How to convert a continuous inverse scale parameter into a physically relevant quantity:(adsbygoogle = window.adsbygoogle || []).push({});

1) What is a CISP, and why is called continuous and why inverse?

2) how do I deal with it:

Example:

On

http://www.apec.umn.edu/faculty/gpederso/documents/4501/risk45DistFunc.pdf [Broken]

the error function is defined as

f(x)= h/sqrt(Pi()) x e^(-(hx)^{2})

Now, in P.G. shewmon. Diffusion in solids. McGrawHill NY, 1963, the function for the diffusion of a solid thin film into a bulk material is given as

c(x,t) = alpha/sqrt(4Pi()Dt) x exp (-x^{2}/4Dt)

if I sub in one equation into the other, then for the first term the continuous inverse scale parameter

h = alpha/sqrt(4Dt)

but for the term in the exponential part of the equation

h = 1/sqrt(4Dt)

So, I MUST set alpha = 1 and that's not physically right for diffusion experiments.

Alpha is the concentration of the solute (i.e. the stuff in the thin film that we want to investigate the diffusion of), in terms of counts or intensity. That changes over distance.

It does not occur within the exponential term.

How do I convert h into physically meaningful data? Do I assume the concentration alpha remains outside the first term equation?

Let's say, concentration alpha is 6000 If I fit my data to the erf, I get my output fitting parameter h as 0.71. What is D now

is it option a:

D = alpha^{2}/(h^{2}4t),

or option b

D = 1/(h^{2}4t), in which I don't take the initial surface concentration into account.

Thanks for your thoughts / help.

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# Continuous inverse scale parameter in error function (Phase Bi-exponential & Laplace)

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