Jessica's Blog

Friday, June 4, 2010:

We had our first day yesterday. Professor Rybkin introduced everyone. He also went over, in general, what we were going to be studying throughout the summer: working with different types of waves, especially observing the bore wave, and the models that represent different waves. Odile gave a presentation on the KdV Equation, along with some problems we were to work out. Some of the material seemed a bit familiar, but there was a lot I knew I would have to learn. We also got the computers set up with our accounts, and programs such as MATlab, gnuplot, and TeXnic.

I have been looking forward to this internship for a while, and I am very excited to have this opportunity to learn applications in a mathematical perspective. Meeting fellow interns, I found that I know Jennifer. She and I had taken Geometry together a few years back. Although I can be shy, I am excited to meet and work with new people. I am also looking forward to learn some new material and become exposed to the mathematical research world. While listening to the introductions and the presentation, I am only familiar with some terms, of which I will need a lot of refreshing in. There are many terms I am still unfamiliar with so I am a bit intimidated. It’s nice to hear that fellow interns are feeling the same way. I can tell that there is a lot to learn. I am both excited and very overwhelmed.

Friday, June 11, 2010:

This week, we worked through problems from the first and second presentations, given by Odile. Presentation 2 entailed the Wave Equation and the d’Alembert Solution. Aside from the problems within each presentation, each intern was given different topics to look up and present to the rest of us:

Deven: Fourier Transform (which was necessary to work out a problem in the KdV presentation)

Jennifer: Burgers’ Equation (which we will later use in shock waves)

Jessica: Airy Function (which appears throughout PDEs, making those such PDEs easier to work with)

Dina: Dirac Delta Function (which is a very useful tool in observing waves with a sharp peak)

Dr. Alexei Rybkin also spoke to each intern, assigning projects. Deven and Jennifer will be giving a presentation at the end of the internship on material learned throughout the summer. Dina and I were assigned the task of creating an eye-attracting webpage for the REU Program. We are to take ideas that we may use in reaching out to future interested students. Prospective interns should be informed of details and how helpful the internship is to our study in math. Dina and I are also in charge of finding out information about the bore wave schedule in Turnagain Arm. We plan to take a field trip to Girdwood to try and catch one of these waves.

This week, I am getting settled into the research routine. I think that this is a great change for me, having the opportunity to learn more mathematics with others. This is a definitely large change from previous jobs that I have worked with. I am not used to sitting in an office for hours on end, doing research. I found that my colleagues are also not used to this sort of routine. It gets a bit tiring, but when I know what I’m doing, the time really goes by fast. I’m excited for our dine-out evening, Monday. We plan on going to Lemon Grass, which is my favorite Thai restaurant in Fairbanks. Also, it seems as though we will be able to make it to Girdwood/Alyeska in August to try and catch the bore wave. I have never heard of a bore wave previous to this internship, so I’m really looking forward to this trip. We are planning the trip around August 10th and 11th, since this time is when the wave is predicted to be large enough to appreciate.

Friday, June 18, 2010:

Monday, we were asked to present problems from the first two presentations: The KdV Equation and the Wave Equation. Along with the presentations, we were given more clarity to the concepts of the research we had been doing. We all understand the information a bit better. Tuesday, we were given a third presentation: Inverse Scattering Transform. We were introduced to the Conservation Laws, Miura’s Transformation, the Galilean Invariance, the Standing Wave Schrӧdinger Equation, and the Scattering Theory, including the Gelfand-Levitan-Marchenko Inverse Scattering Procedure. This presentation was pretty interesting, adding to our research more problems involving the KdV Equation. After being told by Dr. Rybkin that we should work together, we seemed to be more open to sharing our ideas on these problems, which is not what we’re used to in a typical math class. We also worked a little bit more with MATlab, Deven being our “master” of the program. With the graphs that we created through MATlab, referring to the problems we were assigned, the visualization of the different exercises was made clearer. The graphs also looked pretty cool. ;)

Dina and I started working on the website. Dina worked with Adobe Photoshop to create possible images for the website’s header and navigation panel. I downloaded Dreamweaver and watched some tutorial videos, playing with Dreamweaver, learning how the program works.

Although I still feel a bit lost, some of the computations, though challenging, are fun to work out. I especially enjoy the problems given to us in the Inverse Scattering Transform presentation (at least, so far). I managed to get most of them done, with the help of Odile, Deven, and Jennifer. It’s interesting: while in class, working on homework, we are told to submit our own work, yet it is quite the opposite when it comes to research. Being an independent person, it is a bit challenging for me to ask for help with certain problems everyone else seems to understand. Through this internship, however, I am becoming at bit more comfortable asking for help. When we were told that we should work together for better understanding, I was put in a position that was foreign to me. I think that since we are working more together with this set of problems, we will be able to understand the information a lot better. I’m almost sad that I only have a month to work with my colleagues, knowing that they will learn a lot more with their two months of dedicated time towards this internship.

We were also faced with another issue this week. The window’s screen was giving us trouble, not working as it should. There was a crack on the top part of the screen, making it hard for us to keep the window open, while at the same time avoiding the insects of summer. We were visited by a wasp for a few seconds, which led to our mission to close the crack at the top of the screen. It ended up that we had assistance from Saqib, who works in the office. Saqib brought in the duct tape. Oh, the many problems duct tape solves! I just wish it would help solve my current problem: showing which Galilean transformations were used to come up with the original KdV equation.

Wednesday, June 30, 2010:

This week has been a very busy, short 3 days for me. Today is my last day, but there has been a lot going on in the office. Deven and I have been continuing work on the bore wave equation this week.

Odile gives us daily updates about the six kittens and their mother. Mommy cat has been brought to help another litter of kittens who weren’t receiving their nursing from anyone. Odile tells us that the kittens still housed with her and her family are doing well- they are old enough to be independent from their mother. On Monday, Odile was kind enough to bring the kittens to Professor Rybkin’s house. Rybkin’s mother was able to see the kittens.

This week has been pretty busy for UAF’s Office of Information Technology (OIT), or so I presume. A couple weeks ago, I downloaded Dreamweaver onto the computer that I was using so that I can work on the website. Since this is my last week, we were trying to get Dreamweaver onto Dina’s office computer. Unfortunately, there were many issues that prevented Odile from downloading it onto Dina’s computer as quickly as she would have liked. Just as well, Odile has been having trouble with her computer. OIT must expect phone calls from Champan 107 now.

The last day, I worked on my individual REU report mostly. Although I wasn’t given much direction in writing the paper, I had a former intern’s paper from last summer to take guidelines from. I think I went in a slightly different direction, but I plan on revising that and e-mailing Dr. Rybkin my final draft (for possible revision). This definitely was a worthwhile experience! I love meeting new people and I had the pleasure of meeting some great, smart, young women who definitely have bright futures ahead of them. I learned a lot that I always thought to be way above what I can comprehend. Also, it is always a pleasant visit back to Fairbanks, especially in the summertime.