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

  1. Jul 8, 2009 #1
    How to convert a continuous inverse scale parameter into a physically relevant quantity:
    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 (-x2/4Dt)

    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 = alpha2/(h24t),
    or option b
    D = 1/(h24t), in which I don't take the initial surface concentration into account.

    Thanks for your thoughts / help.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 9, 2009 #2
    Re: Continuous inverse scale parameter in error function (Phase Bi-exponential & Lapl

    Update: I devised the following method:
    I traced the maximum in my data, and divided the entire data by that maximum, thus normalizing it to 1. Thus, as a result now all my concentration is normalized to 1, and I can assume alpha = 1.
    Once I calculate the D out of the equation D = 1/(h24t), in the case of 500 h and an h of 0.16283 this comes to D = 0.007406 1/h. I assume the unit of the inverse scale parameter is micrometer.
    Then it would be:
    D=0.007 um/h

    Can I do that? - How can I find the units of my inverse scale parameter?
    Or do I still have to multiply D by the former maximum concentration values?
    What is a continuous inverse scale parameter, and why is called continuous and why is it inverse (and inverse to what?)?
    These links doe not cover my questions:
    https://www.physicsforums.com/showthread.php?t=269208
    https://www.physicsforums.com/showthread.php?t=275747
    https://www.physicsforums.com/showthread.php?t=232883
    https://www.physicsforums.com/showthread.php?t=253505
    https://www.physicsforums.com/showthread.php?t=178318
     
  4. Jul 28, 2009 #3
    Re: Continuous inverse scale parameter in error function (Phase Bi-exponential & Lapl

    anyone who can kindly help me? :shy:
     
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