Journal 7/11

On the first day of biophysics, we got familiar with the Linux environment using basic commands such as mkdir, cd, vi, and ls. Aside from that, everybody introduced themselves using programming experience and grade level, and most of us (besides me) had some experience with python, which we'll be using for the course. I'm excited to learn more about both Linux and Python (and maybe ViM, although it's famously hard to exit), and I'm also wondering what types of simulations we'll be running to integrate physics and biology with CS.

Journal 7/12

Today, we focused on learning Python using Jupyter Notebooks. While much of our time was spent in a heated debate around and/or precedence and short circuit evaluation, I came out of the class with much more knowledge of the language than I had previously (which was zero). We also learned the fundamentals of atomic and molecular physics - specifically, the randomness of particle motion and the sheer number of molecules all around us. My main takeaway was that molecules actually move incredibly fast, but their lack of a consistent direction (disregarding external forces) makes them not very mobile.

No Journal 7/13

Journal 7/14

Our main focus in the lecture today was the nature of temperature. What exactly is temperature, when you think about it? It can be measured by a thermometer, but there are many types of thermometers that all have different methods for gathering data. On the lowest level, temperature is a measure of the kinetic energy of small molecules, and it can be converted from units of energy (J) to units of temperature (K/C/F) using a rate constant (R). It turns out that heat tends to spread from hot to cold because particles moving fast are likely to collide with particles that are moving slowly. When they collide, the faster particle expends some of its energy pushing the slower molecule forwards. Repeat the process, and you end up with a relatively even distribution of energy.

Journal 7/15

Today, we learned about the nature of randomness and how it relates to programming. I've always been interested in the theory that nothing is truly random, and so I was excited when the professor brought up the subject. As it turns out, python's random function is very evenly distributed - we performed tests using a histogram and both 2d and 3d graphs to ensure that consecutive values shared no pattern. Finally, we worked on a Monte Carlo algorithm to estimate the value of pi. The test works by generating random points on a 1x1 square and counting the number that are inside the unit circle. The fraction of points inside versus outside the circle should be pi / 4, so we just had to multiply by 4 to find pi.

Journal 7/18

The lecture today was about common biomolecules, especially water. We focused on water's numerous special properties, including high heat capacity, cohesion, and surface tension. For example, did you know that our body sweats water because we can pour tons of excess heat into it before it vaporizes? That wouldn't work with most other small molecules. After the lecture, we did a bit of python coding and finished up the previous discussion on how to estimate pi.

Journal 7/19

We started off the day with another form of the Monte Carlo pi algorithm. But instead of actually estimating pi, we graphed the standard deviation of pi as it related to the number of random values used. As it turned out, a graph of 1/sqrt(x) vs standard deviation of pi(x) was linear increasing, which means that the standard deviation is predictable for a given number of values used. Afterwards, we had a discussion about the basics of random walks. I thought it was really interesting that a random walk can essentially be modeled as a Pascal's Triangle, just with x values shifted such that you calculate (t choose (t - x) / 2) instead of just (t choose x).

Journal 7/20

Today, we used python to graph various relationships concerning random walks. First, we graphed a bunch of random walks, which didn't tell us that much about the data itself. Then, we graphed the mean result and mean result squared for different walk lengths, and used that to find the diffusion constant. The diffusion constant ended up at 1, which meant that the slope of mean x^2 was approximately 1:1. Finally, I graphed how long it took on average for random walks to reach a target value. The data appeared completely random, mainly because some walks took thousands and thousands of steps to get the target just because they never went the right direction.

Journal 7/22

Today, we continued the random walk simulations in python. The main experiment involved running 10000 random walks of length 1000 each and creating 5 histograms. Each histogram recorded the average X value at a certain point in the walk (200, 400, 600, 800, or 1000 steps). As expected, all of the histograms centered around 0 and had standard distributions.

Journal 7/25

Today, we completed the set of random walk simulations using Jupyter Notebooks. At the end of the lesson, Dr. Singh introduced a game called Gambler's Ruin. Because gambles can go one of two ways (randomly) and bets are always $1, we can simulate this using a single random walk. If the walk ever reaches positive M1, then player 1 has lost. If the walk reaches negative M2 first, player 2 has lost. In other words, +1 represents a dollar gained for player 2, and -1 represents a dollar gained for player 1.

Journal 7/26

Today, we programmed Gambler's Ruin using a similar method to that which is described above. We also graphed length distributions for sets of games, with varying M1, M2, and probability values. Afterwards, Dr. Singh showed us how to prove various probabilities related to Gambler's Ruin, such as the chance that player 1 wins given a set M1 and M2. As it turns out, making the bets uneven dramatically changes the equation, and the proof becomes much harder.

Journal 7/27

We started class with two-dimensional random walks, graphing both the walks themselves and their length distributions. It seemed most realistic to allow the simulated particle to move in any direction (rather than just up, down, left, or right), but this created some problems down the line. Reaching an exact target when your coordinates are almost always precise decimals is practically impossible, and so I had to set up a check to end the function if the particle entered within a given radius of the target. In the future, we'll be organizing into groups and working on a final project for biophysics that's related to the topics we've covered so far.

Journal 7/29

Today, we had a mix of lecture and programming. The lecture concerned the nature of random walks in an energy landscape, and, although some of it took a while to parse, I was generally able to follow along. Basically, particles tend towards lower energy states, which means that there's a lower chance that they move "uphill." The equation is probability = e^(-E / T), where E is the difference in energy for the next state and T is the temperature. This equation tends towards 0 as T decreases or E increases, and 1 as T increases or E decreases. After learning this equation, we set out to program a simple 1d simulation with an energy ratchet. As Dr. Singh predicted, the ratchet proved relatively inefficient until we added occasional bursts of energy to move the particle along.

Journal 8/1

Today, we brainstormed for our final biophysics project. I'll be in a group with Humza, Lucas, and Dhruv, and we're going to be doing an experiment with 3d random walks. We'll be constraining our walks in different cell shapes, such as cubes and spheres. We predict that this will affect the time it takes for a particle to travel from end to end of the container.

Journal 8/2

Today, we spent the entire time experimenting and writing a project report. We ended up with four test cases and then realized a potential error in our data collection. Because our particle had to come within 1 radius of a target on the edge of the cell, different shapes would affect how much of the "target zone" would be exposed. We corrected for this error by placing the target in the center of the cell such that the entire imaginary sphere around the target would be available.

Journal 8/3

No Journal 8/3

Journal 8/4

No Journal 8/4

Biophysics