determining equations parameter: f=(S/V)sqrt[D/K]*[(kt+1/2)erf(sqrt[kt])+sqrt[kt/pi]

[AlirezaP]

Hi,
I'm new to this forum; maybe I should post my problem in some other topics.

I have problem in determining K and D in following Equation, its experimental equation and I have 10 answer for "f" and "t", "s" and "v" are defined quantity

S=4.3589 , V=6.8557

F=[0.022081745 0.039747141 0.079494282 0.125865947 0.183278484 0.20094388 0.214192927 0.304728081 0.359932444 0.388638713 ];

t=[0.083333333 0.291666667 1 2 3 4 5 19 47 90 ];

\(\displaystyle \displaystyle{\text{error func}\text{tion}\, \mbox{erf}(u)\, =\, \dfrac{2}{\sqrt{\strut \pi\,}}\, \cdot\, \int_0^u\, \mbox{exp}(-z^2)\, dz}\)

\(\displaystyle \displaystyle{f\, =\, \dfrac{S}{V}\, \sqrt{\strut \dfrac{D}{K}\,}\, \left[\left(kt\, +\, \dfrac{1}{2}\right)\, \mbox{erf}\sqrt{\strut kt\,}\, +\, \sqrt{k\, \cdot\, \dfrac{t}{\pi}\,}\,\cdot\, \mbox{exp}(-kt)\right]}\)

Can anyone helping me to determine D and K, Its really important to me and I am in hurry,
I will attach equation.
I really appreciate.
tnx

 

[AlirezaP]

determining equations parameter

Hi,
I'm new to this forum,maybe I should post my problem in some other topics.
I have problem in determining K and D in following Equation, its experimental equation and I have 10 answer for "f" and "t", "s" and "v" are defined quantity
S=4.3589 , V=6.8557
F=[0.022081745 0.039747141 0.079494282 0.125865947 0.183278484 0.20094388 0.214192927 0.304728081 0.359932444 0.388638713 ];
t=[0.083333333 0.291666667 1 2 3 4 5 19 47 90 ];
Can anyone helping me to determine D and K, Its really important to me.
I will attach equation.
I really appreciate.
tnx

 

[j-astron]

Okay, so you have an equation for f(t). You have been given ten values of t, and 10 corresponding values of f. I was going to say that any one of those pairs would let you solve for sqrt(D/K), at the very least. But it seems like you have one equation and three unknowns, because in addition to D and K, there is also lowercase k which is not specified.

EDIT: I guess the data points give you 10 equations in 3 unknowns. So are you meant to do some kind of least-squares fit to the data to find the best-fit values of the model parameters D, K, and k?

 

[stapel]

I have problem in determining K and D in following Equation, its experimental equation and I have 10 answer for "f" and "t", "s" and "v" are defined quantity

S=4.3589 , V=6.8557

F=[0.022081745 0.039747141 0.079494282 0.125865947 0.183278484 0.20094388 0.214192927 0.304728081 0.359932444 0.388638713 ];

t=[0.083333333 0.291666667 1 2 3 4 5 19 47 90 ];

\(\displaystyle \displaystyle{\text{error func}\text{tion}\, \mbox{erf}(u)\, =\, \dfrac{2}{\sqrt{\strut \pi\,}}\, \cdot\, \int_0^u\, \mbox{exp}(-z^2)\, dz}\)

\(\displaystyle \displaystyle{f\, =\, \dfrac{S}{V}\, \sqrt{\strut \dfrac{D}{K}\,}\, \left[\left(kt\, +\, \dfrac{1}{2}\right)\, \mbox{erf}\sqrt{\strut kt\,}\, +\, \sqrt{k\, \cdot\, \dfrac{t}{\pi}\,}\,\cdot\, \mbox{exp}(-kt)\right]}\)

Can anyone helping me to determine D and K, Its really important to me and I am in hurry.

Well, then we're gonna need to see what you've tried so far, so we know where you're getting stuck. (You don't want us wasting time explaining the first few steps, say, if you've already gotten past that point!)

When you reply with that information, please also clarify the already-posted material. I'm guessing that the values of S and V are fixed. But what is the meaning of the bracketed strings of numbers for F and t? How does "S" relate to "s", "K" relate to "k", and "V" relate to "v"; and how do these relate to the rest of what you've posted?

Note: Because you appear to have ten variables (only four of which have values, I think) and only one equation, it may be impossible to solve for the values of the two specified variables. (Are you sure that this was what the instructions said to do?)

Thank you!

 

[AlirezaP]

Okay, so you have an equation for f(t). You have been given ten values of t, and 10 corresponding values of f. I was going to say that any one of those pairs would let you solve for sqrt(D/K), at the very least. But it seems like you have one equation and three unknowns, because in addition to D and K, there is also lowercase k which is not specified.

EDIT: I guess the data points give you 10 equations in 3 unknowns. So are you meant to do some kind of least-squares fit to the data to find the best-fit values of the model parameters D, K, and k?

Thank you for your reply,
First off all, there is no difference between K and k, its just a writing mistake and I have only two unknown parameters ( K and D).
Yes I wanna do least square fit to these data to find the best values for my model. I think its kind of curve fitting with custom model.
Thank you.

 

[Deleted member 4993]

Thank you for your reply,
......Yes I wanna do least square fit to these data to find the best values for my model. I think its kind of curve fitting with custom model.
Thank you.

Please share your work/thought so that we know where to begin to help you.