## Saturday, June 25, 2011

### Programming is fun!

 A look at my coding environment
I've started programming about a month ago. I pretty much learned by myself by reading a book or two about C++. Oh, and I skimmed some parts of C++ GUI Programming with Qt 4, by Jasmin Blanchette and Mark Summerfield. So far, I'm liking it.

I use the Qt Creator IDE, which provides graphical tools to edit UI files and pretty much helps at every level of application development.

In short, I'm doing an interface to a PostgreSQL database. I may post screenshots of it when I'm at a more advanced stage. For now, the interface does not do a lot of things.

## Tuesday, June 21, 2011

### IBM turns 100!

IBM has just turned 100. To celebrate this stellar achievement, the company has produced a video that summarizes its century of existence in a rather poignant way.
Enjoy!

## Friday, June 17, 2011

### Integrability and Chaos in Hamiltonian Systems

This last semester, I took a course intitled Nonlinear Dynamics and Chaos (in  French). It was quite a novelty, as undergraduates in physics mostly deal with linear problems (they are much easier to solve analytically. Most nonlinear systems do not possess such solutions and they do, the analytic expression is so complex that it offers no qualitative understanding of the subject.

A dynamicist must make use of a completely different set of tools, mostly numeric, to try to grasp the inner workings of a particular system. Phase space, which shows the relationship between a variable and its nth order derivatives (where n is the dynamical order of the system, if I can use this vocabulary), is an important example of these tools.

In the special context of Hamiltonian mechanics, where momenta and position are related through what is called a symplectic symmetry, the topology of the phase space trajectories are significantly restricted; they are N-tori. That is, as long as the system is integrable (has a closed form solution).

As soon as a perturbation is added that renders the system non-integrable, then the phase space qualitatively evolves as described by what is called the KAM Theorem.

This last theorem was the main topic of a mini research project that was conducted by Raphaël Dubé-Demers and myself throughout the second half of the semester. Following these last few words are the text produced during this research and the Beamer presentation used to introduce the subject to our peers.