fred bertsch <fred.bertsch <at> gmail.com> writes:
White noise of all sorts is frequently expressed in terms of the square root of the dimension of interest. V/sqrt(Hz) is probably the most frequently used unit for electrical noise, for example.
On 6/8/06, Deane Yang <deane_yang <at> yahoo.com> wrote:
Leland Brown wrote:
I suspect (though someone may well correct me!) that fractional dimensions are never strictly necessary, in the sense that the formulas can probably be rewritten to avoid them.
In earlier discussions, there were a few examples of fractional dimensions provided. The one I am familiar with is called "volatility" in finance but probably has a name like "heat conductance" or "diffusion coefficient" in physics. It is the coefficient c in the heat equation:
u_t = c^2 u_xx
You can see that c has units of length/sqrt(time). You can argue that people should use c^2 directly instead of c (this is analogous to using the variance of a Gaussian in place of the standard deviation), but it *is* very useful to be able to work with c itself.
I've been enlightened! Thanks to both of you! And dare I ask now?... Are half exponents the only fractional ones needed? Could we just make the template parameter twice the exponent and thus be able to use integers again? (Since the template parameters are hidden from the casual user anyway.) But I guess I don't even know if there's a real drawback to the rationals. If it ain't broke.... Ragards, -- Leland