Non Dimensionalization Of Self Similar Curves

How can I non dimesionalize these self similar curves along x-axis.

[Torsten]

According to x- and y-axis labels, the curves are already plotted in dimensionless quantities.

And you want to plot them with x-axis label "x" and y-axis label "V" ? To do this, you will have to know L and Vmax for each of the curves.

[SULENDER SAHU]

Actually I want the curves to merge as all are self similar...but I am not sure how to do that

[Torsten]

Plotting the outcomes in non-dimensional quantities (x/L versus V/Vmax) as above seems to show that they exhibit a different behaviour due to some parameter I don't know (35,60,100,135). So merging the curves (whatever you mean by this) does not make sense in my opinion.

There might be one single function f(x/L,s) depending on a spreading parameter s that gives the four curves for different values of this spreading parameter. Is it such a function you are looking for ? Then try exp(-((x/L-60)/s)^2), e.g.

[SULENDER SAHU]

Yes exactly...I need one single function f(x/L,s) and this function will give different curves upon plugging the different values of s into that function

Answer 1

[Torsten]

s = 2:10
f = @(x,a)exp(-((x-60)/a).^2)
x = 40:0.01:80;
for i = 1:numel(s)
    fnum(:,i) = f(x,s(i));
end
plot(x,fnum)

By the way: The attribute "self-similar" is reserved for a phenomenon in connection with fractals. It's wrong in the given context.