one

Before I begin with the report itself, I would like to thank Tracy Tuballa for being everybody's personal assistant. It was she who photocopied AND scanned the figures for us.  On that note, I would NOT like to thank the College of Science Library for deciding to renovate now. Boo.  

Like most "firsts" of any semester or year, I enjoyed it. Much of that had to do with the figure I'd ended up working with (See graph below).  Unlike my classmates' figures, I didn't have to collect a million data points - I didn't even have to collect ten.  My graph, luckily, already had data point markers, making things so much easier.

 

Original Graph of Time Constant vs. Temperature 

Source: "Relaxation  times and the initial conditions 

of the one-dimensional Fokker-Planck Equation" 

by Josefino Z. Villanueva, September 1973

The objective was to use ratio and proportion to find the numerical values of a digitally scanned hand-drawn plot (Activity 1 - Digital Scanning Manual, Applied Physics 186).  It wasn't a straight-forward activity but with repeated reading of the manual (and, yes, eavesdropping on my classmates' discussions), I was able to sink my teeth into the task.  On that note, I acknowledge Mr. Mar Philip Elaurza, Mr. Timothy Joseph Abregana and Mr. James Christopher Pang for answering the steady stream of questions I had for them before we all attempted the task.  Also, I just have to thank Mr. Kirby Cheng who walked from the second floor to the oh-so-far fourth floor just so he could download - and share - the activity manual.  It was because of his effort that we were able to start a good 45 minutes before the class started.  Of course, if I have to thank people, I have to thank Ma'am Jing for instructing me how to convert the pixel data to graph data. Cheers to you all! 

Now, on to what I did!

The first step in all of this was to determine the pixel coordinates of my graph's origin, data point markers and axes points using MS Paint.  Because my computer runs on a Windows 7 OS, my Paint program allowed me to overlay grid lines on the image making it easier to obtain consistent pixel coordinates for the axis intervals.  Also, my graph didn't have proper tick marks along the axes so I had to put a great deal of estimation into that.

When I plotted the raw pixel coordinates I'd gotten, it looked like a vertically-flipped version of the original graph.  I realized that MS Paint took the 0, 0 pixel coordinate to be located at the top left corner of images.  The y-coordinates I used from there on end are converted set of y-pixel coordinates (image height in pixels - y-pixel coordinate).  

To recreate the graph, I remembered the objective of using ratio and proportion and initially thought it was best to use the average of the pixel distances between the x- and y-axis points.  Through simple ratio and proportion (graph distance / pixel distance), I was able to reproduce a shifted version of the graph.  Upon showing this to Ma'am Jing, I was told this was wrong.  She delivered a one-liner, a paraphrased version of it shown below, that clung to me throughout the day.  

"You're physicists, class.  Using the average simply won't do"

She told me that plotting the axes point's pixel and graph distances would allow me to obtain an equation for which if you had one value, you could get the corresponding distance.  Yey!  

 Plot of the pixel versus graph distance of the major intervals along the (top) x- and 

(bottom) y-axis along with the best fit line used to approximate the final graph

Armed with the best fit equations from the above plots, all that was left to do was input the x- and y-pixel coordinates I'd early obtained and voila!  Shown below are the final graphs along side the original, complete with best fit lines (Power Laws) and R^2 values.  Before you get confused, I show you two graphs because OpenOffice Calc - the program I'd been using up to this point - does not do the world's most accurate (or is the term precise?) best line fitting.    

Reconstructed plots of the time constant versus Kelvin using (top) Excel and (bottom) OpenOffice.org Calc

Truthfully enough, Ma'am Jing (for it was her who suggested I attempt a best line fitting in Excel) was right.  The equation given by Excel shows more precision than that given by OpenOffice.org Calc.

I have to admit that my results aren't really as perfect as I'd hoped them to be.  In the throes of my celebration due to the presence of data point markers on my graph, I failed to realize that I should have taken more points in between the markers.  I could have then produced a more accurate result.

I guess I should explain why I only reconstructed the experimental plot.  Suffice to say that I was not aware the graph we'd need to use should only have a single plot on it.  I then had to make a decision between the theoretical or the experimental plot.  I don't think there's a need to explicitly say the choice I made (wink).

With all that said and done, I give myself a score of 9/10.  I understood the lesson - both the principle and the technique behind it.  I was also able to finish the task well before the class had to end (something I attribute to the original graph itself).  For technical correctness, that's a 5.  Although I was able to finish, the quality of the plots that I produced weren't exactly top-notch.  The image of the graph that's been overlayed onto both the Excel and OpenOffice.org Calc results seem too grainy - hence the 4 I graded myself for the Quality of the Presentation.

It might not have been that complicated of an activity, but it was one where I learned a few tips and tricks that might just come in handy in future endeavors - both academic and in research.  I guess I relearned something I was first thought in the second semester of my first year - Simplicity is Key.