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Takes a single set of fission yields and passes them as an additional argument to matrix_func: >>> A = matrix_func(chain, rates, fission_yields) Applied to cf4, epc_rk4, celi, and leqi functions. Assumes that fission yields will not change during a depletion event. This change is probably overshadowed by how much the reaction rates may change, but still worth pointing out.
80 lines
3.1 KiB
Python
80 lines
3.1 KiB
Python
"""Functions to form the special matrix for depletion"""
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def celi_f1(chain, rates, fission_yields=None):
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return (5 / 12 * chain.form_matrix(rates[0], fission_yields)
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+ 1 / 12 * chain.form_matrix(rates[1], fission_yields))
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def celi_f2(chain, rates, fission_yields=None):
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return (1 / 12 * chain.form_matrix(rates[0], fission_yields)
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+ 5 / 12 * chain.form_matrix(rates[1], fission_yields))
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def cf4_f1(chain, rates, fission_yields=None):
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return 1 / 2 * chain.form_matrix(rates, fission_yields)
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def cf4_f2(chain, rates, fission_yields=None):
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return (-1 / 2 * chain.form_matrix(rates[0], fission_yields)
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+ chain.form_matrix(rates[1], fission_yields))
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def cf4_f3(chain, rates, fission_yields=None):
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return (1 / 4 * chain.form_matrix(rates[0], fission_yields)
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+ 1 / 6 * chain.form_matrix(rates[1], fission_yields)
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+ 1 / 6 * chain.form_matrix(rates[2], fission_yields)
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- 1 / 12 * chain.form_matrix(rates[3], fission_yields))
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def cf4_f4(chain, rates, fission_yields=None):
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return (-1 / 12 * chain.form_matrix(rates[0], fission_yields)
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+ 1 / 6 * chain.form_matrix(rates[1], fission_yields)
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+ 1 / 6 * chain.form_matrix(rates[2], fission_yields)
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+ 1 / 4 * chain.form_matrix(rates[3], fission_yields))
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def rk4_f1(chain, rates, fission_yields=None):
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return 1 / 2 * chain.form_matrix(rates, fission_yields)
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def rk4_f4(chain, rates, fission_yields=None):
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return (1 / 6 * chain.form_matrix(rates[0], fission_yields)
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+ 1 / 3 * chain.form_matrix(rates[1], fission_yields)
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+ 1 / 3 * chain.form_matrix(rates[2], fission_yields)
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+ 1 / 6 * chain.form_matrix(rates[3], fission_yields))
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def leqi_f1(chain, inputs, fission_yields):
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f1 = chain.form_matrix(inputs[0], fission_yields)
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f2 = chain.form_matrix(inputs[1], fission_yields)
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dt_l, dt = inputs[2], inputs[3]
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return -dt / (12 * dt_l) * f1 + (dt + 6 * dt_l) / (12 * dt_l) * f2
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def leqi_f2(chain, inputs, fission_yields=None):
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f1 = chain.form_matrix(inputs[0], fission_yields)
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f2 = chain.form_matrix(inputs[1], fission_yields)
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dt_l, dt = inputs[2], inputs[3]
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return -5 * dt / (12 * dt_l) * f1 + (5 * dt + 6 * dt_l) / (12 * dt_l) * f2
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def leqi_f3(chain, inputs, fission_yields=None):
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f1 = chain.form_matrix(inputs[0], fission_yields)
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f2 = chain.form_matrix(inputs[1], fission_yields)
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f3 = chain.form_matrix(inputs[2], fission_yields)
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dt_l, dt = inputs[3], inputs[4]
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return (-dt ** 2 / (12 * dt_l * (dt + dt_l)) * f1
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+ (dt ** 2 + 6 * dt * dt_l + 5 * dt_l ** 2)
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/ (12 * dt_l * (dt + dt_l)) * f2 + dt_l / (12 * (dt + dt_l)) * f3)
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def leqi_f4(chain, inputs, fission_yields=None):
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f1 = chain.form_matrix(inputs[0], fission_yields)
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f2 = chain.form_matrix(inputs[1], fission_yields)
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f3 = chain.form_matrix(inputs[2], fission_yields)
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dt_l, dt = inputs[3], inputs[4]
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return (-dt ** 2 / (12 * dt_l * (dt + dt_l)) * f1
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+ (dt ** 2 + 2 * dt * dt_l + dt_l ** 2)
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/ (12 * dt_l * (dt + dt_l)) * f2
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+ (4 * dt * dt_l + 5 * dt_l ** 2) / (12 * dt_l * (dt + dt_l)) * f3)
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