is it why the bubles in boiling water seem to have a
maximum size? how does it work in this case? is
fractal geometry changing the way physical theories
are interpreted?
--- "a.g.atkins" <[log in to unmask]> wrote:
> Be careful about the concept of fractals in scaling
> designs from small to
> large.
>
> Cube-square scaling is an instance: this is where a
> 'design' depends upon
> two things that scale in different ways. In the
> 'resultant' scaling relation
> expressed as a power of the scaling factor, the
> power is the "fractal
> dimension". For example, in condensation theory the
> size of droplets depends
> on competition between the weight of the droplet (a
> volume term, length
> cubed) and the surface tension/surface energy that
> holds a droplet together
> (an area term, length squared), so that there is a
> 'best size'. Another
> example is Brunel's success in getting his first
> ship (the Great Western
> paddle steamer) from Bristol to New York with coal
> to spare. Critics has
> said it would run out of coal but Brunel realised
> that the resistance to the
> ship going through the water depended on the wetted
> area of the hull whereas
> the amount of coal the ship could carry depended on
> the height of the hull
> (an extra dimension).
>
> The best example of this sort of thing as it relates
> to design is anything
> that will break. The energy required for cracking is
> an area term: energy
> stored or dissipated is a volume term. This is why
> large structures made
> from bodies which appear to be ductile in
> laboratory-sized testpieces can
> break in a brittle fashion, and why large
> energy-absorbing devices do not
> live up to expectations when extrapolated from small
> 'models'. Again, going
> the other way, it is why powders cannot be ground up
> below certain minimum
> sizes.
>
> In all these cases the fractal dimension itself
> depends upon size.
>
> Anyone still awake may wish to look at Jim Gordon's
> books and also at Chap 9
> on scaling in my book with Mai Yiu-Wing 'Elastic and
> Plastic Fracture' Ellis
> Horwood/John Wiley 1985/88. There are also later
> papers to which I could
> refer people.
>
> Tony
>
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