From: crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass)
Newsgroups: sci.physics
Subject: Re: What's new with chaotic dynamics?
Date: 25 Aug 92 22:31:04 GMT
Organization: University of Virginia

In article <l9l9fdINNrf6@news.bbn.com> hagstrop@oberon.mathcs.carleton.edu (Paul Hagstrom) writes:
>I realize that this is an incredibly unfair question to ask, but I will pose it  
>anyway, just to see what the response is..
>
>I'm coming up on the time when I have to write a major undergraduate  
>("comprehensive") paper having something to do with Physics (my major, or at  
>least one of them), and I'm kind of fishing around for ideas.  I've taken an  
>introductory course to chaotical dynamical systems, and so I have rudimentary  
>terminology and very basic understanding of some of the underlying concepts,  
>and I was interested to see what sort of research is going on involving chaotic  
>modelling.. 
>
>Of course, the answer to that is probably "everything", but the thing that I  
>have been told to keep in mind is that, when others have tried their hand at  
>this topic, the main question that the Physics faculty say keeps coming up is:  
>"That's all very neat--where's the physics?"  I'm looking for ideas of physical  
>phenomena well modeled by chaotic dynamics, so that my end paper doesn't end up  
>being entirely an explanation of iteration theory and topology, but at least  
>has a firm grounding in some physical phenomenon.  I'm an undergraduate, but I  
>will have completed the required undergraduate courses in physics, so I should  
>hopefully be able to grasp a fair number of the concepts...
>
>Turbulence?  That occurred to me, but I don't know what's going on in the  
>field..

    Turbulence is currently not well described by the concepts that
    you are likely to have learned in an 'intro to chaotic systems'
    class.   It is unlikely to ever be well described by systems
    of ODE's and bifurcation behavior you likely learned in your class.
    (though if you do discover the transformation that reduces the
    Navier-Stokes equations to low-order ODE's that are easily solvable,
    please send the preprint at the earliest convenience).
    Turbulence *is* a wonderfully mysterous topic and many of the ideas
    that have proven fruitful in areas such as QM have shown their
    limited range of usefulness there.  Current interesting areas of
    research (to me) are Meneveau's (Journal of Fluid Mechanics 232:469 (1991))
    work on wavelet transforms, and Yakhot and Orszag's 
    (J Sci. Comput 1:3 (1986)) work on renormalization ideas (and
    by extension Martin, Siggia and Rose (Phys. Rev. 8:423 (1973)
    and Wyld (Ann. Phys 14:145 1961))).

    A much more appropriate venue for such dynamical systems concepts 
    are systems that are fairly well described by ODE's or delay-differential 
    equations.  Behavior of certain electronic systems would be an appropriate
    *physical* application. 

                                 dale bass
-- 
C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926