def getArrheniusJSMath(A, Aunits, n, nunits, Ea, Eaunits, T0, T0units):
result = '{0!s}'.format(getLaTeXScientificNotation(A))
if n != 0:
if T0 != 1:
result += r' \left( \frac{{T}}{{ {0:g} \ \mathrm{{ {1!s} }} }} \right)^{{ {2:.2f} }}'.format(T0, T0units, n)
else:
result += r' T^{{ {0:.2f} }}'.format(n)
if Ea != 0:
result += r' \exp \left( - \, \frac{{ {0:.2f} \ \mathrm{{ {1!s} }} }}{{ R T }} \right)'.format(Ea, Eaunits)
result += ' \ \mathrm{{ {0!s} }}'.format(Aunits)
return result
def get_temp_specific_rate(kinetics, temperature):
"""
Return the rate in nice units given a specified temperature.
Outputs in pretty Latex scientific notation.
"""
if kinetics is None:
return "// There are no kinetics for this entry."
kunits, kunits_low, kfactor, numReactants = getRateCoefficientUnits(kinetics)
rate = kinetics.getRateCoefficient(temperature)*kfactor
result = '<div class="math">k(T) = {0!s}'.format(getLaTeXScientificNotation(rate))
result += '\ \mathrm{{ {0!s} }}</div>'.format(kunits)
return mark_safe(result)
def get_specific_rate(kinetics, eval):
"""
Return the rate in nice units given a specified temperature.
Outputs in pretty Latex scientific notation.
"""
if kinetics is None:
return "// There are no kinetics for this entry."
temperature, pressure = eval
kunits, kunits_low, kfactor = getRateCoefficientUnits(kinetics)
rate = kinetics.get_rate_coefficient(temperature, pressure)*kfactor
result = '<script type="math/tex; mode=display">k(T, P) = {0!s}'.format(getLaTeXScientificNotation(rate))
result += '\ \mathrm{{ {0!s} }}</script>'.format(kunits)
return mark_safe(result)
def getArrheniusJSMath(A, Aunits, n, nunits, Ea, Eaunits, T0, T0units):
result = '{0!s}'.format(getLaTeXScientificNotation(A))
if n != 0:
if T0 != 1:
result += r' \left( \frac{{T}}{{ {0:g} \ \mathrm{{ {1!s} }} }} \right)^{{ {2:.2f} }}'.format(T0, T0units, n)
else:
result += r' T^{{ {0:.2f} }}'.format(n)
if Ea > 0:
result += r' \exp \left( - \, \frac{{ {0:.2f} \ \mathrm{{ {1!s} }} }}{{ R T }} \right)'.format(Ea, Eaunits)
elif Ea < 0:
result += r' \exp \left(\frac{{ {0:.2f} \ \mathrm{{ {1!s} }} }}{{ R T }} \right)'.format(-Ea, Eaunits)
result += ' \ \mathrm{{ {0!s} }}'.format(Aunits)
return result
def get_specific_rate(kinetics, eval):
"""
Return the rate in nice units given a specified temperature.
Outputs in pretty Latex scientific notation.
"""
if kinetics is None:
return "// There are no kinetics for this entry."
temperature, pressure = eval
kunits, kunits_low, kfactor, numReactants = getRateCoefficientUnits(kinetics)
rate = kinetics.getRateCoefficient(temperature, pressure)*kfactor
result = '<script type="math/tex; mode=display">k(T, P) = {0!s}'.format(getLaTeXScientificNotation(rate))
result += '\ \mathrm{{ {0!s} }}</script>'.format(kunits)
return mark_safe(result)
def render_thermo_math(thermo, user=None):
"""
Return a math representation of the given `thermo` using jsMath. If a
`user` is specified, the user's preferred units will be used; otherwise
default units will be used.
"""
# Define other units and conversion factors to use
if user and user.is_authenticated():
user_profile = UserProfile.objects.get(user=user)
Tunits = str(user_profile.temperatureUnits)
Punits = str(user_profile.pressureUnits)
Cpunits = str(user_profile.heatCapacityUnits)
Hunits = str(user_profile.energyUnits)
Sunits = str(user_profile.heatCapacityUnits)
Gunits = str(user_profile.energyUnits)
else:
Tunits = 'K'
Punits = 'bar'
Cpunits = 'cal/(mol*K)'
Hunits = 'kcal/mol'
Sunits = 'cal/(mol*K)'
Gunits = 'kcal/mol'
Tfactor = Quantity(1, Tunits).getConversionFactorFromSI()
Pfactor = Quantity(1, Punits).getConversionFactorFromSI()
Cpfactor = Quantity(1, Cpunits).getConversionFactorFromSI()
Hfactor = Quantity(1, Hunits).getConversionFactorFromSI()
Sfactor = Quantity(1, Sunits).getConversionFactorFromSI()
Gfactor = Quantity(1, Gunits).getConversionFactorFromSI()
# The string that will be returned to the template
result = ''
if isinstance(thermo, ThermoData):
# The thermo is in ThermoData format
result += '<table class="thermoEntryData">\n'
if thermo.H298 is not None:
result += '<tr>'
result += r' <td class="key"><span class="math">\Delta H_\mathrm{f}^\circ(298 \ \mathrm{K})</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0:.2f} \ \mathrm{{ {1!s} }}</span></td>'.format(thermo.H298.value_si * Hfactor, Hunits)
result += '</tr>\n'
if thermo.S298 is not None:
result += '<tr>'
result += r' <td class="key"><span class="math">\Delta S_\mathrm{f}^\circ(298 \ \mathrm{K})</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0:.2f} \ \mathrm{{ {1!s} }}</span></td>'.format(thermo.S298.value_si * Sfactor, Sunits)
result += '</tr>\n'
if thermo.Tdata is not None and thermo.Cpdata is not None:
for T, Cp in zip(thermo.Tdata.value_si, thermo.Cpdata.value_si):
result += '<tr>'
result += r' <td class="key"><span class="math">C_\mathrm{{p}}^\circ({0:g} \ \mathrm{{ {1!s} }})</span></td>'.format(T * Tfactor, Tunits)
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0:.2f} \ \mathrm{{ {1!s} }}</span></td>'.format(Cp * Cpfactor, Cpunits)
result += '</tr>\n'
result += '</table>\n'
elif isinstance(thermo, Wilhoit):
# The thermo is in Wilhoit format
result += '<div class="math">\n'
result += r'\begin{split}'
result += r'C_\mathrm{p}(T) &= C_\mathrm{p}(0) + \left[ C_\mathrm{p}(\infty) -'
result += r' C_\mathrm{p}(0) \right] y^2 \left[ 1 + (y - 1) \sum_{i=0}^3 a_i y^i \right] \\'
result += r'H^\circ(T) &= H_0 + \int_0^\infty C_\mathrm{p}(T) \ dT \\'
result += r'S^\circ(T) &= S_0 + \int_0^\infty \frac{C_\mathrm{p}(T)}{T} \ dT\\'
result += r'y &\equiv \frac{T}{T + B}'
result += r'\end{split}'
result += '</div>\n'
result += '<table class="thermoEntryData">\n'
result += '<tr>'
result += r' <td class="key"><span class="math">C_\mathrm{p}(0)</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0:.2f} \ \mathrm{{ {1!s} }}</span></td>'.format(thermo.cp0.value_si * Cpfactor, Cpunits)
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">C_\mathrm{p}(\infty)</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0:.2f} \ \mathrm{{ {1!s} }}</span></td>'.format(thermo.cpInf.value_si * Cpfactor, Cpunits)
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_0</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(thermo.a0))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_1</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(thermo.a1))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_2</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(thermo.a2))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_3</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(thermo.a3))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">H_0</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0:.2f} \ \mathrm{{ {1!s} }}</span></td>'.format(thermo.H0.value_si * Hfactor, Hunits)
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">S_0</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0:.2f} \ \mathrm{{ {1!s} }}</span></td>'.format(thermo.S0.value_si * Sfactor, Sunits)
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">B</span></td>'
result += r' <td class="equals">=</td>'
result += r' <td class="value"><span class="math">{0:.2f} \ \mathrm{{ {1!s} }}</span></td>'.format(thermo.B.value_si * Tfactor, Tunits)
result += '</tr>\n'
result += '</table>\n'
elif isinstance(thermo, NASA):
# The thermo is in NASA format
result += '<div class="math">\n'
result += r'\frac{C_\mathrm{p}^\circ(T)}{R} = a_{-2} T^{-2} + a_{-1} T^{-1} + a_0 + a_1 T + a_2 T^2 + a_3 T^3 + a_4 T^4'
result += '</div>\n'
result += '<div class="math">\n'
result += r'\frac{H^\circ(T)}{RT} = -a_{-2} T^{-2} + a_{-1} \frac{\ln T}{T} + a_0 + \frac{1}{2} a_1 T + \frac{1}{3} a_2 T^2 + \frac{1}{4} a_3 T^3 + \frac{1}{5} a_4 T^4 + \frac{a_5}{T}'
result += '</div>\n'
result += '<div class="math">\n'
result += r'\frac{S^\circ(T)}{R} = -\frac{1}{2} a_{-2} T^{-2} - a_{-1} T^{-1} + a_0 \ln T + a_1 T + \frac{1}{2} a_2 T^2 + \frac{1}{3} a_3 T^3 + \frac{1}{4} a_4 T^4 + a_6'
result += '</div>\n'
result += '<table class="thermoEntryData">\n'
result += '<tr>'
result += r' <td class="key">Temperature range</td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value">{0:g} to {1:g} {2!s}</td>'.format(polynomial.Tmin.value_si * Tfactor, polynomial.Tmax.value_si * Tfactor, Tunits)
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_{-2}</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.cm2))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_{-1}</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.cm1))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_0</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.c0))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_1</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.c1))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_2</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.c2))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_3</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.c3))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_4</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.c4))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_5</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.c5))
result += '</tr>\n'
result += '<tr>'
result += r' <td class="key"><span class="math">a_6</span></td>'
result += r' <td class="equals">=</td>'
for polynomial in thermo.polynomials:
result += r' <td class="value"><span class="math">{0!s}</span></td>'.format(getLaTeXScientificNotation(polynomial.c6))
result += '</tr>\n'
result += '</table>\n'
elif isinstance(thermo, list):
# The thermo is a link
index = thermo[1]
url = reverse('database.views.thermoEntry', {'section': section, 'subsection': subsection, 'index': index})
result += '<table class="thermoEntryData">\n'
result += '<tr>'
result += r' <td class="key">Link:</td>'
result += r' <td class="value"><a href="{0!s}">{1}</a></td>'.format(url, index)
result += '</tr>\n'
result += '<\table>\n'
# Temperature range
if isinstance(thermo, (ThermoData, Wilhoit, NASA)):
result += '<table class="thermoEntryData">'
if thermo.Tmin is not None and thermo.Tmax is not None:
result += '<tr><td class="key">Temperature range</td><td class="equals">=</td><td class="value">{0:g} to {1:g} {2!s}</td></tr>'.format(thermo.Tmin.value_si, thermo.Tmax.value_si, Tunits)
result += '</table>'
return mark_safe(result)
def render_kinetics_math(kinetics, user=None):
"""
Return a math representation of the given `kinetics` using jsMath. If a
`user` is specified, the user's preferred units will be used; otherwise
default units will be used.
"""
if kinetics is None:
return mark_safe("<p>There are no kinetics for this entry.</p>")
# Define other units and conversion factors to use
if user and user.is_authenticated():
user_profile = UserProfile.objects.get(user=user)
Tunits = str(user_profile.temperatureUnits)
Punits = str(user_profile.pressureUnits)
Eunits = str(user_profile.energyUnits)
else:
Tunits = 'K'
Punits = 'bar'
Eunits = 'kcal/mol'
kunits, kunits_low, kfactor, numReactants = getRateCoefficientUnits(kinetics, user=user)
Tfactor = Quantity(1, Tunits).getConversionFactorFromSI()
Pfactor = Quantity(1, Punits).getConversionFactorFromSI()
Efactor = Quantity(1, Eunits).getConversionFactorFromSI()
if kunits == 's^-1':
kunits = 's^{-1}'
# The string that will be returned to the template
result = ''
if isinstance(kinetics, Arrhenius):
# The kinetics is in Arrhenius format
result += r'<div class="math">k(T) = {0!s}</div>'.format(getArrheniusJSMath(
kinetics.A.value * kfactor, kunits,
kinetics.n.value, '',
kinetics.Ea.value * Efactor, Eunits,
kinetics.T0.value * Tfactor, Tunits,
))
elif isinstance(kinetics, ArrheniusEP):
# The kinetics is in ArrheniusEP format
result += r'<div class="math">k(T) = {0!s}'.format(getLaTeXScientificNotation(kinetics.A.value * kfactor))
if kinetics.n.value != 0:
result += r' T^{{ {0:.2f} }}'.format(kinetics.n.value)
result += r' \exp \left( - \, \frac{{ {0:.2f} \ \mathrm{{ {1!s} }} + {2:.2f} \Delta H_\mathrm{{rxn}}^\circ }}{{ R T }} \right)'.format(kinetics.E0.value * Efactor, Eunits, kinetics.alpha.value)
result += ' \ \mathrm{{ {0!s} }}</div>'.format(kunits)
elif isinstance(kinetics, KineticsData):
# The kinetics is in KineticsData format
result += r'<table class="KineticsData">'
result += r'<tr><th>Temperature</th><th>Rate coefficient</th></tr>'
for T, k in zip(kinetics.Tdata.values, kinetics.kdata.values):
result += r'<tr><td><span class="math">{0:g} \ \mathrm{{ {1!s} }}</span></td><td><span class="math">{2!s} \ \mathrm{{ {3!s} }}</span></td></tr>'.format(T * Tfactor, Tunits, getLaTeXScientificNotation(k * kfactor), kunits)
result += r'</table>'
# fit to an arrhenius
arr = kinetics.toArrhenius()
result += "Fitted to an Arrhenius:"
result += r'<div class="math">k(T) = {0!s}</div>'.format(getArrheniusJSMath(
arr.A.value * kfactor, kunits,
arr.n.value, '',
arr.Ea.value * Efactor, Eunits,
arr.T0.value * Tfactor, Tunits,
))
elif isinstance(kinetics, PDepArrhenius):
# The kinetics is in PDepArrhenius format
for P, arrh in zip(kinetics.pressures.values, kinetics.arrhenius):
result += r'<div class="math">k(T, \ {0:g} \ \mathrm{{ {1!s} }}) = {2}</div>'.format(
P * Pfactor, Punits,
getArrheniusJSMath(
arrh.A.value * kfactor, kunits,
arrh.n.value, '',
arrh.Ea.value * Efactor, Eunits,
arrh.T0.value * Tfactor, Tunits,
),
)
elif isinstance(kinetics, Chebyshev):
# The kinetics is in Chebyshev format
result += r"""<div class="math">
\begin{split}
\log k(T,P) &= \sum_{t=1}^{N_T} \sum_{p=1}^{N_P} C_{tp} \phi_t(\tilde{T}) \phi_p(\tilde{P}) [\mathrm{ {{ kineticsParameters.coeffs.1 }} }] \\
\tilde{T} &\equiv \frac{2T^{-1} - T_\mathrm{min}^{-1} - T_\mathrm{max}^{-1}}{T_\mathrm{max}^{-1} - T_\mathrm{min}^{-1}} \\
\tilde{P} &\equiv \frac{2 \log P - \log P_\mathrm{min} - \log P_\mathrm{max}}{\log P_\mathrm{max} - \log P_\mathrm{min}}
\end{split}</div><br/>
<div class="math">\mathbf{C} = \begin{bmatrix}
"""
for t in range(kinetics.degreeT):
for p in range(kinetics.degreeP):
if p > 0: result += ' & '
result += '{0:g}'.format(kinetics.coeffs[t,p])
result += '\\\\ \n'
result += '\end{bmatrix}</div>'
elif isinstance(kinetics, Troe):
# The kinetics is in Troe format
Fcent = r'(1 - \alpha) \exp \left( -T/T_3 \right) + \alpha \exp \left( -T/T_1 \right) + \exp \left( -T_2/T \right)'
if kinetics.T2 is not None:
Fcent += r' + \exp \left( -T_2/T \right)'
result += r"""<div class="math">
\begin{{split}}
k(T,P) &= k_\infty(T) \left[ \frac{{P_\mathrm{{r}}}}{{1 + P_\mathrm{{r}}}} \right] F \\
P_\mathrm{{r}} &= \frac{{k_0(T)}}{{k_\infty(T)}} [\mathrm{{M}}] \\
\log F &= \left\{{1 + \left[ \frac{{\log P_\mathrm{{r}} + c}}{{n - d (\log P_\mathrm{{r}} + c)}} \right]^2 \right\}}^{{-1}} \log F_\mathrm{{cent}} \\
c &= -0.4 - 0.67 \log F_\mathrm{{cent}} \\
n &= 0.75 - 1.27 \log F_\mathrm{{cent}} \\
d &= 0.14 \\
F_\mathrm{{cent}} &= {0}
\end{{split}}
</div><div class="math">\begin{{split}}
""".format(Fcent)
result += r'k_\infty(T) &= {0!s} \\'.format(getArrheniusJSMath(
kinetics.arrheniusHigh.A.value * kfactor, kunits,
kinetics.arrheniusHigh.n.value, '',
kinetics.arrheniusHigh.Ea.value * Efactor, Eunits,
kinetics.arrheniusHigh.T0.value * Tfactor, Tunits,
))
result += r'k_0(T) &= {0!s} \\'.format(getArrheniusJSMath(
kinetics.arrheniusLow.A.value * kfactor * kfactor, kunits_low,
kinetics.arrheniusLow.n.value, '',
kinetics.arrheniusLow.Ea.value * Efactor, Eunits,
kinetics.arrheniusLow.T0.value * Tfactor, Tunits,
))
result += r'\alpha &= {0:g} \\'.format(kinetics.alpha.value)
result += r'T_3 &= {0:g} \ \mathrm{{ {1!s} }} \\'.format(kinetics.T3.value * Tfactor, Tunits)
result += r'T_1 &= {0:g} \ \mathrm{{ {1!s} }} \\'.format(kinetics.T1.value * Tfactor, Tunits)
if kinetics.T2 is not None:
result += r'T_2 &= {0:g} \ \mathrm{{ {1!s} }} \\'.format(kinetics.T2.value * Tfactor, Tunits)
result += r'\end{split}</div>'
elif isinstance(kinetics, Lindemann):
# The kinetics is in Lindemann format
result += r"""<div class="math">
\begin{{split}}
k(T,P) &= k_\infty(T) \left[ \frac{{P_\mathrm{{r}}}}{{1 + P_\mathrm{{r}}}} \right] \\
P_\mathrm{{r}} &= \frac{{k_0(T)}}{{k_\infty(T)}} [\mathrm{{M}}] \\
\end{{split}}
</div><div class="math">\begin{{split}}
""".format()
result += r'k_\infty(T) &= {0!s} \\'.format(getArrheniusJSMath(
kinetics.arrheniusHigh.A.value * kfactor, kunits,
kinetics.arrheniusHigh.n.value, '',
kinetics.arrheniusHigh.Ea.value * Efactor, Eunits,
kinetics.arrheniusHigh.T0.value * Tfactor, Tunits,
))
result += r'k_0(T) &= {0!s} \\'.format(getArrheniusJSMath(
kinetics.arrheniusLow.A.value * kfactor * kfactor, kunits_low,
kinetics.arrheniusLow.n.value, '',
kinetics.arrheniusLow.Ea.value * Efactor, Eunits,
kinetics.arrheniusLow.T0.value * Tfactor, Tunits,
))
result += r'\end{split}</div>'
elif isinstance(kinetics, ThirdBody):
# The kinetics is in ThirdBody format
result += r"""<div class="math">
k(T,P) = k_0(T) [\mathrm{{M}}]
</div><div class="math">
""".format()
result += r'k_0(T) = {0!s}'.format(getArrheniusJSMath(
kinetics.arrheniusHigh.A.value * kfactor * kfactor, kunits_low,
kinetics.arrheniusHigh.n.value, '',
kinetics.arrheniusHigh.Ea.value * Efactor, Eunits,
kinetics.arrheniusHigh.T0.value * Tfactor, Tunits,
))
result += '</div>'
elif isinstance(kinetics, MultiKinetics):
# The kinetics is in MultiKinetics format
result = ''
start = ''
for i, k in enumerate(kinetics.kineticsList):
res = render_kinetics_math(k, user=user)
start += '{0} + '.format(res.split(' = ')[0].replace('<div class="math">k(T', 'k_{{ {0:d} }}(T'.format(i+1), 1))
result += res.replace('k(T', 'k_{{ {0:d} }}(T'.format(i+1), 1) + '<br/>'
result = r"""<div class="math">
k(T,P) = {0!s}
</div><br/>
""".format(start[:-3]) + result
# Collision efficiencies
if hasattr(kinetics, 'efficiencies'):
result += '<table>\n'
result += '<tr><th colspan="2">Collision efficiencies</th></tr>'
for smiles, eff in kinetics.efficiencies.iteritems():
result += '<tr><td>{0}</td><td>{1:g}</td></tr>\n'.format(getStructureMarkup(smiles), eff)
result += '</table><br/>\n'
# Temperature and pressure ranges
result += '<table class="kineticsEntryData">'
if kinetics.Tmin is not None and kinetics.Tmax is not None:
result += '<tr><td class="key">Temperature range</td><td class="equals">=</td><td class="value">{0:g} to {1:g} {2!s}</td></tr>'.format(kinetics.Tmin.value * Tfactor, kinetics.Tmax.value * Tfactor, Tunits)
if kinetics.Pmin is not None and kinetics.Pmax is not None:
result += '<tr><td class="key">Pressure range</td><td class="equals">=</td><td class="value">{0:g} to {1:g} {2!s}</td></tr>'.format(kinetics.Pmin.value * Pfactor, kinetics.Pmax.value * Pfactor, Punits)
result += '</table>'
return mark_safe(result)
def render_kinetics_math(kinetics, user=None):
"""
Return a math representation of the given `kinetics` using MathJax. If a
`user` is specified, the user's preferred units will be used; otherwise
default units will be used.
"""
if kinetics is None:
return mark_safe("<p>There are no kinetics for this entry.</p>")
# Define other units and conversion factors to use
if user and user.is_authenticated:
user_profile = UserProfile.objects.get(user=user)
Tunits = user_profile.temperature_units
Punits = user_profile.pressure_units
Eunits = user_profile.energy_units
else:
Tunits = 'K'
Punits = 'Pa'
Eunits = 'J/mol'
kunits, kunits_low, kfactor = getRateCoefficientUnits(kinetics, user=user)
Tfactor = Quantity(1, Tunits).get_conversion_factor_from_si()
Pfactor = Quantity(1, Punits).get_conversion_factor_from_si()
Efactor = Quantity(1, Eunits).get_conversion_factor_from_si()
if kunits == 's^-1':
kunits = 's^{-1}'
# The string that will be returned to the template
result = ''
if isinstance(kinetics, (Arrhenius, SurfaceArrhenius, StickingCoefficient)):
# The kinetics is in Arrhenius format
result += r'<script type="math/tex; mode=display">k(T) = {0!s}</script>'.format(getArrheniusJSMath(
kinetics.A.value_si * kfactor, kunits,
kinetics.n.value_si, '',
kinetics.Ea.value_si * Efactor, Eunits,
kinetics.T0.value_si * Tfactor, Tunits,
))
elif isinstance(kinetics, (ArrheniusEP, SurfaceArrheniusBEP, StickingCoefficientBEP)):
# The kinetics is in ArrheniusEP format
result += r'<script type="math/tex; mode=display">k(T) = {0!s}'.format(getLaTeXScientificNotation(kinetics.A.value_si * kfactor))
if kinetics.n.value_si != 0:
result += r' T^{{ {0:.2f} }}'.format(kinetics.n.value_si)
result += r' \exp \left( - \, \frac{{ {0:.2f} \ \mathrm{{ {1!s} }} + {2:.2f} \Delta H_\mathrm{{rxn}}^\circ }}{{ R T }} \right)'.format(kinetics.E0.value_si * Efactor, Eunits, kinetics.alpha.value_si)
result += r' \ \mathrm{{ {0!s} }}</script>'.format(kunits)
elif isinstance(kinetics, ArrheniusBM):
# The kinetics is in ArrheniusBM format
result += r'<script type="math/tex; mode=display">\begin{{split}}k(T) &= {0!s}'.format(getLaTeXScientificNotation(kinetics.A.value_si * kfactor))
if kinetics.n.value_si != 0:
result += r' T^{{ {0:.2f} }}' .format(kinetics.n.value_si)
result += r' \exp \left(- \, \frac{{ E_\mathrm{{a}} }}{{RT}} \right) \ \mathrm{{ {0!s} }} \\'.format(kunits)
result += r'''
E_\mathrm{{a}} &= \frac{{ \left( w_{{0}} + 0.5 \Delta H_\mathrm{{rxn}} \right)
\left( V_\mathrm{{p}} - 2 w_{{0}} + \Delta H_\mathrm{{rxn}} \right) ^ {{2}} }}
{{ V_\mathrm{{p}} ^ {{2}} - \left( 2 w_{{0}} \right) ^ {{2}} + \Delta H_\mathrm{{rxn}} ^ {{2}} }} \\
V_\mathrm{{p}} &= 2 w_{{0}} \left( \frac{{ w_{{0}} + E_{{0}} }} {{ w_{{0}} - E_{{0}} }} \right) \\
w_{{0}} &= {0:.2f}\ \mathrm{{ {1!s} }} \\
E_{{0}} &= {2:.2f}\ \mathrm{{ {1!s} }} \end{{split}}</script>
'''.format(kinetics.w0.value_si * Efactor, Eunits, kinetics.E0.value_si * Efactor)
elif isinstance(kinetics, KineticsData):
# The kinetics is in KineticsData format
result += r'<table class="KineticsData">'
result += r'<tr><th>Temperature</th><th>Rate coefficient</th></tr>'
for T, k in zip(kinetics.Tdata.value_si, kinetics.kdata.value_si):
result += r'<tr><td><script type="math/tex">{0:g} \ \mathrm{{ {1!s} }}</script></td><td><script type="math/tex">{2!s} \ \mathrm{{ {3!s} }}</script></td></tr>'.format(T * Tfactor, Tunits, getLaTeXScientificNotation(k * kfactor), kunits)
result += r'</table>'
# fit to an arrhenius
arr = kinetics.to_arrhenius()
result += "Fitted to an Arrhenius:"
result += r'<script type="math/tex; mode=display">k(T) = {0!s}</script>'.format(getArrheniusJSMath(
arr.A.value_si * kfactor, kunits,
arr.n.value_si, '',
arr.Ea.value_si * Efactor, Eunits,
arr.T0.value_si * Tfactor, Tunits,
))
elif isinstance(kinetics, PDepArrhenius):
# The kinetics is in PDepArrhenius format
for P, arrh in zip(kinetics.pressures.value_si, kinetics.arrhenius):
if isinstance(arrh, Arrhenius):
result += r'<script type="math/tex; mode=display">k(T, {0} \mathrm{{ {1!s} }}) = {2}</script>'.format(
getLaTeXScientificNotation(P * Pfactor), Punits,
getArrheniusJSMath(
arrh.A.value_si * kfactor, kunits,
arrh.n.value_si, '',
arrh.Ea.value_si * Efactor, Eunits,
arrh.T0.value_si * Tfactor, Tunits,
),
)
elif isinstance(arrh, MultiArrhenius):
start = (r'<script type="math/tex; mode=display">'
r'k(T, {0} \mathrm{{ {1!s} }}) = '.format(getLaTeXScientificNotation(P * Pfactor), Punits))
res = ''
for i, k in enumerate(arrh.arrhenius):
start += 'k_{{ {0:d} }}(T, {1} \mathrm{{ {2!s} }}) + '.format(i + 1, getLaTeXScientificNotation(P * Pfactor), Punits)
res += r'<script type="math/tex; mode=display">k_{{ {0:d} }}(T, {1} \mathrm{{ {2!s} }}) = {3}</script>'.format(
i + 1, getLaTeXScientificNotation(P * Pfactor), Punits,
getArrheniusJSMath(
k.A.value_si * kfactor, kunits,
k.n.value_si, '',
k.Ea.value_si * Efactor, Eunits,
k.T0.value_si * Tfactor, Tunits,
),
)
result += start[:-3] + '</script>\n' + res + '<br/>'
elif isinstance(kinetics, Chebyshev):
# The kinetics is in Chebyshev format
result += r"""<script type="math/tex; mode=display">
\begin{split}
\log k(T,P) &= \sum_{t=1}^{N_T} \sum_{p=1}^{N_P} C_{tp} \phi_t(\tilde{T}) \phi_p(\tilde{P}) [\mathrm{""" + kinetics.kunits + r""" }] \\
\tilde{T} &\equiv \frac{2T^{-1} - T_\mathrm{min}^{-1} - T_\mathrm{max}^{-1}}{T_\mathrm{max}^{-1} - T_\mathrm{min}^{-1}} \\
\tilde{P} &\equiv \frac{2 \log P - \log P_\mathrm{min} - \log P_\mathrm{max}}{\log P_\mathrm{max} - \log P_\mathrm{min}}
\end{split}</script><br/>
<script type="math/tex; mode=display">\mathbf{C} = \begin{bmatrix}
"""
for t in range(kinetics.degreeT):
for p in range(kinetics.degreeP):
if p > 0:
result += ' & '
result += '{0:g}'.format(kinetics.coeffs.value_si[t, p])
result += '\\\\ \n'
result += '\end{bmatrix}</script>'
elif isinstance(kinetics, Troe):
# The kinetics is in Troe format
Fcent = r'(1 - \alpha) \exp \left( -T/T_3 \right) + \alpha \exp \left( -T/T_1 \right) + \exp \left( -T_2/T \right)'
if kinetics.T2 is not None:
Fcent += r' + \exp \left( -T_2/T \right)'
result += r"""<script type="math/tex; mode=display">
\begin{{split}}
k(T,P) &= k_\infty(T) \left[ \frac{{P_\mathrm{{r}}}}{{1 + P_\mathrm{{r}}}} \right] F \\
P_\mathrm{{r}} &= \frac{{k_0(T)}}{{k_\infty(T)}} [\mathrm{{M}}] \\
\log F &= \left\{{1 + \left[ \frac{{\log P_\mathrm{{r}} + c}}{{n - d (\log P_\mathrm{{r}} + c)}} \right]^2 \right\}}^{{-1}} \log F_\mathrm{{cent}} \\
c &= -0.4 - 0.67 \log F_\mathrm{{cent}} \\
n &= 0.75 - 1.27 \log F_\mathrm{{cent}} \\
d &= 0.14 \\
F_\mathrm{{cent}} &= {0}
\end{{split}}
</script><script type="math/tex; mode=display">\begin{{split}}
""".format(Fcent)
result += r'k_\infty(T) &= {0!s} \\'.format(getArrheniusJSMath(
kinetics.arrheniusHigh.A.value_si * kfactor, kunits,
kinetics.arrheniusHigh.n.value_si, '',
kinetics.arrheniusHigh.Ea.value_si * Efactor, Eunits,
kinetics.arrheniusHigh.T0.value_si * Tfactor, Tunits,
))
result += r'k_0(T) &= {0!s} \\'.format(getArrheniusJSMath(
kinetics.arrheniusLow.A.value_si * kfactor * kfactor, kunits_low,
kinetics.arrheniusLow.n.value_si, '',
kinetics.arrheniusLow.Ea.value_si * Efactor, Eunits,
kinetics.arrheniusLow.T0.value_si * Tfactor, Tunits,
))
result += r'\alpha &= {0:g} \\'.format(kinetics.alpha)
result += r'T_3 &= {0:g} \ \mathrm{{ {1!s} }} \\'.format(kinetics.T3.value_si * Tfactor, Tunits)
result += r'T_1 &= {0:g} \ \mathrm{{ {1!s} }} \\'.format(kinetics.T1.value_si * Tfactor, Tunits)
if kinetics.T2 is not None:
result += r'T_2 &= {0:g} \ \mathrm{{ {1!s} }} \\'.format(kinetics.T2.value_si * Tfactor, Tunits)
result += r'\end{split}</script>'
elif isinstance(kinetics, Lindemann):
# The kinetics is in Lindemann format
result += r"""<script type="math/tex; mode=display">
\begin{{split}}
k(T,P) &= k_\infty(T) \left[ \frac{{P_\mathrm{{r}}}}{{1 + P_\mathrm{{r}}}} \right] \\
P_\mathrm{{r}} &= \frac{{k_0(T)}}{{k_\infty(T)}} [\mathrm{{M}}] \\
\end{{split}}
</script><script type="math/tex; mode=display">\begin{{split}}
""".format()
result += r'k_\infty(T) &= {0!s} \\'.format(getArrheniusJSMath(
kinetics.arrheniusHigh.A.value_si * kfactor, kunits,
kinetics.arrheniusHigh.n.value_si, '',
kinetics.arrheniusHigh.Ea.value_si * Efactor, Eunits,
kinetics.arrheniusHigh.T0.value_si * Tfactor, Tunits,
))
result += r'k_0(T) &= {0!s} \\'.format(getArrheniusJSMath(
kinetics.arrheniusLow.A.value_si * kfactor * kfactor, kunits_low,
kinetics.arrheniusLow.n.value_si, '',
kinetics.arrheniusLow.Ea.value_si * Efactor, Eunits,
kinetics.arrheniusLow.T0.value_si * Tfactor, Tunits,
))
result += r'\end{split}</script>'
elif isinstance(kinetics, ThirdBody):
# The kinetics is in ThirdBody format
result += r"""<script type="math/tex; mode=display">
k(T,P) = k_0(T) [\mathrm{{M}}]
</script><script type="math/tex; mode=display">
""".format()
result += r'k_0(T) = {0!s}'.format(getArrheniusJSMath(
kinetics.arrheniusLow.A.value_si * kfactor * kfactor, kunits_low,
kinetics.arrheniusLow.n.value_si, '',
kinetics.arrheniusLow.Ea.value_si * Efactor, Eunits,
kinetics.arrheniusLow.T0.value_si * Tfactor, Tunits,
))
result += '</script>'
elif isinstance(kinetics, (MultiArrhenius, MultiPDepArrhenius)):
# The kinetics is in MultiArrhenius or MultiPDepArrhenius format
result = ''
start = r'<script type="math/tex; mode=display">k(T, P) = '
for i, k in enumerate(kinetics.arrhenius):
res = render_kinetics_math(k, user=user)
start += 'k_{{ {0:d} }}(T, P) + '.format(i+1)
result += res.replace('k(T', 'k_{{ {0:d} }}(T'.format(i+1)) + '<br/>'
result = start[:-3] + '</script><br/>' + result
# Collision efficiencies
if hasattr(kinetics, 'efficiencies') and kinetics.efficiencies:
result += '<table>\n'
result += '<tr><th colspan="2">Collision efficiencies</th></tr>'
for smiles, eff in kinetics.efficiencies.items():
result += '<tr><td>{0}</td><td>{1:g}</td></tr>\n'.format(getStructureMarkup(smiles), eff)
result += '</table><br/>\n'
# Temperature and pressure ranges
result += '<table class="kineticsEntryData">'
if kinetics.Tmin is not None and kinetics.Tmax is not None:
result += '<tr><td class="key">Temperature range</td><td class="equals">=</td><td class="value">{0:g} to {1:g} {2!s}</td></tr>'.format(kinetics.Tmin.value_si * Tfactor, kinetics.Tmax.value_si * Tfactor, Tunits)
if kinetics.Pmin is not None and kinetics.Pmax is not None:
result += '<tr><td class="key">Pressure range</td><td class="equals">=</td><td class="value">{0:g} to {1:g} {2!s}</td></tr>'.format(kinetics.Pmin.value_si * Pfactor, kinetics.Pmax.value_si * Pfactor, Punits)
result += '</table>'
return mark_safe(result)
