Arav · Aziza · E · Essey · Monica · Ruben
Imagine you just stepped onto a train on a perfectly mild spring day. The weather outside is totally fine — nothing extreme, nothing dramatic. But somehow, halfway through the ride, you find yourself either sweating or reaching for your jacket.
This is actually a real engineering problem! Modern electric trains use automated climate-control systems to keep passengers comfortable, but these systems are working in a constantly changing environment. Doors open and close at every stop, passengers come and go, and the outside temperature drifts throughout the journey. The system has to continuously predict how the interior temperature is going to evolve and adjust accordingly — and sometimes it does not get it quite right.
So here is the question we are trying to answer:
Can noticeable temperature swings happen inside a train carriage even when the outside temperature seems perfectly mild and stable?
To answer this, we are going to build mathematical models from scratch using the tools we have developed in MAT 433 combined with our own research.
This Repo is the computational engine behind our paper. Here is the roadmap:
| Section | What We Do |
|---|---|
| Task 1 | Take 299 discrete outside temperature readings and build a smooth, continuous function |
| Task 2 | Use |
| Task 3 | Upgrade the model with thermal inertia — a second-order ODE that makes the system respond more realistically |
| Task 4 | Compute the thermal exposure $E = \int |
- All three datasets are loaded at the top. Each one represents a different outside temperature scenario — one mild, one gradually cooling, one dropping dramatically.
- Our comfort temperature is $T_c = 72^\circ$F throughout.
- There are a ton of colors for graphs and such data.
- If you are running this for the first time, just hit Runtime → Run All and everything will generate automatically.
Let's go!