First day
Today was the first official day of classes.
My non-linear physics class (PHY484) has just three students. This course is cross-listed with a graduate course (PHYS848) and has one student. That makes four students. Dr. Bechhoefer, my instructor has more or less combined the course with a math course - “The Mathematical Origins of Patterns” by Dr. Muraki. That brings in another five students. Fun.
After we got past the administrative details, Dr. Bechhoefer gave us examples of patterns we see in nature. Because of the multi-disciplinary nature of this course, not all students have the same background. I’m the only engineer in the crowd. We were asked to fill out a three page survey so that the professors can better understand the backgrounds and strengths of the class. Obviously, I took this opportunity to state what I expected to learn from this course: dynamics. Be it fluid dynamics, molecular dynamics, agent based economics or chemistry, hopefully the analysis is transferable between problem domains.
The first class was a “warmup” session, barely leading into the classification of dynamical systems. Broadly, we have two kinds based on the equations of motion:
- Differential Equations (ordinary and partial)
- Iterated Maps (also known as difference equations)
The only difference between the two is whether time is continuous or not. Obviously, iterated maps (with discrete time) translate to computer programs quite easily.
I guess the rest of the week will be looking at trajectories in phase space. Allow me to share this “riddle” that I was once asked when discussing phase space with a friend:
A one-dimensional harmonic oscillator demonstrates oscillations, but one-dimensional systems do not undergo oscillatory motions. What’s wrong?
The answer is that the phase space of the one-dimensional oscillator is actually two-dimensional (space and the first derivative of space.) It is one-dimensional in only space.
The rest of the day was spent running around getting paperwork done. The MIAL is co-directed by people from computing science and engineering, so things are a bit scattered around. Hopefully, all of this is settled by the end of this week.
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