Re: [Phys-L] no spin decay

[brian whatcott <betwys1@sbcglobal.net>]

An afterthought....

On 9/18/2017 11:02 AM, David Bowman wrote: /in part/
> /snip/
>
> Brian W wrote:
>
>
>   rate = 13.7123447*exp( -0.0891256151* time^(2/3) )
>
> The plot of this fit given here:
> <http://s880.photobucket.com/user/betwys/media/rotation.jpg.html?sort=3&o=0>
> /snip/
> This fit is admittedly pretty good for a simple 2 parameter fit over the time range shown.  But unfortunately it can't asymptotically have the correct behavior in the long time limit.  All fits to such a family of functions will not decay as fast as the actual data do at long times.  We know at long times the behavior has to approach a usual exponential decay, but the family of fitting curves has the constant exponent, 2/3, of the time, t, in the exponential.  If you look carefully at the fit you will notice that the data begin to fall below the fit at large times simply because the fitting function simply can't decay fast enough there./snip/
> dv/dt = -(2/3)*(B^(3/2))*v/sqrt(ln(A) - ln(v)) .
>
> Needless to say such a functional form for the dissipative force as a function of the spinning velocity is quite peculiar, to say the least.
>
> David Bowman
I added a further data pair to my model - using 10 times the longest 
time measured for a zero rate.
The statistics stay good - surprisingly - though not as good as your model.
Perhaps a hint that the Reynolds Number built into a Cd is not the only 
way of modeling fluid dynamics.

Brian W