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Fixing typo
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Andrew Lee committed Nov 5, 2024
1 parent 3f5b609 commit cc3516a
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"id": "a7ca07c1",
"metadata": {},
"source": [
"Whilst a bit harder to read due to the size of the constraint, you can see that it involves the term $\\rho \\times c_p \\times F \\times (T - {T_ref})$, where $c_p$ is the specific molar heat capacity of the solution, $T$ is temperature and $T_{ref}$ is the reference temperature. Given that $\\rho$ is of order 1E4 (a) and $c_p \\times (T-T_{ref})$ is of order 1E3, this means that the partial derivative with respect to the volumetric flowrate is even larger than that for the H2O balance. This also explains the appearance of the outlet temperature as well, as we can see that it is multiplied by a number of large values as well and thus has a large partial derivative.\n",
"Whilst a bit harder to read due to the size of the constraint, you can see that it involves the term $\\rho \\times c_p \\times F \\times (T - T_{ref})$, where $c_p$ is the specific molar heat capacity of the solution, $T$ is temperature and $T_{ref}$ is the reference temperature. Given that $\\rho$ is of order 1E4 (a) and $c_p \\times (T-T_{ref})$ is of order 1E3, this means that the partial derivative with respect to the volumetric flowrate is even larger than that for the H2O balance. This also explains the appearance of the outlet temperature as well, as we can see that it is multiplied by a number of large values as well and thus has a large partial derivative.\n",
"\n",
"It is also important to mention that having a large value in the Jacobian does not mean a variable is \"important\" (and conversely a small value is not unimportant). What is important is how sensitive the constraint residual is to that change in variable, which is often difficult to assess from the Jacobian alone (which is where the ``SVDToolbox`` can assist).\n",
"\n",
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Expand Up @@ -670,7 +670,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Whilst a bit harder to read due to the size of the constraint, you can see that it involves the term $\\rho \\times c_p \\times F \\times (T - {T_ref})$, where $c_p$ is the specific molar heat capacity of the solution, $T$ is temperature and $T_{ref}$ is the reference temperature. Given that $\\rho$ is of order 1E4 (a) and $c_p \\times (T-T_{ref})$ is of order 1E3, this means that the partial derivative with respect to the volumetric flowrate is even larger than that for the H2O balance. This also explains the appearance of the outlet temperature as well, as we can see that it is multiplied by a number of large values as well and thus has a large partial derivative.\n",
"Whilst a bit harder to read due to the size of the constraint, you can see that it involves the term $\\rho \\times c_p \\times F \\times (T - T_{ref})$, where $c_p$ is the specific molar heat capacity of the solution, $T$ is temperature and $T_{ref}$ is the reference temperature. Given that $\\rho$ is of order 1E4 (a) and $c_p \\times (T-T_{ref})$ is of order 1E3, this means that the partial derivative with respect to the volumetric flowrate is even larger than that for the H2O balance. This also explains the appearance of the outlet temperature as well, as we can see that it is multiplied by a number of large values as well and thus has a large partial derivative.\n",
"\n",
"It is also important to mention that having a large value in the Jacobian does not mean a variable is \"important\" (and conversely a small value is not unimportant). What is important is how sensitive the constraint residual is to that change in variable, which is often difficult to assess from the Jacobian alone (which is where the ``SVDToolbox`` can assist).\n",
"\n",
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Original file line number Diff line number Diff line change
Expand Up @@ -670,7 +670,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Whilst a bit harder to read due to the size of the constraint, you can see that it involves the term $\\rho \\times c_p \\times F \\times (T - {T_ref})$, where $c_p$ is the specific molar heat capacity of the solution, $T$ is temperature and $T_{ref}$ is the reference temperature. Given that $\\rho$ is of order 1E4 (a) and $c_p \\times (T-T_{ref})$ is of order 1E3, this means that the partial derivative with respect to the volumetric flowrate is even larger than that for the H2O balance. This also explains the appearance of the outlet temperature as well, as we can see that it is multiplied by a number of large values as well and thus has a large partial derivative.\n",
"Whilst a bit harder to read due to the size of the constraint, you can see that it involves the term $\\rho \\times c_p \\times F \\times (T - T_{ref})$, where $c_p$ is the specific molar heat capacity of the solution, $T$ is temperature and $T_{ref}$ is the reference temperature. Given that $\\rho$ is of order 1E4 (a) and $c_p \\times (T-T_{ref})$ is of order 1E3, this means that the partial derivative with respect to the volumetric flowrate is even larger than that for the H2O balance. This also explains the appearance of the outlet temperature as well, as we can see that it is multiplied by a number of large values as well and thus has a large partial derivative.\n",
"\n",
"It is also important to mention that having a large value in the Jacobian does not mean a variable is \"important\" (and conversely a small value is not unimportant). What is important is how sensitive the constraint residual is to that change in variable, which is often difficult to assess from the Jacobian alone (which is where the ``SVDToolbox`` can assist).\n",
"\n",
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Original file line number Diff line number Diff line change
Expand Up @@ -670,7 +670,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"Whilst a bit harder to read due to the size of the constraint, you can see that it involves the term $\\rho \\times c_p \\times F \\times (T - {T_ref})$, where $c_p$ is the specific molar heat capacity of the solution, $T$ is temperature and $T_{ref}$ is the reference temperature. Given that $\\rho$ is of order 1E4 (a) and $c_p \\times (T-T_{ref})$ is of order 1E3, this means that the partial derivative with respect to the volumetric flowrate is even larger than that for the H2O balance. This also explains the appearance of the outlet temperature as well, as we can see that it is multiplied by a number of large values as well and thus has a large partial derivative.\n",
"Whilst a bit harder to read due to the size of the constraint, you can see that it involves the term $\\rho \\times c_p \\times F \\times (T - T_{ref})$, where $c_p$ is the specific molar heat capacity of the solution, $T$ is temperature and $T_{ref}$ is the reference temperature. Given that $\\rho$ is of order 1E4 (a) and $c_p \\times (T-T_{ref})$ is of order 1E3, this means that the partial derivative with respect to the volumetric flowrate is even larger than that for the H2O balance. This also explains the appearance of the outlet temperature as well, as we can see that it is multiplied by a number of large values as well and thus has a large partial derivative.\n",
"\n",
"It is also important to mention that having a large value in the Jacobian does not mean a variable is \"important\" (and conversely a small value is not unimportant). What is important is how sensitive the constraint residual is to that change in variable, which is often difficult to assess from the Jacobian alone (which is where the ``SVDToolbox`` can assist).\n",
"\n",
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