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

Author: sampere

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


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.


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 Mon Oct 18 11:28:43 2004