Why my graph not same as research paper?

Hello, I want to ask why I did not get the correct graph as above?

This is my code that i have try:

clc

%for t1=0.1%
x=0.0:0.5:2.0;
alpha=0.5;
t1=0.1;
D=15.2;
u=0.144;

b=sqrt(alpha/(4*pi*D*t1));
c= -(alpha/4*D*t1);
d=x-(u*(t1/alpha));

C1=b*exp(c*(d.^2));
plot(x,C1)

hold on
x=0.0:0.5:2.0;
alpha=0.7;
t1=0.1;
D=15.2;
u=0.144;

b=sqrt(alpha/(4*pi*D*t1));
c= -(alpha/4*D*t1);
d=x-(u*(t1/alpha));

C2=b*exp(c*(d.^2));
plot(x,C2)
ylabel('Concentration');
xlabel('t/tres');

[Sam Chak]

Hi @Nur

I'm a little confused. Are you the same nur in this question?

https://www.mathworks.com/matlabcentral/answers/1736375-why-my-graph-not-same-as-research-paper

As advised by @Torsten, "sometimes it's better to start anew".

[Nur]

Thank you for your reply. Ouhh I'm different person. I'm not that nur.

Answer 1

[Sam Chak]

Hi @Nur

Sorry for the misidentity because the name, the title, and the topic look exactly the same.

Anyway, I have fixed some equations in the code. Please check. Is true?

alpha1 = 0.5;
alpha2 = 0.7;
t1     = 0.1;    % t_alpha
D      = 15.2;   % D_alpha
u      = 0.144;

a1     = sqrt(alpha1/(4*pi*D*t1^alpha1));   % amplitude 1
b1     = alpha1/(4*D*t1^alpha1)
c1     = (u*t1^alpha1)/alpha1;              % center 1
C1     = a1*exp(- b1*(x - c1).^2);

a2     = sqrt(alpha2/(4*pi*D*t1^alpha2));   % amplitude 2
b2     = alpha2/(4*D*t1^alpha2)
c2     = (u*t1^alpha2)/alpha2;              % center 2
C2     = a2*exp(- b2*(x - c2).^2);

The Gaussian functions are computed as follows but the centers are very close to zero. Their amplitudes are also relatively large compated to the paper.

[Nur]

Hi @Sam Chak. Thank you for your reply. For the value of D, I'm actually not too sure if the value is true or not because in the paper that I referred to, the researchers said they referred to experimental data provided by another paper. For the value of t1, I just let it with 0.1 because they did not state the value in the research paper, so I'm not really sure if it is correct or not.

Below is the data from that other paper:

And I would like to ask why I did not get the correct graph as above, like what you have shown?

This is my code that i have try referring to your code:

x=-10:5.0:10.0;
alpha1 = 0.5;
t1     = 0.1;    % t_alpha
D      = 15.2;   % D_alpha
u      = 0.144;
a1     = sqrt(alpha1/(4*pi*D*t1^alpha1));   % amplitude 1
b1     = alpha1/(4*D*t1^alpha1);
c1     = (u*t1^alpha1)/alpha1;              % center 1
C1     = a1*exp(- b1*(x - c1).^2);

plot(x,C1)
hold on

x=-10:5.0:10.0;
alpha2 = 0.7;
t1     = 0.1;    % t_alpha
D      = 15.2;   % D_alpha
u      = 0.144;
a2     = sqrt(alpha2/(4*pi*D*t1^alpha2));   % amplitude 2
b2     = alpha2/(4*D*t1^alpha2);
c2     = (u*t1^alpha2)/alpha2;              % center 2
C2     = a2*exp(- b2*(x - c2).^2);

plot(x,C2)
hold on

x=-10:5.0:10.0;
alpha3 = 0.9228;
t1     = 0.1;    % t_alpha
D      = 15.2;   % D_alpha
u      = 0.144;
a3     = sqrt(alpha3/(4*pi*D*t1^alpha3));   % amplitude 3
b3     = alpha3/(4*D*t1^alpha3);
c3     = (u*t1^alpha3)/alpha3;              % center 3
C3     = a3*exp(- b3*(x - c3).^2);

plot(x,C3)
hold on

x=-10:5.0:10.0;
alpha4 = 1.0;
t1     = 0.1;    % t_alpha
D      = 15.2;   % D_alpha
u      = 0.144;
a4     = sqrt(alpha4/(4*pi*D*t1^alpha4));   % amplitude 4
b4     = alpha4/(4*D*t1^alpha4);
c4     = (u*t1^alpha4)/alpha4;              % center 4
C4     = a4*exp(- b4*(x - c4).^2);

plot(x,C4)
xlabel('t/tres')
ylabel('Concentration')
legend({'\alpha=0.5','\alpha=0.7','\alpha=0.9228','\alpha=1.0'},'Location','northeast')

[Torsten]

Five x-values are not enough to get a smooth curve.

[Sam Chak]

Hi @Nur

No worries. Take it slowly. You have created the vector x from -10 to 10 with a uniform spaced interval of 5.

x = -10 : 5 : 10;

There are only 5 points: [-10, -5, 0, 5, 10], and this is very coarse when the C1 and C2 points are generated from the Gaussian function:

The plot will become smoother if a relatively small interval is set, for example:

x = -10 : 0.05 : 10;

(Previously, I didn't show this in my Answer).

Honestly, I don't know why your plotted graphs are different from the paper. Maybe there are misprints in the formulas or the values of the parameters. You will need to find out from various literature.

You can check the amplitude a that sets the height of the Gaussion function, as well as the center c, where the peak of the Gaussian function is.

[Torsten]

My guess is that in the plots, x is fixed and t varies since the independent variable on the axis is called t/tres.