The Beginning...

Everyone starts somewhere.

I intend for this blog to be an aid for my Masters year. I intend to post papers I produce, thoughts on subjects I am taking, links to things that interest me (and maybe you) and perhaps the occasional insight into my thought processes. But as everyone knows, the best laid plans of mice and men...

I'm currently almost 'half' way through but I'll do my best to get you up to speed as best I can. My hope is to post once a week but don't hate me if I don't always manage it- I'll do my best to make up for it when possible.

So to give an overview...I am a final year student at the University of Bristol reading (as we say in the UK) Engineering Mathematics. We are currently 8 weeks into the year and so far I have written two papers, about to finish a third (this one is a group one) and none are getting published but they will all contribute to the degree I get out at the end. I have weekly labs, many hours of lectures and there is always work to be done in the form of my Final Year Project. Yep, I know, capitals seem silly here but the doom that surrounds it requires them really - it is, after all, contributing to 16.7% of my final degree classification which is more than my whole second year is worth. Oh, not forgetting the constant reading of required texts plus extensive reading around the subject in areas of interest.

As you can see, the workload is extensive and I bet you are wondering how I possibly have time to maintain this blog. Well, you see I hope that the small amount of extra work this may be will allow others to get a glimpse into an area of research that very few know about and even fewer really understand - Nonlinear Dynamics and Chaos - and how it fits in with engineering. Most people have heard of the Butterfly Effect but they do not really understand it - how exactly can a bat of the wings of a small butterfly change the weather on the other side of the world? Well, chaos theory explains phenomenon like this through understanding systems with "sensitive dependence on initial conditions".

Nonlinear dynamics and chaos is a rich field of research and crosses many other areas of science. I will not be spending this whole blog paraphrasing many better introductions and explanations. Instead, I will be discussing my studies directly and in each case will point the reader in the direction of preceding and/or related work. If nothing else, Wikipedia provides a great intro to the area. The best book for anyone of a mathematical persuasion is "Nonlinear Dynamics and Chaos" by Steven Strogatz. Any for those who are not, "Chaos" by James Gleick is a great read.

The relevance of this field to all science cannot be underestimated. Most engineers only look at systems in their most simplistic using assumptions that mean the system can be understood by classical mechanics. Those engineers trained in chaos can explore all the possibilities in the system. The best example of this is a system which most people have come across at some point: the pendulum. Remember the step the teachers did in class where they assumed that sin x = x for small angles and from then on the maths was really easy and you could understand how clocks work? Well, I know what happens when the pendulum swings over a big angle and it is really very elegant. Do you want to know too?