Day 2 - Group Assignment#
Day 2 contains three possible homework tasks. Divide the tasks up among your team members. Each person should complete one task for homework and review the task of at least one teammate.
For each task, create a jupyter notebook with a file name of the format lastname_firstname_task_x.ipynb where x is your task number.
Reviewing your teammate’s change#
You may need too pull the changes from your teammate’s branch when you are reviewing their pull request. You can pull their branch to your local computer by doing
git switch main
git fetch
git switch -c TEAMMATE_BRANCH --track origin/TEAMMATE_BRANCH
You should then be able to see your teammates files. You should open their Jupyter notebook and review their code. If any changes are needed, leave this in your review on GitHub.
Task 1 - Systematic Investigation of Error in Monte Carlo Calculation#
For this task, you will return to your notebook where we calculated the value of \(\pi\) using Monte Carlo Methods.
Your task is to investigate the effect of increasing the number of samples on the error of the calculation.
Modify your Monte Carlo code to print the percent error in your pi calculation for 10, 100, 1000, 10,000, 100,000, and 1,000,000 points. For an extra challenge, try visualizing your results using matplotlib.
Reference Values
You can use math.pi as a reference value and math.fabs to get an absolute value when calculating your percent error.
In your submission, include a markdown cell that contains a reflection (at least five sentences) on your approach and observations.
Task 2 - Investigating the Lennard Jones Equation#
Write a calculate_LJ function that includes parameters for setting \(\sigma\) and \(\epsilon\).
After writing the function, perform a set of calculations with \(\sigma\) and \(\epsilon\) both equal to one. Using these values, calculate the Lennard Jones potential energy for a range of distances, r, from r = 0.1 to r = 5 in increments of 0.1. Save your results in a list.
Next, perform a set of calculations where \(\sigma\) is equal to 2 and \(\epsilon\) is equal to one. Then set \(\sigma\) equal to 1 and \(\epsilon\) equal to two. For each set of calculations, save your result in a list.
Visualize all three results on a graph using matplotlib.
In your submission, include a markdown cell that contains a reflection (at least five sentences) on your approach and observations.
Task 3 - Calculating the distance betweent two points#
Write a function called calculate_distance that takes in two coordinates as lists([x, y, z]) and returns the distance between the two points.
Use the information in the following docstring to write your funtion:
def calculate_distance(coord1, coord2):
"""
Calculate the distance between two 3D coordinates.
Parameters
----------
coord1, coord2: list
The atomic coordinates
Returns
-------
distance: float
The distance between the two points.
"""
After writing your function, include a few test cases “sanity checks” to ensure that your function is behaving correctly.
The distance function
You cannot use a predefined distance function like math.dist
for this task.
In your submission, include a markdown cell that contains a reflection (at least five sentences) on your approach and observations.