Graduate nonlinear dynamics/chaos studies

In summary, the conversation discusses the topic of chaos theory in graduate school and its real world applications. The speaker mentions two universities, University of Maryland and Cornell, as offering studies in this field. They also mention various real world applications of chaos theory, such as controlling global weather and fluid dynamics. The conversation concludes with a suggestion to take up chaos theory as a research class and the idea that chaos is present in many aspects of the world.
  • #1
Olaf.of.Ísland
10
0
Is there anyone here studying chaos in graduate school? I have read a little on the subject and find it interesting. I cannot however, find many graduate schools offering studies in this field. (I know of only two, University of Maryland and Cornell) Also, what kind of real world applications does the field hold? I caught a show on National Geo about chaos theory being used in a model for controlling global weather but this is my very limited experience with the theory applied to "real life".

Any input/links would be great. Thanks in advance.
 
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  • #2
Chaos theory applies to just about everything.

I remember one paper came out of Santa Cruz on fluid flow from a leaky faucet.

Weather patterns, fluid dynamics, flux vortices in type II superconductors (one of my professors is working on that one), laser diffraction patterns in gas layer, convection, the list goes on and on and on.
 
  • #3
franznietzsche said:
Chaos theory applies to just about everything.

Think of it this way, if you have more than two things interacting, you have chaos. franz is right and unfortunately in most UG courses you only cover the easy linear/non-chaotic problems. See if any of your profs are doing a course in chaos theory, if not try to take it up as one of your research classes. Believe me, it is well worth it. My UG research project dealt with non-linear stochastics and I covered many topics of investigation: the 3-body problem, predator-prey models, stadium problem, the numerical computation and analysis of these models, and on and on. What was interesting was in the end it was found that if you took a line of neurons and added the right noise intensity to it the "firing" pattern became well behaved and demonstrated that stochastics(noise) could have an impact on the behavior of a non-linear system. NEAT STUFF!

So don't worry, chaos is everywhere and I am sure you won't have too look to hard to find a professor to guide you in the right direction. The subject is more "real world" than most of you're course work.
 

1. What is nonlinear dynamics/chaos?

Nonlinear dynamics/chaos refers to the study of complex, dynamic systems that cannot be described by traditional linear equations. These systems exhibit sensitive dependence on initial conditions, meaning that small changes in the starting conditions can lead to drastically different outcomes over time.

2. How is nonlinear dynamics/chaos relevant to real-world applications?

Nonlinear dynamics/chaos has applications in a wide range of fields, including physics, biology, economics, and engineering. It can help us understand and predict the behavior of complex systems such as weather patterns, stock market fluctuations, and biological systems.

3. What are some common techniques used in graduate nonlinear dynamics/chaos studies?

Some common techniques used in graduate nonlinear dynamics/chaos studies include phase space analysis, Lyapunov exponents, bifurcation analysis, and fractal geometry. These tools allow researchers to visualize and quantify the behavior of complex systems.

4. What are the main challenges in studying nonlinear dynamics/chaos?

One of the main challenges in studying nonlinear dynamics/chaos is the complexity of these systems. They often involve a large number of variables and can exhibit unpredictable behavior. Additionally, obtaining accurate data and designing experiments to study these systems can be difficult.

5. What are some potential applications of graduate nonlinear dynamics/chaos studies in the future?

As technology advances, there are endless potential applications for graduate nonlinear dynamics/chaos studies. Some potential areas of interest include developing more accurate weather prediction models, understanding and predicting economic trends, and improving the design and control of complex engineering systems.

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