Convert Continuous Inverse Scale Parameter to Physically Relevant Units

In summary, the continuous inverse scale parameter is a quantity that is continuous and inverse to the physical relevant quantity. It is used to convert a continuous inverse scale parameter into a physically relevant quantity.
  • #1
Salish99
28
0
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:
Physics news on Phys.org
  • #2


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
 
  • #3


anyone who can kindly help me? :shy:
 

1. What is a continuous inverse scale parameter?

A continuous inverse scale parameter is a mathematical constant used in statistical analysis to adjust for the scale of the data. It is the reciprocal of the scale parameter, which determines the spread or variability of the data.

2. Why is it important to convert continuous inverse scale parameter to physically relevant units?

Converting the continuous inverse scale parameter to physically relevant units allows for better understanding and interpretation of the data. Physically relevant units are more easily relatable and meaningful, making it easier to draw conclusions and make decisions based on the data.

3. How do you convert a continuous inverse scale parameter to physically relevant units?

To convert a continuous inverse scale parameter to physically relevant units, you need to know the original scale parameter and the appropriate conversion factor. The conversion factor depends on the specific units being used and can be found through mathematical calculations or by consulting a conversion chart.

4. What are some examples of physically relevant units for a continuous inverse scale parameter?

Examples of physically relevant units for a continuous inverse scale parameter include time, distance, weight, volume, and temperature. These units are commonly used in everyday life and can be easily understood and interpreted by most people.

5. Are there any limitations to converting continuous inverse scale parameter to physically relevant units?

While converting to physically relevant units can improve understanding and interpretation of the data, it is important to note that the conversion may not always be exact. Additionally, some units may not have a direct conversion, making it necessary to use approximations. It is also important to consider the potential for rounding errors when converting units.

Similar threads

  • Calculus and Beyond Homework Help
Replies
8
Views
2K
Replies
0
Views
2K
  • Other Physics Topics
Replies
1
Views
1K
  • Advanced Physics Homework Help
Replies
6
Views
1K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
2K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
3K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
1
Views
2K
Back
Top