Skip to content

Tiago project 1 #149

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom
Open
tmigliat wants to merge 2 commits into
base: main
Choose a base branch
from
Open

Tiago project 1 #149

tmigliat wants to merge 2 commits into from

Conversation

@tmigliat
Copy link

@tmigliat tmigliat commented Nov 2, 2023

More specific descriptions can be found on Gradescope!! @adowling2

-- Minor editing:

  • Ensured consistent section numbers
  • Fixed equations that are not rendered correctly on the class website
  • Checked and fixed links to other notebooks
  • Moved all solutions, including discussion solutions, to between ### BEGIN SOLUTION and ### END SOLUTION in code block.
  • Spelling and grammar checked
  • Ensured all images were rendered correctly, and also added pattern to the graphs
  • At the top of the notebook after the original creators, added “Edited by: Tiago Thomaz Migliati Zanon, [[email protected]]

-- Substantial intellectual contribution:

  • Added a new sensitivity analysis and discussion question
  • Compared different numeric integration methods
  • Added a section connecting results back to engineering science theory

@adowling2 adowling2 changed the title Add files via upload Tiago project 1 Dec 5, 2023
adowling2
adowling2 requested changes Dec 5, 2023
View reviewed changes
Copy link
Contributor

@adowling2 adowling2 left a comment

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Please take a look at the comments below. There are a few major conceptual issues/errors that should be addressed.

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
"* [Visualization with matplotlib](https://ndcbe.github.io/data-and-computing/notebooks/01/Matplotlib.html)\n",
"* [Preparing Publication Quality Figures in Python](https://ndcbe.github.io/data-and-computing/notebooks/01/Publication-Quality-Figures.html)\n",
"* [Euler Forward Method](https://ndcbe.github.io/data-and-computing/notebooks/07/Forward-and-Backward-Euler.html)\n",
"* [Crank-Nicolson (Trapezoid Rule)](https://dcbe.github.io/data-and-computing/notebooks/07/Trapezoid-Rule.html)"
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This link is broken

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
"# Numerically solve the differential equations using Forward Euler Method\n",
"\n",
"### BEGIN SOLUTION ###\n",
"for t in t_values[:-1]:\n",
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This should instead be the generic method implemented as a function. Then, you apply the function to this specific problem. This separates the logic of a generic method from the specific problem. It is also the best practice we used in the class (see other notebooks).

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
" Cc_next = Cc_values[-1] + k2 * Cb_values[-1] * h\n",
"\n",
" # Print intermediate results\n",
" print(\"\\nt =\", t)\n",
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This should have a flag to toggle on/off between printing.

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
" print(\"Cb =\", Cb_next)\n",
" print(\"Cc =\", Cc_next)\n",
"\n",
" Ca_values.append(Ca_next)\n",
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Recommend preallocating an array to store these results. You already know how many steps will be taken for the method.

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
],
"image/png": "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
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Instead call this section "Comparing Errors"

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
],
"image/png": "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
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This discussion of error rate would be best supported by scaling plots like we did in class. You want to plot the log error of the methods versus the step size. You can then talk about the slope of the plot.

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
],
"image/png": "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
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This would be much more effective if you made a plot that compared the solution profiles. You could make subplots for species A, B, and C. Then, on each subplot, you can compare the forward Euler, Crank-Nicolson, and a higher-order method (with scipy).

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
"RHS_Cc = lambda Cb, t: k2 * Cb\n",
"\n",
"# Function to perform Crank-Nicolson method\n",
"def crank_nicolson(RHS_Ca, RHS_Cb, RHS_Cc, Ca0, Cb0, Cc0, dt, numsteps, LOUD=False):\n",
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

You should instead implement this as a generic function without the problem-specific information. You want to define your problem as returning a vector:
https://ndcbe.github.io/data-and-computing/notebooks/07/Trapezoid-Rule.html
https://ndcbe.github.io/data-and-computing/notebooks/07/Systems-of-Differential-Equations-and-Scipy.html#crank-nicolson

Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This is a linear ODE. You should instead use our generic implementation of Crank-Nicolson from class:
https://ndcbe.github.io/data-and-computing/notebooks/07/Systems-of-Differential-Equations-and-Scipy.html#crank-nicolson

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
"\n",
" # Crank-Nicolson Method\n",
"### BEGIN SOLUTION ###\n",
" Ca_half = Ca[n-1] + 0.5 * dt * RHS_Ca(Ca[n-1], Cb[n-1], t[n])\n",
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

This calculation is incorrect. Crank-Nicolson is an implicit method, meaning you must solve a (non)linear system of equations each iteration.

Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

https://ndcbe.github.io/data-and-computing/notebooks/07/Systems-of-Differential-Equations-and-Scipy.html#crank-nicolson

notebooks/contrib-dev/Stochastic_Simu_Chem_Rxn.ipynb
"text/plain": [
"<Figure size 600x600 with 1 Axes>"
],
"image/png": "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
Copy link
Contributor

@adowling2 adowling2 Dec 5, 2023

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Please use LaTeX for subscripts, e.g., k$_1$ and k$_2$. Please update this throughout the entire notebook

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Reviewers

@adowling2 adowling2 adowling2 requested changes

Requested changes must be addressed to merge this pull request.

Assignees

No one assigned

Labels

graded

Projects

None yet

Milestone

No milestone

Development

Successfully merging this pull request may close these issues.

2 participants

@tmigliat @adowling2