)
# header for visco
cw.writer(fstream)
cw.writer(fstream)
cw.writer(fstream, cw.comment("Poly fits for the viscosities, dim NO*KK"))
# visco coefs
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
cw.writer(fstream, "void egtransetCOFETA(amrex::Real* COFETA) {")
for spec in species_info.nonqssa_species:
for i in range(4):
cw.writer(
fstream,
f"{'COFETA'}[{spec.idx * 4 + i}] = {cofeta[spec.idx][3 - i]:.8E};",
)
cw.writer(fstream, "}")
# header for cond
cw.writer(fstream)
cw.writer(fstream)
cw.writer(fstream, cw.comment("Poly fits for the conductivities, dim NO*KK"))
# visco coefs
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
cw.writer(fstream, "void egtransetCOFLAM(amrex::Real* COFLAM) {")
for spec in species_info.nonqssa_species:
for i in range(4):
cw.writer(
fstream,
f"{'COFLAM'}[{spec.idx * 4 + i}] = {coflam[spec.idx][3 - i]:.8E};",
)
cw.writer(fstream, "}")
def diffcoefs(fstream, species_info, species_transport, ntfit):
"""Write the diffusion coefficients."""
# REORDERING OF SPECS
spec_ordered = []
n_species = species_info.n_species
for i in range(n_species):
for spec in species_transport:
if spec.idx == i:
spec_ordered.append(spec)
break
# compute single constants in g/cm/s
na = 6.02214199e23
# conversion coefs
a2cm = 1.0e-8
debye2cgs = 1.0e-18
patm = 0.1013250000000000e07
# temperature increment
dt = (species_info.high_temp - species_info.low_temp) / (ntfit - 1)
# diff coefs (4 per spec pair)
cofd = []
for i, spec1 in enumerate(spec_ordered):
cofd.append([])
if i != spec1.idx:
print("Problem in _diffcoefs computation")
sys.exit(1)
for j, spec2 in enumerate(spec_ordered[0 : i + 1]):
if j != spec2.idx:
print("Problem in _diffcoefs computation")
sys.exit(1)
# eq. (9)
sigm = (
0.5
* (
float(species_transport[spec1][2])
+ float(species_transport[spec2][2])
)
* a2cm
) * xi(spec1, spec2, species_transport) ** (1.0 / 6.0)
# eq. (4)
m_red = spec1.weight * spec2.weight / (spec1.weight + spec2.weight) / na
# eq. (8) & (14)
epsm_k = (
np.sqrt(
float(species_transport[spec1][1])
* float(species_transport[spec2][1])
)
* xi(spec1, spec2, species_transport) ** 2.0
)
# eq. (15)
conversion = debye2cgs * debye2cgs / cc.kb
dst = (
0.5
* conversion
* float(species_transport[spec1][3])
* float(species_transport[spec2][3])
/ (epsm_k * sigm**3)
)
if not xi_bool(spec1, spec2, species_transport):
dst = 0.0
# enter the loop on temperature
spdiffcoef = []
tlog = []
for n in range(ntfit):
t = species_info.low_temp + dt * n
tr = t / epsm_k
# eq. (3)
# note: these are "corrected" in chemkin not in CANTERA... we chose not to
difcoeff = (
3.0
/ 16.0
* 1
/ patm
* (
np.sqrt(2.0 * np.pi * t**3 * cc.kb**3 / m_red)
/ (np.pi * sigm * sigm * om11_chemkin(tr, dst))
)
)
# log transformation for polyfit
tlog.append(np.log(t))
spdiffcoef.append(np.log(difcoeff))
cofd[i].append(np.polyfit(tlog, spdiffcoef, 3))
# use the symmetry for upper triangular terms
# note: starting with this would be preferable (only one bigger loop)
# note2: or write stuff differently !
# for i,spec1 in enumerate(spec_ordered):
# for j,spec2 in enumerate(spec_ordered[i+1:]):
# cofd[i].append(cofd[spec2.id][spec1.id])
# header for diffusion coefs
cw.writer(fstream)
cw.writer(fstream)
cw.writer(
fstream,
cw.comment("Poly fits for the diffusion coefficients, dim NO*KK*KK"),
)
# coefs
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
cw.writer(fstream, "void egtransetCOFD(amrex::Real* COFD) {")
for i, _ in enumerate(spec_ordered):
for j, _ in enumerate(spec_ordered[0 : i + 1]):
for k in range(4):
cw.writer(
fstream,
f"{'COFD'}[{i * n_species * 4 + j * 4 + k}] ="
f" {cofd[i][j][3 - k]:.8E};",
)
for j, _ in enumerate(spec_ordered[i + 1 :]):
for k in range(4):
cw.writer(
fstream,
f"{'COFD'}[{i * n_species * 4 + (j + i + 1) * 4 + k}]"
f" = {cofd[j + i + 1][i][3 - k]:.8E};",
)
cw.writer(fstream, "}")
def light_specs(fstream, speclist):
"""Write list of specs with small weight, dim n_lite."""
# header
cw.writer(fstream)
cw.writer(fstream)
cw.writer(fstream, cw.comment("List of specs with small weight, dim NLITE"))
# coefs
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
if len(speclist) > 0:
cw.writer(fstream, "void egtransetKTDIF(int* KTDIF) {")
else:
cw.writer(fstream, "void egtransetKTDIF(int* /*KTDIF*/) {")
for i in range(len(speclist)):
cw.writer(fstream, f"{'KTDIF'}[{i}] = {speclist[i]};")
cw.writer(fstream, "}")
def thermaldiffratios(
fstream,
species_info,
species_transport,
light_spec_list,
ntfit,
):
"""Write thermal diffusion ratios."""
n_species = species_info.n_species
# This is an overhaul of chemkin version III
# REORDERING OF SPECS
spec_ordered = []
for i in range(n_species):
for spec in species_transport:
if spec.idx == i:
spec_ordered.append(spec)
break
# compute single constants in g/cm/s
# conversion coefs
debye2cgs = 1.0e-18
a2cm = 1.0e-8
# temperature increment
dt = (species_info.high_temp - species_info.low_temp) / (ntfit - 1)
# diff ratios (4 per spec pair involving light species)
coftd = []
k = -1
for i, spec1 in enumerate(spec_ordered):
if i != spec1.idx:
print("Problem in _thermaldiffratios computation")
sys.exit(1)
if spec1.idx in light_spec_list:
k = k + 1
if light_spec_list[k] != spec1.idx:
print("Problem in _thermaldiffratios computation")
sys.exit(1)
coftd.append([])
epsi = float(species_transport[spec1][1]) * cc.kb
sigi = float(species_transport[spec1][2]) * a2cm
poli = float(species_transport[spec1][4]) * a2cm * a2cm * a2cm
# eq. (12)
poli_red = poli / sigi**3
for j, spec2 in enumerate(spec_ordered):
if j != spec2.idx:
print("Problem in _thermaldiffratios computation")
sys.exit(1)
# eq. (53)
wji = (spec2.weight - spec1.weight) / (spec1.weight + spec2.weight)
epsj = float(species_transport[spec2][1]) * cc.kb
sigj = float(species_transport[spec2][2]) * a2cm
dipj = float(species_transport[spec2][3]) * debye2cgs
# eq. (13)
dipj_red = dipj / np.sqrt(epsj * sigj**3)
eps_ratio = epsj / epsi
tse = 1.0 + 0.25 * poli_red * dipj_red**2 * np.sqrt(eps_ratio)
eok = tse**2 * np.sqrt(
float(species_transport[spec1][1])
* float(species_transport[spec2][1])
)
# enter the loop on temperature
spthdiffcoef = []
t_tab = []
for n in range(ntfit):
t = species_info.low_temp + dt * n
tslog = np.log(t) - np.log(eok)
# eq. (53)
thdifcoeff = (
15.0
/ 2.0
* wji
* (2.0 * astar(tslog) + 5.0)
* (6.0 * cstar(tslog) - 5.0)
/ (
astar(tslog)
* (16.0 * astar(tslog) - 12.0 * bstar(tslog) + 55.0)
)
)
# log transformation for polyfit
t_tab.append(t)
spthdiffcoef.append(thdifcoeff)
coftd[k].append(np.polyfit(t_tab, spthdiffcoef, 3))
# header for thermal diff ratios
cw.writer(fstream)
cw.writer(fstream)
cw.writer(
fstream,
cw.comment("Poly fits for thermal diff ratios, dim NO*NLITE*KK"),
)
# visco coefs
cw.writer(fstream, "AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE")
if len(coftd) > 0:
cw.writer(fstream, "void egtransetCOFTD(amrex::Real* COFTD) {")
else:
cw.writer(fstream, "void egtransetCOFTD(amrex::Real* /*COFTD*/) {")
for i in range(len(coftd)):
for j in range(n_species):
for k in range(4):
cw.writer(
fstream,
f"{'COFTD'}[{i * 4 * n_species + j * 4 + k}] ="
f" {coftd[i][j][3 - k]:.8E};",
)
cw.writer(fstream, "}")
def astar(tslog):
"""Compute astar."""
a_tab = [
0.1106910525e01,
-0.7065517161e-02,
-0.1671975393e-01,
0.1188708609e-01,
0.7569367323e-03,
-0.1313998345e-02,
0.1720853282e-03,
]
a = a_tab[6]
for i in range(6):
a = a_tab[5 - i] + a * tslog
return a
def bstar(tslog):
"""Compute bstar."""
b_tab = [
0.1199673577e01,
-0.1140928763e00,
-0.2147636665e-02,
0.2512965407e-01,
-0.3030372973e-02,
-0.1445009039e-02,
0.2492954809e-03,
]
b = b_tab[6]
for i in range(6):
b = b_tab[5 - i] + b * tslog
return b
def cstar(tslog):
"""Compute cstar."""
c_tab = [
0.8386993788e00,
0.4748325276e-01,
0.3250097527e-01,
-0.1625859588e-01,
-0.2260153363e-02,
0.1844922811e-02,
-0.2115417788e-03,
]
c = c_tab[6]
for i in range(6):
c = c_tab[5 - i] + c * tslog
return c
def om22_chemkin(tr, dst):
"""Compute OM22."""
# This is an overhaul of CANTERA version 2.3
# range of dst
dst_tab = [0.0, 0.25, 0.50, 0.75, 1.0, 1.5, 2.0, 2.5]
# range of tr
tr_tab = [
0.1,
0.2,
0.3,
0.4,
0.5,
0.6,
0.7,
0.8,
0.9,
1.0,
1.2,
1.4,
1.6,
1.8,
2.0,
2.5,
3.0,
3.5,
4.0,
5.0,
6.0,
7.0,
8.0,
9.0,
10.0,
12.0,
14.0,
16.0,
18.0,
20.0,
25.0,
30.0,
35.0,
40.0,
50.0,
75.0,
100.0,
]
# tab of omega22 corresp. to (tr, dst)
# CANTERA
omega_tab = [
4.1005,
4.266,
4.833,
5.742,
6.729,
8.624,
10.34,
11.89,
3.2626,
3.305,
3.516,
3.914,
4.433,
5.57,
6.637,
7.618,
2.8399,
2.836,
2.936,
3.168,
3.511,
4.329,
5.126,
5.874,
2.531,
2.522,
2.586,
2.749,
3.004,
3.64,
4.282,
4.895,
2.2837,
2.277,
2.329,
2.46,
2.665,
3.187,
3.727,
4.249,
2.0838,
2.081,
2.13,
2.243,
2.417,
2.862,
3.329,
3.786,
1.922,
1.924,
1.97,
2.072,
2.225,
2.614,
3.028,
3.435,
1.7902,
1.795,
1.84,
1.934,
2.07,
2.417,
2.788,
3.156,
1.6823,
1.689,
1.733,
1.82,
1.944,
2.258,
2.596,
2.933,
1.5929,
1.601,
1.644,
1.725,
1.838,
2.124,
2.435,
2.746,
1.4551,
1.465,
1.504,
1.574,
1.67,
1.913,
2.181,
2.451,
1.3551,
1.365,
1.4,
1.461,
1.544,
1.754,
1.989,
2.228,
1.28,
1.289,
1.321,
1.374,
1.447,
1.63,
1.838,
2.053,
1.2219,
1.231,
1.259,
1.306,
1.37,
1.532,
1.718,
1.912,
1.1757,
1.184,
1.209,
1.251,
1.307,
1.451,
1.618,
1.795,
1.0933,
1.1,
1.119,
1.15,
1.193,
1.304,
1.435,
1.578,
1.0388,
1.044,
1.059,
1.083,
1.117,
1.204,
1.31,
1.428,
0.99963,
1.004,
1.016,
1.035,
1.062,
1.133,
1.22,
1.319,
0.96988,
0.9732,
0.983,
0.9991,
1.021,
1.079,
1.153,
1.236,
0.92676,
0.9291,
0.936,
0.9473,
0.9628,
1.005,
1.058,
1.121,
0.89616,
0.8979,
0.903,
0.9114,