Nonlinear Dynamics and Mathematical Physics

In summary, the conversation discusses the topic of nonlinear dynamics and mathematical physics for a PhD. The person is looking for US universities with strong departments in these subjects and mentions Cornell as a good option for dynamics and chaos. Other potential universities mentioned for dynamical systems include Suny Stony Brook, Rutgers, Boston University, Caltech, Princeton, and MIT. For mathematical physics, the person suggests looking into Rutgers, Alabama, Indiana, Stony Brook, BU, MIT, Caltech, Princeton, Columbia, and NYU. The conversation also touches on the distinction between chaos and dynamical systems, with the former being more applied and the latter being more theoretical. The person also mentions that they received their PhD in Aerospace from Southern Cal, but are
  • #1
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I'm interested in focusing on nonlinear dynamics or mathematical physics for my PhD and was wondering if anyone could tell me what US universities have strong departments in these topics. I've heard that Cornell is good for dynamics and chaos but haven't heard much about other colleges.

Thanks.
 
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  • #2
Some I know off the top of my head for dynamical systems:

Suny Stony Brook (Milnor was/is here)
Rutgers
Boston University (Devaney is here - he wrote the book on it)
Caltech has an interdisciplinary group
Princeton?
MIT?

Check out wikipedia on dynamical systems

Mathematical physics... not sure what you consider that, (not sure myself what I consider that) But Rutgers, Alabama, Indiana?, Stony, BU, MIT. Caltech, Princeton, Columbia, and NYU are good places to start.

Hope that helps. I have similar interests to you. Maybe "Chaos" belongs more to the applied maths and physics people. Dynamical Systems maybe more to the topologists and other pure mathematicians. Depends on what you want to do with it.
 
  • #4
I received my PhD in Aerospace from Southern Cal and was very challenging. Don't know about their physics side.
 

1. What is nonlinear dynamics and mathematical physics?

Nonlinear dynamics and mathematical physics is a branch of science that deals with the study of dynamic systems that exhibit complex and unpredictable behavior. It uses mathematical and computational tools to understand and analyze the behavior of systems that are not easily described by simple linear relationships.

2. What are some examples of nonlinear systems?

Examples of nonlinear systems include weather patterns, population dynamics, chaotic systems, and biological systems. These systems exhibit behavior that cannot be predicted by simple linear equations and are highly sensitive to initial conditions.

3. How is nonlinear dynamics and mathematical physics used in real-world applications?

Nonlinear dynamics and mathematical physics have a wide range of applications in fields such as engineering, biology, economics, and social sciences. It is used to model and predict the behavior of complex systems, design control systems, and understand the dynamics of biological and ecological systems.

4. What are some common tools and techniques used in nonlinear dynamics and mathematical physics?

Some common tools and techniques used in nonlinear dynamics and mathematical physics include chaos theory, fractal geometry, bifurcation analysis, and numerical simulations. These tools help scientists to understand and analyze the behavior of complex systems and make predictions about their future behavior.

5. What are the challenges in studying nonlinear systems?

Studying nonlinear systems can be challenging due to the complexity and unpredictability of their behavior. These systems are highly sensitive to initial conditions, making it difficult to make accurate predictions. Additionally, numerical simulations may be required due to the lack of analytical solutions for many nonlinear systems, which can be computationally expensive and time-consuming.

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