Date: Mon, 18 Oct 2004 14:34:23 -0400

Author: sampere

Subject: Re: localized energy mode demo, i.e pendulum revisited

Post:

I'm glad you guys are taking care of the theory. I'm just happy to know
that pasta and clams are yummy!

You can find a java applet for anything. I'm still not a big fan of
'video game' physics.

Sam

Andrew Graham wrote:

> Andrew Dougherty wrote:
>
>> On Mon, 18 Oct 2004, Andrew Graham wrote:
>>
>>
>>
>>> Thanks for sharing this. The physical model you describe is the basis
>>> for the famous Sine-Gordon wave equation. This is closely akin to the
>>> area of theoretical physics that I work in. The kink-antikink
>>> solutions
>>> are well studied, and represent the "particle-antiparticle" pair
>>> created
>>> when one pendulum goes through a full rotation and back to the
>>> equilibrium position, producing two stationary twists along the row of
>>> pendula. ( I have a similar demo that I copied from one made by Dick
>>> Berg.) However, the solution you describe is a small oscillation
>>> effect
>>> and very interesting. Do you have a reference to a publication
>>> discussing this effect? There is probably an analogous solution in the
>>> system I study.
>>>
>>
>>
>> Offhand, it sounds like an example of FPU (Fermi, Pasta, and
>> Ulam) Recurrence. There's a nice simulation of this in the Wiley CUPS
>> series "Waves and Optics Simulations" by Antonelli, Christian, Fischer,
>> Giles, James, and Stoner. There are probably nice Java applets posted
>> somewhere on the web to do the same thing these days.
>>
>>
>>
> Andrew,
>
> Thanks for that clarification. You are correct that the apparatus Sam
> described is an FPU model. I should have said that this is the
> discrete model that gives, in the continuum limit (as the separation
> between adjacent pendula goes to zero), the Sine-Gordon wave
> equation. My research begins with a discrete linear lattice of masses
> connected with springs, and in the continuum limit gives the
> Klein-Gordon wave equation.
>
> andy graham

From sampere@physics.syr.edu Mon Oct 18 11:28:43 2004

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