Re: Models, etc.

[twayburn@juno.com (Thomas L Wayburn)]

On Thu, 30 Oct 1997 16:56:38 EST Tim Sullivan x5830 <sullivan@kenyon.edu>
writes:
> > Can anybody think of a process in nature (excepting quantum 
> mechanical
> > phenomina) which can be modeled by an equation which is not 
> continuous
> > and which does not have continuous derivitives of all orders?
>
> 1. Magnetisation as a function of applied field below the Curie 
> temperature of
> a ferromagnet is continuous but has discontinuous first derivative. 
> Similar
> quantities can be found in any first order phase transition.
>
> 2. At the liquid-gas critical point, the density as a function of 
> position in
> space is fractal. Likewise any system modeled as a fractal will have 
> ill
> defined derivatives of something.
>
> Tim Sullivan
> sullivan@kenyon.edu
3. Shock waves.  Lightning. - TLW

P.S. I never get anything with two continuous derivatives everywhere,
which is what I need for most numerical methods.  Damn, one is lucky to
get a Lipschitz condition.   But, I don't think I work in what you call
the "real world".   [It's as though physical problems had to be solved by
what optimizers call *infeasible path methods*.   You have to leave the
world to find something in the world.]