Engines, which power much of modern society from automobiles to heating systems, are applications of a concept in physics known as heat cycles. Heat cycles are a series of thermodynamic transitions that return a system back to its original state. This concept is taught in almost every introductory physics class, but can be tricky to grasp at first. My research is to design and develop 3D printable versions of two common heat engines. This project is threefold. I will need to research the engines and the physics behind them, so I can better understand how they work and are designed. Then, I will need learn the techniques of 3D printing. 3D printing is tremendously powerful, but it has large weaknesses that I need to design around. For example, it is difficult to print smooth surfaces with a 3D printer. Finally, I must plan and engineer the actual engines, troubleshooting as necessary. The goal of my research is to release the models online so they could be accessed by any student, teacher, or professor, as having a physical model would have a positive impact on teaching and learning.
I continue here where I left off before in my last post. This is my final post, and it details the results and conclusions of my research:
In this post, I will describe in greater detail the underpinnings of both the Qweak Experiment and my work. The material is extracted from a paper that I wrote for the REU (Research Experience for Undergraduates) program in physics. I’ll spare anyone reading this from the math in the actual paper, which I will describe qualitatively here:
I recently finished up the final stages of applying the Kalman filter, and obtained estimates of the test-beam particles’ momentum errors, which was the main purpose of this project. I have discussed in previous posts how I propagated the Kalman filter through the beamline, and hinted in my last post that I had finally taken momentum errors into account. The method to do this was iterative in nature; I first applied the Kalman filter through the beamline and obtained values for the directional errors at wirechambers 2 and 3. These could be used to obtain the error in the measured bend angle, and this could be used to find a momentum error. We then ran the filter again, but used this new bend error to obtain improved errors in the wirechamber 3 directional error. We then found an improved bend and momentum error, etc. This process was repeated 3 or 4 times, by which point the further iterations made almost no improvement on the values obtained.