Post #13 February Summary - March Goals

Straight from my January Summary:

Stuff I am hoping to finish in February:

1. Sew my first dress (will also be in the February sewing blog)
2. An alien makeup inspired by a deep sea creature

3. Chapter 2 of Gurnett and Bhattacharjee

4. Submit my first first-author paper

5. Have my thesis proposal mostly done.
6. Finish the C210k Trainer

I did complete my first dress as you have seen in post #11.

Also, I did attempt to create an alien inspired by an angler fish, post #12, albeit nearly a week late.

I have been slacking on the plasma textbook. I only completed up to the section I posted on earlier this months: post #10.

I have not submitted my paper yet...

I still have no real thought on my thesis proposal...

Technically, I have not finished the C210k Trainer, instead I have started the marathon trainer by Zen Labs. I am not doing this because I aspire to run a marathon, I am running off the adage "Go big or go home," pun intended. I ran outside during the beautiful weather we had last week, and failed miserably, so instead of trying to continue with the free version of C210k, I would just do the one time payment of the marathon trainer and be good to go until I can run on my own for any distance. So who knows, six months from now, maybe I will be capable of running 26.2 miles. (Don't worry if you laughed, I am laughing, and anyone who knows me would laugh. I am not a marathon runner, I like pizza entirely too much. Though if I do make it, this whole section will be fun to read, and make a great part of my Success Story.)

So 2 out of 6 goals completed... eh. Here's to a successful March:

Stuff I am hoping to finish in March:

1. Sew a vest, some beach apparel, and my Tea Party dress

2. An angel/devil makeup inspired by a good/bad personality trait

3. Chapter 2 of Gurnett and Bhattacharjee

4. Submit my first first-author paper

5. Have my thesis proposal done.

6. Finish weeks 2, 3, 4, and 5 of the Marathon Trainer

Post #10 "It is a relatively simple matter to show that..." (Physics post)

From Gurnett and Bhattacharjee (hereafter known as G&B): "It is a relatively simple matter to show that..."

This is a fairly common phrase in physics textbooks, and most of the time a student reads that phrase and immediately laughs because usually it is not 'simple' to show whatever it is they want to be shown. It could be simple if a couple key notes were added in the text, I am going to use the above example from G&B.

"It is a relatively simple matter to show that the root-mean-square velocity is given by (root 3) times (C sub s), where C sub s equals (root (kappa times T sub s) divided by m sub s)." I will include a screen shot of my LaTex file, so don't worry so much about the "math into words" I have decided to add:

First things first, root-mean-square velocity. For this problem it is:

Also from an earlier 'easy to show' in chapter 2 of G&B, we know that the denominator is equal to the density of a particular species of particle, n sub s. So the above equation becomes:

The distribution function, f(v), in this case is the following:

So now you can plug it in to the numerator and solve for the root-mean-square velocity. But wait, there is more math that is not for the faint of heart, (feint of heart?). Cue the Google-ing of "definite integral of exponential." Thank you Wikipedia. Skip to this one:

Where n = 4, and alpha equals m sub s divided by (2 kappa T sub s), and don't forget to carry the constants in front of the v and exponential:

To get a cleaner version of the integral in the general form I direct you to a blog post by a friend and colleague: Conrad's blog, and a YouTube video that I found very helpful.
So plugging stuff into this:

You get this:

and after canceling out and putting it back in the numerator of the root-mean-square velocity equation:

you see "It is a relatively simple matter to show that..."

Ta-Da.

Hope this post was sufficiently physics-y and look forward to next weeks post on my sewing projects, including my first circle skirt, and my first dress. Also, two weeks from now I will have my special effects makeup post, featuring my take on an alien inspired by a deep sea creature.