how can i plot this function?

I have to plot this formula:

on matlab:

%Meyer-Peter Muller
taus=0.01:1;
tausc1=0.047;
fi1=8*(taus-tausc1).^(3/2);

and I have write like this:

subplot (2,2,1)                       %Meyer-Peter Muller
hold on
plot(taus,fi1,'LineWidth',3)
grid on
axis([0.01 1 0.001 10])
set(gca,'XScale','log');
set(gca,'YScale','log');
xlabel('\tau_*')
ylabel('\phi_o')

but there is this error:

Warning: Imaginary parts of complex X and/or Y arguments ignored. 

Answer 1

[Sam Chak]

Hi @FRANCESCA CANALE

Because that is not an ordinary plot, but a plot using base-10 logarithmic scale on the x-axis and the y-axis. I have made changes in 3 lines. See comments.

https://www.mathworks.com/help/matlab/ref/loglog.html

% Meyer-Peter Muller
taus = linspace(0.048, 10, 4977);       % ← Changes in this line
tausc1=0.047;
fi1=8*(taus-tausc1).^(3/2);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%               Figures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% subplot (2,2,1)                       % Meyer-Peter Muller
% hold off
loglog(taus,fi1,'LineWidth',3)          % ← Changes in this line
grid on
axis([1e-2 1e0 1e-4 1e1])               % ← Changes in this line
set(gca,'XScale','log');
set(gca,'YScale','log');
xlabel('\tau_*')
ylabel('\phi_o')

Answer 2

[Walter Roberson]

0.01 minus 0.047 is negative. negative raised to 3/2 is complex. Your x are non-negative real but your fi1 are a mix of real and complex values.

You also ask for log scale for both axes. log of a complex value would be complex, so it is not obvious what you want plotted.

0.01:1 is the single value 0.01. Remember that the default increment is 1

What do you expect a log plot of complex values to look like?

[FRANCESCA CANALE]

thanks! So i write this:

%Meyer-Peter Muller
taus=0.05:10;
tausc1=0.047;
fi1=8*(taus-tausc1).^(3/2);


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%               Figures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
subplot (2,2,1)                       %Meyer-Peter Muller
hold off
plot(taus,fi1,'LineWidth',3)
grid on
axis([0.05 10 0.00001 10])
set(gca,'XScale','log');
set(gca,'YScale','log');
xlabel('\tau_*')
ylabel('\phi_o')

but the plot on Matlab is very different by the real results and i don't know why:

[Walter Roberson]

I plotted the formula as given. I also used the general form of the formula, and read off some readings from the graph, and solve simultaneous equations to get approximate solutions.

Notice that the mulitiplier found through reading from the graph is fairly close to the 4 you already have, and that the exponent found through approximation is fairly close to the 3/2 you already have. The value supportraced has a notable difference though.

I had to choose representative values from the graph; it is possible that I did not pick consistent values.

syms a b c x
f(x,a,b,c) = a * (x-b)^c

f(x, a, b, c) = 

eqn1 = f(10^-1.75, a, b, c) == 10^-4

eqn1 = 

eqn2 = f(10^0, a, b, c) == 10^0.6

eqn2 = 

eqn3 = f(10^-1, a, b, c) == 10^-1

eqn3 = 

sol = solve([eqn1, eqn2, eqn3], a, b, c)

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

sol = struct with fields:
    a: 4.0839873445232330597052367247964
    b: 0.016976209741709958313669490402208
    c: 1.4906441506377382534818813178019

f0 = f(x, 4, 0.047, 3/2)

f0 = 

f1 = subs(f(x,a,b,c), sol)

f1 = 

vpa(f1, 10)

ans = 

fplot([f0, f1], [0.05, 1])
set(gca, 'XScale', 'log', 'YScale', 'log')
legend({'Meyer-Peter Muller', 'Approximated from graph'})
xlim([10^-2, 10^0])
ylim([10^-4, 10^1])